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This is the perfect calculator for simple right up to extremely complex financial calculations and even for basic stuff the RPN input makes calculations much faster than on other calculators. Strongly recommended, note this version allows traditional algebraic input if preferred
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Core Plus Course 1 (9th grade) contains about a dozen simultaneous equations problems, none involving more than two variables, and all with one of the variables isolated on the left side of the two equations as above. Thus, one variable is already "solved for," and the other one, appearing in two expressions that are equal to one another, can be solved for in a few easy steps.
Wentworth's New School Algebra contains many hundreds of simultaneous equations, many involving three variables, some with the variables in the denominators. Solving them involves multiple algebraic manipulations.
Relate this contrast to the amount of explanation given by the Core-Plus textbook (the entirety of which you see here) to the amount of explanation given by Wentworth above for just one of several algebraic methods.
3 comments:
Funny, i have most of my g-grandfathers school books from the mid 1870s, among them a copy of Frenchs Common Arithmetic. Our district uses TERC Investiigations (trying to get rid of). Not only is the currciulum in the book published in 1869 clearer--my ggrandfather had a habit of working problems in the margins and end pages.
Finally took it into a Board of Ed meeting one night and actually showed them how an 11 year old kid who went ot a one room school house on the Illinois prairie actually had better math fluency at the same age as his gg grandaughter, who attends a supposedly first class Westchester County NY public school. Were the problem sets not geared to a farmers offspring--lots in rods, furlongs, bushels etc--I'd just teach her from the old book.
The newer problems are an example of what I see in my kids public middle school algebra: they take as much of the algebra out as they can. There is almost no manipulation of expressions except for the simplest equation solving. They introduce 2x2 systems like this, with both lines already in point-slope form and lots of questions about what you would do with a table? a graph? etc? It gets really depressing when they get to exponentials. Instead of algebra (manipulating expressions) they make tables and graphs, tables and graphs. They eliminate the handicraft aspect of algebra
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Find a West New York Algebra 2The idea of a function and its inverse is introduced. Extensive use is made of exponential and logarithmic functions, including graphing and solving equations. Applications include compound interest problems and radioactive decay
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More About
This Textbook
Overview
Elayn Martin-Gay's success as a developmental math author starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions to this edition provide new pedagogy and resources to build reader confidence and help readers develop basic skills and understand concepts. Martin-Gay's 4-step problem solving process-Understand, Translate, Solve and Interpret-is integrated throughout. Also includes new features such as Study Skills Reminders, "Integrated Reviews", and "Concept Checks." For readers interested in learning or revisiting essential skills in beginning and intermediate algebra through the use of lively and up-to-date 2005
Excellent title
I have had a great deal of difficulty with Math. It appears that this author understands what students struggle with in math. Many of the extra examples and tips were exactly what I needed to understand what I was doing wrong. Best math book I have used. MyMathLab software must be the best on the market. It taught me math! Practice makes perfect and MyMathLab excels in this area. If you get the problem wrong, it shows you step by step how to get it right and lets you try a new problem of the same type. It dosen't get any better.
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I find that soon I'll be working with high school students that are struggling with math. In particular, we'll be talking a lot about algebra and some basic trigonometry. The latter I have experience with (via working with students in calculus and "pre-calculus"), but I have legitimately no idea how one would teach algebra. If I see $3x+5=14$, it's obvious to me what to do, and unlike, say, calculus, I can't really even see how someone would get confused on that (even though I know they do!)
This is a bit broad, but how do you teach introductory algebra? Do you have any references for new teachers?
Part of your problem is what is called "expert blindness" or similar: the subject is so familiar to you that the trouble your students have becomes incomprehensible. First step is obviously to see the phenomenon, next step is to find out what specific problems are common and how to handle them.
–
vonbrandApr 21 at 4:25
4
@vonbrand I'm unfortunately aware. My struggle is that I don't know how to solve it. I have to admit no experience teaching algebra in the past, and I'm a bit worried I'll show up and do poorly without some practice/background.
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Mike MillerApr 21 at 4:56
I can only hope you find help here. Also check previous questions/answers. More than that I can't help, I haven't ever been in that situation. Perhaps check with colleagues, ask people with experience tutoring.
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vonbrandApr 21 at 5:06
4
For the symbol-manipulation side, I would recommend having them play with DragonBox ( dragonboxapp.com ). It doesn't explain any of the theory behind why the rules are what they are, so it's not sufficient by itself, but it's fantastically good in teaching the rules and making it seem fun. I once saw a 5-year old solving (with assistance, but still) about a hundred first-degree equations within a couple of hours when playing with it, and also later on some older kids arguing over who gets to play and solve algebraic equations next.
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Kaj_SotalaApr 21 at 8:34
3
All of the technical advice offered here is golden. I wouldn't change a syllable! On some level, I envy you. My own life was changed 40 years ago by a man who had the patience to do the job you now face. His name was Mr. Shetler. He taught me that I wasn't an idiot and that this stuff isn't magic. There are simple rules that we apply to do algebra. Learn the rules and the problems solve themselves. Above all I council patience.
–
user1168Apr 22 at 9:34
10 Answers
10
As a personal tutor, I've been teaching algebra to kids from ages 8 to 16 for many years. Mostly I find myself in the position of picking up the pieces when the kids are failing and fearing more failure.
The root of the problem, in my experience, is the way algebra is taught as something alien, and in particular, different from arithmetic, which it really isn't (at least in the early years).
So first off, constant emphasis on the fact that "$x$ is just a number you don't know yet". So it behaves like a number, and you can do all the stuff to it, that you can do to numbers.
Next, the nature of equality $2 + 3 = 4 + 1$.
And from there, the fact that when you do the same thing to both sides, you still end up with two things that are equal.
Always "do the same thing to both sides" (since this is clearly based on the nature of equality), never "move this from one side to the other and change the sign" (which is a magic rule that makes no sense until you have a deeper understanding).
Once you get them happy with the idea that doing the same thing to both sides is the way to go, you can give them suggestions for which things to do in which order, but stress that provided they rigorously write down the consequence of the thing they decide to do to both sides, they won't go wrong (although some ways are harder – look out for these as a pointer that choosing another way will be easier).
The manipulation of each line is easy, once you've got them to decide what they're going to do at each stage.
For instance, in the example, $3x + 5 = 14$:
First, decide what to do to both sides (subtract 5)
Write down first what you have ($3x + 5$), then do what you've decided. So you get $3x + 5 - 5$, and on the RHS, $14 - 5$.
Then collect terms and simplify to get $3x = 9$.
Then repeat for division by 3.
Emphasise that once you've decided what to do at each stage, there's very little thinking, since you're just writing – starting with what you had on the previous line, and adding on the chosen operation.
Figuring out what to do (add or multiply, subtract or divide) needs to come after they are truly grounded in the principle that doing the same thing to both sides is the key.
They will also need help with things like why $3x/3 = x$. Again, use numbers to illustrate, and stress that $x$ is just a number, so it behaves the same way as a number.
In school, we had to put a long vertical line to the right of the equation and had to write next to it what we did to go to the next line ($-5$ and $/3$ in this case).
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user11235Apr 21 at 14:47
Yes, I've seen this, and a couple of variants. Personally, I don't like it, for two reasons. 1: It takes longer to write it all out, and anything that makes things take longer to write risks losing the child's attention, and/or making the problem seem laborious and hence dull. 2: If you get used to writing what you start with first (the 3x + 5 in this case), and then the thing that you're doing (the -5), you can still see clearly what's going on. This encourages a systematic approach to laying out the solution that minimises the additional thinking required.
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ChrisAApr 21 at 18:47
How is it less work to write $-5$ twice instead of once?
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user11235Apr 21 at 20:22
The variants I've seen have the school insist on writing, for instance, the -5 underneath both sides of the equation. Because they're not yet familiar with collecting the terms without writing out all the terms to collect (ie, + 5 - 5 on the left, and 14-5 on the right, they tend to then write that as well. So it's more work. Obviously there are ways of doing less writing. As I say, I prefer having them write successive lines of algebra where it includes the decision and the terms to collect. Because then there's no habit of writing something other than the lines of algebra to get out of.
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ChrisAApr 21 at 21:02
3
Exactly. I think you may have misunderstood me. The habit of writing the vertical line, and what you've done to get to the next line, is what they need to get out of. My point is that in going from 3x + 5 = 14, to 3x + 5 - 5 = 14 - 5, to 3x = 9, it becomes a natural progression to miss out the middle line, more so than no longer writing the vertical line stuff. You may find something else easier - that's fine. I'm only commenting on my experience.
–
ChrisAApr 21 at 22:32
For some students, the difficulty with solving $3x+5=14$ is even more basic than figuring out what operations to do in what order in order to reach the goal. Before getting to that, they need to know what the goal is. "Everybody knows" that, when solving an equation with one variable $x$, the goal is to end up with a statement of the form $x=$ some specific number. Unfortunately, this "everybody" doesn't really include everybody; some students have never had the goal made clear. Moreover, in some cases, once they understand the goal, they're remarkably good at finding strategies for working toward it.
I saw this question and laughed, "That is way too broad!", but I've been in your position. I was a classroom teacher for 10yrs in the public school system and was often tasked with teaching something that I hadn't had training in.
What you are looking for initially is a "Scope and Sequence" - a guide showing the steps in teaching a subject. Your 'expert blindness' makes it hard to make one on your own, but it is also redundant - experts have already done this. You can put together a S&S by look at roughly 2 sources:
State or privately developed curriculums - some states offer there curriculum online in the form of "Standards". You can look at what is required at each grade level and get an idea of what you need to teach. You'll need to assess your student against current grade level requirements and then work backwards until you get to the point they understand. That reveals their 'deficiency'. Then you remediate. So, the curriculum will tell you at 8th grade they need to know 'this' and at ninth, 'this'. You teach what they sequentially through the curriculum.
Books and guides - academic textbook are often set up in a proper sequence that will show you a framework of what needs to be learned first. You can obtain these often at libraries, but you may need to dig. Ideally you can find the books the students have used in their classes. Homeschooling resources are also readily available and can be found to meet a lot of different special needs.
This is a tough nut to crack. It really highlights the fact that 'Teaching' is far more than knowledge of a subject! Teaching is its own skill. Good luck!
I think this is the most useful answer to such a broad question. We all have our favorite tips and tricks and points of view of what is important, but the first thing a new teacher needs to know and understand is scope and sequence. Understanding scope and sequence will give the framework around which to develop a point of view about what is important to emphasize. I would only add that there is a third resource that the questioner should seek out: excellent veteran teachers.
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jbaldusApr 25 at 2:00
I think you will need to be very cognizant of student conceptions of how to solve algebraic problems. It may be useful to not try and immediately show them how to solve problems, but rather to ask them how they would go about solving the problems. This will enable you to learn about their mathematical thinking and possible misconceptions they may have. In the example you gave, a student my try to divide both sides by 3 but then simplify it to x + 5 = 14/3. Students solving linear equations often forget to apply the operation to both entire sides and are very focused on eliminating a particular coefficient or term.
First, I want to comment on something that @ChrisA seemed to have glossed over in his detailed description.
For instance, in the example, $3x+5=14$:
First, decide what to do to both sides (subtract 5)
In my experience as a teacher and tutor, I have noticed that this is not easy for novice Algebraists. However, I have found that there is a way that you can help to make this "decision."
We are all familiar with the order of operations and PEMDAS. This is applicable for evaluating expressions and complicated/fabricated arithmetic problems. This can be used in Algebra as well. The decision on what to do is the reverse of the order of operations. The two operations in the given example are multiplication and addition. According to the order of operations, multiplication goes first and then addition. According to Algebra, you need to do the opposite of addition (subtraction) first, and the opposite of multiplication (division) second. I have found that making this thought process explicit has helped some of my students more easily determine this "decision."
Second, there is a lot of value in rewriting the equations in two different ways. I have seen students who prefer each style, so you may want to try both:
You're right, I did gloss over that in the interests of brevity, and I agree that it's often not obvious to novices. Reversing the order of operations is certainly helpful. I try to build in the understanding of what to do from much simpler examples, eg x + 1 - 1 = x (with several numerical examples of x), and (x/3).3 = x, again with numbers as examples. If they can be persuaded to grasp that, remembering a rule (which I'm usually dead against!!) becomes unnecessary.
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ChrisAApr 22 at 15:54
If your curriculum allows you the flexibility to do this, I prefer to start with what are variables (a letter representing a number that varies), then what are expressions (a plan what you'll do once you know the variable's value), then how can we evaluate the expression for a particular variable value.
Stick with various expressions for at least a few days before turning the page to equations. With all this practice evaluating expressions, the guessing-game nature of equations will be clear: you guess the value of $x$, evaluate the LH expression, evaluate the RH expression, and see if they're equal, meaning the $x$ you guessed is a valid solution to the original equation.
Once the problems get too hard to solve by guessing, finally follow ChrisA's answer to teach a methodical way to solve equations, always preserving equality by doing the same thing to both sides.
I would recommend looking at Dan Chazan's excellent book, Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom, which grapples with many of the issues you raise. In particular Chazan narrates the challenges of working with struggling students like the one you anticipate working with, and he spends a lot of time unpacking fundamental issues like "What does an equation mean?".
Teach the students that they can (and should) check their own work. A student who knows that their check-by-substitution worked will be a lot more confident that they learned that day's lesson than a student who is waiting until the next day to find out they got some answers wrong. Also, it is great practice for professions (like accounting and programming) that need to "tie out" or "unit test" their work.
Here is how I was taught to check my work. In the examples, most of the "·" signs are optional:
1) Write out my answer, such as
x = 3
If it is the answer to a story problem, include a note about what the answer means, such as
x = 3 \$/toy. Each toy can cost an average of 3 dollars.
2) Circle the answer in a fluffy cloud.
3) Write "CBS:" below the answer.
4) Substitute in the answer into the original problem. Put a question mark over the equals sign. For example,
3 toys · 3 $/toy + 1 hat · 5 $/hat ≟ 14 $
5) Do the math on both sides of the equals sign. Keep the question mark over the equals sign until it is obvious that the equation is true. Put each version of the equation on a following line, and try to line up the equals signs. For example,
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Math Center
Math Center
DCTC's Math Center offers fun, free, professional tutoring to all enrolled DCTC students. The Math Center works with students on any math assignment or project at DCTC.
Mission
The Math Center staff is committed to providing quality math assistance and tutoring to students wishing to become confident, independent mathemeticians.
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ACCT1000-2400 Accounting
Description
HEAL 1150 This course will assist students in mastering the skills necessary to determine drug dosages. Applicable basic skills will be reviewed, followed by proportions and a study of the metric system and the apothecaries' system. A major portion of the time will be spent solving drug dosage word problems. Prerequisite: Qualifying scores on ACCUPLACER Arithmetic test.
Description
MATS 0200 This course is designed to develop and increase the student's ability to perform basic math operations and to solve mathematical problems relevant to technical education. Topics covered include whole numbers, fractions, decimals, percents, and problem solving. All instruction is individualized. A student may enroll in this course for more than one term. Prerequisites: None
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MATS 0600 Students with a basic algebra background are prepared for college-level mathematics courses such as college algebra, statistics, math for liberal arts, and concepts in math for elementary teachers. After reviewing linear equations and factoring methods, students move on to study rational expressions and equations, radical expressions and equations, rational exponents, quadratic equations and their solution in the complex number system, coordinate geometry including lines and circles, and functions and their graphs.
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MATS 1300 This course develops a student's ability to analyze and work with functions and graphs, as part of the preparation for a rigorous calculus sequence (taking this course together with MATS1320 is equivalent to precalculus). Topics include tests for symmetry, finding intercepts and asymptotes, constructing piece wise-defined functions, transformations, polynomial and rational functions, composite and inverse functiions, and exponential and logarithmic functions. Techniques for solving linear, quadratic, rational, radical, exponential and logarithmic equations (with applications) are emphasized throughout the course. Systems of linear equations and matrix algebra are introduced, after wich sequences and series are also briefly introduced.
Meets MnTC Goal 4
Description
MATS 1350 A college level course designed to build a student's appreciation of both the beauty and utility of mathematics as it is used in society. Topics include voting and apportionment, fair division, scheduling and route planning, patterns of growth, and basic probability and statistics concepts including the bell curve. NOTE that this course does not serve as a prerequisite for any other math course.
Meets MnTC Goal 4
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The Enjoyment of Math
Publisher:
Princeton University Press
Number of Pages:
208
Price:
42.00
ISBN:
978-0-691-02351-9
This is a serious math book that has minimal prerequisites: geometry and college algebra, but no trig or calculus. It contains 28 largely independent chapters that solve a variety of famous and difficult math problems, mostly in the areas of plane geometry and number theory. The problems include: Fermat's last theorem for exponent 4, unique factorization in number fields, a number of geometrical maximization problems including several versions of the isoperimetric problem, some transfinite numbers, the 5-color map coloring theorem, and the arithmetic mean - geometric mean inequality. There's no analysis per se in the book, but several topics depend on the analytic ideas of continuity and variation.
This book was first published in German in 1930 and in English in 1957 as The Enjoyment of Mathematics, and is still in print today in both languages. This implies that there is still an audience for it, but it is hard to imagine exactly what this audience is. The book was developed out of a series of public lectures and was intended as a "popular math" book. While it is very clear and well-written, the reasoning in all the chapters is very intricate (especially in the geometric problems), and the book is much more difficult than anything that appears in popular math books being written today. It's also too difficult for a math appreciation text. The modern (2000) Preface to the German edition suggests that the book is suited for bright high-school students who are hungry for learning, and maybe this is its real audience today. Eager college students would instead get enrichment activities related to their course work, and professional mathematicians, although they would admire the book, would probably look up the material in a more specialized text and not here.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning.
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Find a Channelview Precalculus
...Thomas and received an A in the course. Linear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science
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Synopses & Reviews
Publisher Comments:
Find yourself stuck on the tracks when two trains are traveling at different speeds? Help has arrived Math Word Problems Demystified, Second Edition is your ticket to problem-solving success.
Based on mathematician George Polya's proven four-step process, this practical guide helps you master the basic procedures and develop a plan of action you can use to solve many different types of word problems. Tips for using systems of equations and quadratic equations are included. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning
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A Helpful Technique in Calculus and Pre-Calculus: The Sign Pattern [NOOK Book] ...
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This Book concave down, is discontinuous and where maxima, minima and inflection points are located. In order to accomplish this task a student must calculate which values of the independent variable, x, make y'(x) and y''(x) positive , zero, negative, undefined, imaginary or indeterminate.
This phase of the solution is generally "glossed over", or made arithmetically difficult. The examples in most texts include a few sample arithmetic calculations to test the sign of y' and y'', for specific values of x. Students are then left with the challenge of choosing "appropriate" sample values of x when solving future problems. The result is a lack of confidence in applying curve sketching techniques to more general functions.
The purpose of this booklet is to introduce a technique which tremendously simplifies the task of curve sketching functions that are encountered in introductory calculus. The method is the Sign Pattern Technique. This technique is not new. However, its application to curve sketching problems is rarely described in great detail. The benefit of constructing a Sign Pattern is that it dramatically reduces the number of error-prone arithmetic calculations normally required in problem solving. This allows a user to clearly visualize an entire problem in a compact manner.
Sections 1.0 through 8.0 develop the approach using many example problems. To demonstrate the generality of the technique, Sections 9.1, 9.2 and 9.3 contain several examples describing the application of the Sign Pattern to the solution of inequalities, to the determination of the domain of square root functions and to the evaluation of infinite limits or vertical asymptotes. Section 9.4 is the major application section of this booklet. It contains a wide variety of example problems describing the application of the Sign Pattern to curve sketching.
The beauty of the Sign Pattern Technique is its wide applicability, combined with its graphic simplicity.
Hopefully, it will serve you, the student, as a valuable problem-solving tool.
Jason R. Taylor
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Jason R. Taylor has authored more than 35 technical papers in national and international journals, three mathematical textbooks and a total of thirteen books. He has taught at MIT, Northeastern University and is currently Professor Emeritus of Bentley College. His latest ongoing project is a series of humerous educational books for elementary school students, entitled EduFables—Educational Fables. The purpose of this series is to demystify traditionally complex subjects and teach youngsters advanced science and math concepts so they will be encouraged to pursue careers in the sciences. If successful, this will help fill a growing need
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Vernalis PhysicsAlgebra 1 is just the beginning! Algebra 2 is a little challenging, but it can be very useful for classes such as physics, higher level math classes, and many more science based classes. Improve your chances at succeeding in school and being hired for a job by improving your grammar
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Topics in Contemporary Mathematics, Enhanced for the Math for Liberal Arts course, TOPICS IN CONTEMPORARY MATHEMATICS helps users see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the book demonstrate how math relates to subjects—such as sociology, psychology, business, and technology—that generally interest users. This Enhanced Edition includes instant access to WebAssign®, the most widely-used and reliable homework system. WebAssign® presents over 500 problems, as well as links to relevant book sections, that help users grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this book. This guide contains instructions to help users learn the basics of WebAssign quickly.
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32 aus mathematics curriculumDocument Transcript
Draft Consultation version 1.0.1 Australian Curriculum Learning area Mathematics Curriculum elements Rationale/Aims Organisation Content descriptions Achievement standards Year levels Kindergarten Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 10A Mathematics | Rationale/Aims Rationale Learning mathematics enriches the lives of, and creates opportunities for, all Australians. The Australian mathematics curriculum provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals required of mathematical specialists and professional users of mathematics. Mathematics has its own value and beauty and it is intended that students will appreciate the elegance and power in mathematical reasoning. Mathematical ideas have evolved over centuries and across all cultures and they continue to expand. Digital technologies are contributing to this expansion of ideas and provide access to new tools for continuing mathematical exploration and invention. The Australian mathematics curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought processes and problem-solving skills to enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently. The Australian mathematics curriculum ensures that the links between the various components of mathematics, and to other disciplines, are made clear. Mathematics is composed of multiple but interrelated and interdependent concepts and systems which students apply in other disciplines. In science, for example, understanding sources of error and their impact on the confidence of conclusions is vital, as is the use of mathematical models; in geography, interpretation of data underpins the study of human populations and their physical environments; in history, students need to be able to imagine timelines and time frames to reconcile relativities of related events; and in English, deriving quantitative and spatial information is an important aspect of making meaning of texts. The curriculum is written with the expectation that schools will ensure that all students benefit from access to the power of mathematical reasoning and be able to apply their mathematical understanding creatively and efficiently. The mathematics curriculum provides students with carefully paced, in-depth study of critical skills and concepts. It encourages teachers to facilitate students to become self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences. Aims The Australian mathematics curriculum aims to ensure that students are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens. It aims to ensure students develop increasingly sophisticated understanding of mathematical concepts and fluency with processes, able to pose and solve problems and reason in number and algebra; measurement and geometry; and statistics and probability. It aims to ensure students recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study.ACARA Australian Curriculum Consultation Portal 5/03/2010 1
Draft Consultation version 1.0.1 Australian Curriculum Mathematics | Organisation Content strands Content strand descriptors The Australian Curriculum: mathematics is organised around the interaction of three content strands and four proficiency strands. The content strands are Number and algebra, Statistics and probability, and Measurement and geometry. They describe 'what' is to be taught and learnt. The proficiency strands are Understanding, Fluency, Problem solving, and Reasoning, and describe 'how' content is explored or developed ie the thinking and doing of mathematics. They provide the language to build in the developmental aspects of the learning of mathematics and have been incorporated into the content descriptions of the three content strands described above. This approach has been adopted to ensure students' proficiency in mathematical skills is developed throughout the curriculum and becomes increasingly sophisticated over the years of schooling. Content strands Number and algebra Number and algebra are developed together since each enriches the study of the other. Students apply number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range of strategies for computation and understand the connections between operations. They recognise pattern and understand the concepts of variable and function. They build on their understanding of the number system to describe relationships and formulate generalisations. They recognise equivalence and solve equations and inequalities. They apply their number and algebra skills to conduct investigations, solve problems and communicate their reasoning. Statistics and probability Statistics and probability initially develop in parallel. Progressively the curriculum builds the links between them. Students recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful investigations involving the collection and interpretation of data. They assess likelihood and assign probabilities using experimental and theoretical approaches. They critique the use of chance and data concepts and make reasoned judgments and decisions. They develop an increasingly sophisticated ability to critically evaluateACARA Australian Curriculum Consultation Portal 5/03/2010 2
Draft Consultation version 1.0.1 Australian Curriculum chance and data concepts and make reasoned judgments and decisions. They develop an increasingly sophisticated ability to critically evaluate statistical information and build intuitions about data. Measurement and geometry Measurement and geometry are presented together to emphasise their interconnections, enhancing their practical relevance. Students develop increasing sophistication in their understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three- dimensional objects in space. They investigate properties and use their understanding of these properties to define, compare and construct figures and objects. They learn to develop geometric arguments. They make meaningful measurements of quantities, choosing appropriate metric units of measurement. They understand connections between units and calculate derived measures such as area, speed and density. Proficiency strands Understanding Students build robust knowledge of adaptable and transferable mathematical concepts, make connections between related concepts and develop the confidence to use the familiar to develop new ideas, and the 'why' as well as the 'how' of mathematics. Fluency Students develop skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Problem solving Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Reasoning Students develop increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying, and generalising. Mathematics across K–10 Although the curriculum will be developed year by year, this document provides a guideline across three year-groupings: Years K–2: typically students from 5 to 8 years of age Years 3–6: typically students from 8 to 12 years of age Years 7–10: typically students from 12 to 15 years of age What follows for each year grouping is a description of the major content emphases either as points of exposure, introduction, consolidation or extension; some of the underlying principles (and rationale) that apply in these considerations; key models or representations; and possible connections across strands and year levels.ACARA Australian Curriculum Consultation Portal 5/03/2010 3
Draft Consultation version 1.0.1 Australian Curriculum connections across strands and year levels. Years K–2 (typically from 5 to 8 years of age) The early years (5–8 years of age) lay the foundation for learning mathematics. Students at this level can access powerful mathematical ideas relevant to their current lives. Learning the language of mathematics is vital in these years. Children have the opportunity to access mathematical ideas by developing a sense of number, order, sequence and pattern; understanding quantities and their representations; learning about attributes of objects and collections, position, movement and direction; developing an awareness of the collection, presentation and variation of data and a capacity to make predictions about chance events. These understandings and the experiences in the early years provide a foundation for algebraic, statistical and multiplicative thinking that will develop in later years. They provide a foundation also for children to pose basic mathematical questions about their world, identify simple strategies to investigate solutions, and strengthen their reasoning to solve personally meaningful problems. Years 3–6 (typically from 8 to 12 years of age) These years focus on the importance of students studying coherent, meaningful and purposeful mathematics that is relevant to their lives. Students still require active experiences that allow them to construct key mathematical ideas, but there is a trend to move to using models, pictures and symbols to represent these ideas. The curriculum develops key understandings by extending the number, measurement, geometric and statistical learning from the early years; building foundations for future studies by emphasising patterns that lead to generalisations; describing relationships from data collected and represented, making predictions; and introducing topics that represent a key challenge in these years such as fractions and decimals. Particularly in these years of schooling, it is important for students to develop deep understanding of whole numbers to build reasoning in fractions and decimals and develop their conceptual understanding of place value. With these understandings, students are able to develop proportional reasoning and flexibility with number through mental computation skills. These understandings extend students' number sense and statistical fluency. Years 7–10 (typically from 12 to 15 years of age) Traditionally, during these years of schooling, the nature of the mathematics needs to include a greater focus on the development of more abstract ideas, for example, through explorations that enable students to recognise patterns and explain why these patterns apply in these situations. From such activities abstract thoughts can develop, and the types of thinking associated with developing such abstract ideas can be highlighted. The foundations built in the previous years, provide a solid basis for preparing for this change. The mathematical ideas built previously can be drawn upon in unfamiliar sequences and combinations to solve non-routine problems and develop more complex mathematical ideas. However, to motivate them during these years, students need an understanding of the connections between the mathematics concepts and their application in their world in contexts that are directly related to topics of relevance and interest to them. During these years students need to be able to represent numbers in a variety of ways; develop an understanding of the benefits of algebra, through building algebraic models and applications, and the various applications of geometry; estimate and select appropriate units of measure; explore ways of working with data to allow a variety of representations; and make predictions about events based on their observations. The curriculum lists fewer detailed topics with the intention to encourage the development of important ideas in more depth, and promote the interconnectedness of the mathematical concepts. An obvious concern is the preparation of students who are intending to continue studying mathematics in the senior secondary years. It is argued that it is possible to extend the more mathematically able students appropriately using challenges and extensions within available topics and the expectations for proficiency can reflect this. This can lead to deeper understandings of the mathematics in the curriculum and hence a greater potential to use this mathematics to solve non-routine problems they encounter at this level and at later stages in their mathematics education.ACARA Australian Curriculum Consultation Portal 5/03/2010 4
Draft Consultation version 1.0.1 Australian Curriculum The national mathematics curriculum will be compulsory to the end of Year 10 for all students. It is important to acknowledge that from Year 10 the curriculum should enable pathway options that will need to be created and available for all students. This will enable all students to access one or more of the senior years' mathematics courses. Implications for teaching and learning In mathematics, challenging problems can be posed using basic content, and content acceleration may not be the best way to extend students. Choosing engaging experiences as contexts for a variety of tasks assists in making mathematics inclusive, differentiating both for students experiencing difficulty and those who complete tasks easily. The proficiency strands apply expectations of the range and nature of how mathematical content is enacted, and can help in focusing teaching. Teachers should base their teaching on what the students already know, should make explicit the subsequent key ideas, should ensure tasks are posed at an appropriate level of challenge, and should offer feedback on activities, standards and directions as often as possible. The development of key ideas across the years enables teachers to make informed classroom decisions, including the use of digital technologies to enhance the relevance of mathematics content and processes for learning. General capabilities The Australian Curriculum, Assessment and Reporting Authority (ACARA) has identified 10 general capabilities that will be specifically covered in the curriculum. In mathematics, there is specific reference to five of these in the content descriptions and achievement standards. Literacy is an important aspect of mathematics. There is a particular way of writing and interpreting mathematical texts. Students will be taught to interpret mathematical symbols, understand the meaning of the language of mathematics and to read and write reports of their investigations. Numeracy is fundamentally the responsibility of mathematics and is applied in other learning areas. It is crucial that the mathematics curriculum provides the opportunity to apply mathematical understanding and skills in context, both in other learning areas and in real world contexts. A particularly important context for the application of number and algebra is financial mathematics. In measurement and geometry there is an opportunity to apply understanding to design. The world in the 21st century is information driven and statistics and probability provide opportunities for students to interpret data and make informed judgements about events involving chance. Information and communication technologies (ICT) allow students to solve problems and perform tasks that previously have been onerous. Calculators of all types from the simple four operations versions to the more complex graphical and CAS calculators allow students to make calculations, draw graphs and interpret data in ways that previously have not been possible. There are spreadsheets, dynamic geometry programs and other software that can engage students and promote understanding of key concepts. It is expected that mathematics classrooms will make use of all available ICT in teaching and learning situations. Notwithstanding this, there will be occasions where teachers will ask students to undertake tasks without using the technology. For example, it is still important for students sometimes to make geometric constructions using a ruler and compass or to work out calculations using mental or written strategies. Thinking skills are key to developing mathematical understanding. This general capability overlaps with the mathematics proficiency strands of reasoning and problem solving. The mathematics curriculum is designed to promote students thinking and reasoning about solutions to problems and the strategies they can use to find these solutions. Students will be encouraged to be critical thinkers, justifying for example, their choice of a particular calculation strategy or identifying the questions that need to be asked and answered when undertaking a statistical investigation. Creativity is the essence of mathematical problem solving. The mathematics curriculum encourages approaching problems in different ways. For example, by identifying that a problem is similar to a previous one; that drawing diagrams could help; or that simplifying a problem to control some variables is a way of understanding and arriving at a solution. The other general capabilities of self-management, teamwork, intercultural understanding, ethical behaviour and social competence are all relevant to the pedagogy used by teachers of mathematics. It is important that students are encouraged to take responsibility for their own learning in mathematics and work collaboratively in teams.ACARA Australian Curriculum Consultation Portal 5/03/2010 5
Draft Consultation version 1.0.1 Australian Curriculum Teamwork should be inherent in explorations and investigations, which are essential processes through which students learn to be mathematicians. There is also the opportunity for students to use mathematics to examine issues of ethical behaviour and social competence. Intercultural understanding can be enhanced if students are exposed to other cultures' view of mathematics, for example, through examining Aboriginal and Torres Strait Islander peoples' perceptions of time and weather patterns, the networks embedded in family relationships and the algebraic concepts inherent in storytelling. It is equally important for mathematics classes to explore the influences and contributions of many cultures, from the early work on geometry by the philosophers of ancient Greece to the origins of algebra that can be found in ancient Indian mathematics. Cross-curriculum dimensions Cross-curriculum dimensions are not explicitly tagged in the content descriptions. Aboriginal and Torres Strait Islander dimensions are included in the elaborations. It is imperative that all Australian students learn from the wisdom of the first Australians. For example, when considering the idea of seasons in measurement and geometry, the European tradition of four seasons can be compared and contrasted with the different constructs used by Aboriginal and Torres Strait Islander people in different parts of the country. The idea of using symbols as a way of generalising relationships can be enhanced by drawing on the perspectives of Indigenous Australians. The cross-curriculum dimension of commitment to sustainable living and the knowledge and understandings related to Asia and Australia's engagement with Asia provide engaging and rich contexts for mathematics learning. Links to other learning areas The Australian National Numeracy Review Report (2008) identified numeracy as requiring an across-the-school commitment, including mathematical, strategic and contextual aspects. This across-the-school commitment can be managed by including specific reference to other curriculum areas in the mathematics curriculum, and identification of key numeracy capacities in the descriptions of other curriculum areas being developed. For example, the following are indications of some of the numeracy perspectives that could be relevant to history, English, and science. English: One aspect of the link with English and literacy is that, along with other elements of study, numeracy can be understood and acquired only within the context of the social, cultural, political, economic and historical practices to which it is integral. Students need to be able to draw on quantitative and spatial information to derive meaning from certain types of texts encountered in the subject of English. Science: Practical work and problem solving across all the sciences require the capacity to: organise and represent data in a range of forms; plot, interpret and extrapolate graphs; estimate and solve ratio problems; use formulas flexibly in a range of situations; perform unit conversions; and use and interpret rates including concentrations, sampling, scientific notation, and significant figures. History: Learning in history includes interpreting and representing large numbers and a range of data such as those associated with population statistics and growth, financial data, figures for exports and imports, immigration statistics, mortality rates, war enlistments and casualty figures, chance events, correlation and causation; imagining timelines and timeframes to reconcile relativities of related events; and the perception and spatial visualisation required for geopolitical considerations, such as changes in borders of states and in ecology.ACARA Australian Curriculum Consultation Portal 5/03/2010 6
Draft Consultation version 1.0.1 Australian Curriculum Mathematics | Strands Kindergarten Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Counting 1. Data representation 1. Geometry Say, understand and reason with number Collect, represent and interpret data from Sort, describe, name, and represent familiar sequences, initially to and from 20, and then simple questions with objects and drawings two-dimensional shapes and three- beyond, moving to any starting point where one object or drawing represents one dimensional objects in the environment data value 2. Numeration 2. Comparison 2. Data investigation Understand numbers to 10, including Use direct and indirect comparison to decide matching number names, numerals and Solve problems by collecting data and which is longer, heavier and holds more and quantities, and work fluently with small answering questions about obvious attributes explain reasoning in everyday language numbers including subitising and partitioning of themselves and familiar objects and events 3. Time 3. Comparing collections Read time on the hour on digital and Compare and order collections, initially to 20, analogue clocks, and make connections and then beyond, and explain reasoning between common sequences such as days of the week and other familiar events and 4. Addition and subtraction actions Model, represent and solve problems 4. Location concerning additive and sharing situations involving combining, change and missing Describe the position and movement of elements objects, including themselves 5. Pattern Sort and classify familiar objects, explain reasons for these classifications and copy, continue and create patterns with objects and drawings Achievement standard (Kindergarten) By the end of Kindergarten, students are able to confidently recall the sequence of numbers to 20, matching names and numerals and find the total of small collections by counting. They subitise small quantities, partition numbers to 10 and use one-to-one relations to share and count out quantities. Students collect data from straightforward questions about themselves and familiar events and, with assistance, can organise this data. They readily use everyday language to describe measurements found by direct comparison and sort and classify familiar shapes.ACARA Australian Curriculum Consultation Portal 5/03/2010 7
Draft Consultation version 1.0.1 Australian Curriculum Year 1 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Counting 1. Data representation 1. Geometry Say, understand and reason with number Represent data using pictographs where one Recognise, visualise and classify familiar two- sequences to and from 100 by ones from any picture represents one data value dimensional shapes and three-dimensional starting point, and say number sequences of objects using obvious features such as 2. Data interpretation twos, fives and tens starting from zero number of corners or faces or length of sides Read and make connections between lists, 2. Numeration 2. Length and capacity tables and pictographs Recognise, model and represent numbers to Measure length and capacity using uniform 3. Chance 100, and read, write and order those numbers informal units and compare measures Identify outcomes arising from familiar chance explaining reasoning in everyday language 3. Place value events and describe using everyday language 3. Time Understand and work fluently with counting such as yes, no or maybe collections to 100 by grouping in tens, and Read analogue and digital clocks to the half counting the tens, and use place value to hour and describe duration using months, partition and regroup those numbers weeks, days and hours 4. Fractions 4. Money Understand one-half as one of two equal Recognise, describe and order Australian parts, and recognise and create halves of coins collections 5. Location 5. Addition and subtraction Give and follow directions to familiar locations Model, represent and solve problems involving additive and sharing situations using efficient strategies including counting on 6. Number patterns Copy, continue, create and describe patterns with objects and numbers to 100 Achievement standard (Year 1) By the end of Year 1, students are able to quantify collections to 20 and can count forwards and backwards to 100. They understand and are fluent with partitioning numbers to 10. They can read, write, order and model two-digit numbers and understand that these numbers are comprised of units of tens and ones. They are beginning to understand the relationship between addition and subtraction and use this knowledge to model and solve simple additive problems. Students collect data about themselves and their peers and represent these data in lists, tables and pictographs. They use everyday language to describe simple geometry and measurement ideas and use uniform informal units to measure and compare length and capacity and use hours and half-hours to describe time.ACARA Australian Curriculum Consultation Portal 5/03/2010 8
Draft Consultation version 1.0.1 Australian Curriculum Year 2 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Counting 1. Data representation 1. Geometry Say, understand and reason with number Record data using tallies and represent data Describe features of two-dimensional shapes sequences increasing by twos, fives and tens using tables, pictographs and bar and column and three-dimensional objects, draw them from any starting point including using graphs and use materials to make models of these calculators 2. Data interpretation 2. Metric units 2. Numeration Read and make connections between lists, Measure and compare length and capacity Recognise, model and represent numbers to tables and graphs showing data from familiar using uniform informal and familiar metric 130, and read, write and order those numbers contexts, and explain interpretations units and measure mass using balance scales with familiar metric units 3. Place value 3. Chance 3. Area Work fluently with counting increasingly larger Experiment with chance devices and describe collections up to 1000, grouping in hundreds outcomes as likely or unlikely and identify Compare the area of regular and irregular and tens and counting the tens and hundreds some events as certain or impossible shapes directly and use place value to partition and regroup 4. Time these numbers Read analogue and digital clocks to the 4. Fractions quarter hour and to use a calendar to identify Recognise and interpret common uses of the date, and name and order months and halves, quarters and thirds of everyday seasons shapes, objects and collections 5. Money 5. Addition and subtraction Count and order small collections of Model, represent and make connections Australian coins between simple additive situations, solving 6. Transformations them using efficient written and calculator strategies and explaining the choice of Predict and draw the effect of 1-step sliding, strategy flipping and turning of familiar shapes and objects including using digital technology and 6. Multiplication and division identify half and quarter turns from any Model, represent and make connections starting point between simple multiplicative situations such 7. Location as groups of, arrays, sharing, solving them using efficient mental and written strategies Interpret simple maps of familiar locations and calculators and explaining their choice of such as the classroom to identify the relative strategy position of key features 7. Number patterns Copy, continue, create and describe patterns with numbers, especially place value patterns and identify missing elements Achievement standard (Year 2) By the end of Year 2, students are able to understand the sequence of numbers to 130, recognising patterns in units of 10 and 100. They apply this understanding to efficiently represent collections larger than 100 and to partition numbers into units of tens and ones. They describe and connect patterns of twos, fives and tens, solve multiplicative problems and model everyday simple functions. Students describe events produced by simple chance devices and understand different ways of representing data. Students compare lengths, capacities and masses using informal units and familiar metric units and areas by direct comparison. They identify and describe properties of familiar shapes and objects, can visualise and represent them, and can use simple maps.ACARA Australian Curriculum Consultation Portal 5/03/2010 9
Draft Consultation version 1.0.1 Australian Curriculum Year 3 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Counting 1. Data investigation 1. Symmetry Understand and reason with number Investigate data-oriented questions about Use symmetry, identifying its occurrence in sequences increasing and decreasing by familiar situations, predict what the data might the environment to create symmetrical twos, fives and tens from any starting point, show, carry out the investigation and report patterns, pictures and shapes moving to other sequences, emphasising the results 2. Metric units patterns and explaining relationships 2. Data representation Use direct and indirect comparison to order 2. Numeration Construct, read and make connections and compare objects by length and develop Recognise, model, represent and visualise between tables, diagrams and graphs 'real life' benchmarks for familiar metric units numbers initially to 1000 and then beyond, including dot plots with prepared baselines of length, mass and capacity including and read, write and order those numbers centimetre, metre, kilogram and litre 3. Chance 3. Place value 3. Area Conduct chance experiments and recognise Justify various uses of the place value system that there will be variation in results as well as Measure and compare areas using uniform to describe numbers to 1000, using the having expected outcomes informal units, explaining reasoning in hundreds and tens as units, and to partition everyday language and regroup those numbers to assist 4. Time calculation and solve problems Read analogue and digital clocks to the five 4. Addition and subtraction minutes and compare and order events Model, represent and solve problems according to their duration involving additive situations using efficient 5. Money mental and written strategies and calculators Represent money values in multiple ways and 5. Multiplication and division count out the change of simple transactions Model, represent and solve problems 6. Angles involving multiplicative situations including for each and times as many using efficient Create angles and recognise that equivalence mental and written strategies and calculators in angles such as two quarter turns is the same as a straight angle 6. Fractions 7. Location Solve problems involving everyday uses of fractions as equal parts of regular shapes or Create and interpret simple maps to show collections and as numbers, building position and pathways between objects connections between the number of parts and the size of the fraction 7. Calculation Understand and become fluent with addition and related subtraction facts to 10 plus 10 and multiplication facts of 1, 2, 5 and 10 8. Number patterns Copy, continue, create, describe and identify missing elements in patterns with numbers including patterns resulting from performing one operation and place value patterns Achievement standard (Year 3)ACARA Australian Curriculum Consultation Portal 5/03/2010 10
Draft Consultation version 1.0.1 Australian Curriculum By the end of Year 3, students are able to understand place value to 1000 and connect this to comparing and ordering length, mass and capacity. They apply this understanding to choose efficient strategies (mental, written and calculator) to solve problems in everyday situations. They understand the relationship between the number of parts and the size of fractions, and use this understanding to solve everyday problems including describing quarter and half turns. They use number patterns including those found in the multiples of 2, 5 and 10 and apply these in contexts such as reading clocks to five minutes and using money. Students collect, represent and interpret data in tables, graphs and diagrams and conduct simple chance events. Students estimate and order length, mass and capacity using personal benchmarks. They use symmetry in designs and can represent positions and direction using simple maps.ACARA Australian Curriculum Consultation Portal 5/03/2010 11
Draft Consultation version 1.0.1 Australian Curriculum Year 4 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Factors and multiples 1. Data investigation 1. Geometry Work and reason with number sequences Plan and undertake surveys, such as with the Generalise about the two-dimensional shapes increasing and decreasing from any starting whole class, to answer questions posed, that form the surfaces of common three- point, and to recognise multiples of 2, 5, 10 represent the data and report the results, dimensional objects and make connections and factors of those numbers including using ICT with the nets of these objects justifying reasoning 2. Numeration 2. Data representation 2. Metric units Recognise, represent, visualise and work Construct, read, interpret and make fluently with reading, writing and ordering connections between tables and simple Use metric units to estimate, measure and numbers to 1 million graphs with many-to-one correspondence compare the length, mass and capacity of between data and symbols, including using familiar objects reading scales to the nearest 3. Place value ICT graduation Justify various uses of the place value system 3. Chance 3. Area and volume to describe large numbers, and to partition and regroup those numbers to assist Predict the outcomes of chance experiments Measure and compare area using familiar calculation and solve problems involving equally likely events, and compare metric units and compare volumes using and contrast the predictability of outcomes of uniform informal units 4. Fractions experiments with small numbers of trials to 4. Time Compare and contrast everyday uses of those with large numbers including using ICT halves, thirds, quarters, fifths, eighths and to generate the trials Read analogue and digital clocks to the tenths, work fluently with renaming to find minute, understand equivalent 4. Unequal outcomes equivalent fractions and solve problems representations of 12-hour time, and involving fractions as operators Justify representations of simple situations sequence daily and weekly events with unequal outcomes such as constructing 5. Counting – fractions 5. Angle spinners using technology Understand fractions as rational numbers, Describe the connection between turns and including working fluently with counting by angles and create and classify angles as quarters, and halves including with mixed equal to, greater than or less than a right numbers, and representing these numbers on angle a number line 6. Location 6. Multiplication and division Create, interpret and use basic maps using Understand and become fluent with simple scales and legends and directions multiplication facts and related division facts such as left, right, forward and backward of 2, 3, 5 and 10 extending to 4, 6, 8 and 9 7. Visualising 7. Calculation Visualise the result of combining and splitting Select, explain, justify and apply mental, shapes and to represent all possible written strategies and use calculators to solve combinations of small numbers of triangles problems involving addition, subtraction and and squares multiplication with one- and two-digit numbers and division by one digit numbers without remainders 8. Number patterns Copy, continue, create, describe and identify missing elements in patterns with numbers including large numbers as well as patterns resulting from performing two operationsACARA Australian Curriculum Consultation Portal 5/03/2010 12
Draft Consultation version 1.0.1 Australian Curriculum Achievement standard (Year 4) By the end of Year 4, students are fluent with and evaluate the efficiency of mental and written strategies with one- and two-digit numbers and use these to solve problems. They identify and describe number patterns involving one or two operations and can find missing numbers in these patterns. Students pose questions that can be answered by data and plan and undertake data investigations, including the analysis of secondary data sets. They report their results using tables and graphs using one to one relationships between the data and the representation and evaluate their investigation. They can describe likelihood of familiar chance events using everyday language. They fluently choose appropriate tools and metric units to measure and compare the length, mass and capacity of objects and compare volumes using informal units. They can read scales to the nearest graduation. Their understanding of time extends to reading clocks to five minute intervals and to sequencing daily and weekly events, interpreting calendars and estimating duration. They confidently classify angles as equal to, greater than or less than a right angle and use these classifications to solve problems. They can identify obvious features of shapes and objects and visualise results of combining small numbers of squares and triangles.ACARA Australian Curriculum Consultation Portal 5/03/2010 13
Draft Consultation version 1.0.1 Australian Curriculum Year 5 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Decimals 1. Data investigation 1. Geometry Recognise and represent numbers involving Solve problems involving the collection of Make connections between different types of tenths and hundredths; read, write and order data over time, carry out the investigation and triangles and quadrilaterals using their those numbers and connect them to fractions report the results, including using ICT, and features, including symmetry and explain justify conclusions about the relationship reasoning 2. Place value between the variables 2. Time Justify various uses of the place value system 2. Summary statistics to describe decimal numbers, and to partition Solve realistic problems involving time and regroup those numbers to assist Identify the mode and median in lists and on duration including using 12- and 24-hour time calculations and solve problems dot plots 3. Scales 3. Fractions and decimals 3. Data representations Read and interpret scales using whole Solve problems involving making Use and compare the effectiveness of a numbers of metric units for length, capacity, comparisons using equivalent fractions and range of data representations including for mass and temperature decimals and everyday uses of percentages, specific situations 4. Perimeter, area, volume relating them to parts of 100 and hundredths 4. Chance Explore different ways of calculating 4. Multiplication and division Quantify chance with fractions, and apply this perimeter and area of rectangles and volume Solve realistic problems involving to investigate complementary events of rectangular prisms using metric units multiplicative situations with large numbers 5. Transformations including division by one-digit numbers Visualise, demonstrate and describe the 5. Fractions effects of translations, reflections, and Understand and become fluent with and solve rotations of two-dimensional shapes and realistic additive problems involving addition describe line and simple rotational symmetry, and subtraction of fractions with the same or including using ICT related denominators and fractions as 6. Location operators Describe locations and routes using a 6. Estimation coordinate system such as road maps, the Use estimation and rounding to check the four main compass directions and the reasonableness of answers language of direction and distance 7. Algebraic thinking Copy, continue, create and describe patterns with numbers and use graphs, tables and rules to describe those patterns 8. Factors and multiples Identify and describe properties of numbers including factors, multiples and composites and solve problems involving those properties Achievement standard (Year 5) By the end of Year 5 students are able to describe the place value system for whole numbers and can extend its use to two decimal places. Students choose efficient mental and written strategies for calculations with whole numbers, solve additive problems with fractions and relate fractions to decimals and percentages. Students choose appropriate graphs for single variable data, and begin to represent change in data over time. They use representation of single variable data to describe distributions including the use of median, mode and range. They use measurements effectively including time and can devise and use efficient ways of calculating perimeter, area and volume. They can describe locations and routes and describe and demonstrate the effects of transformations.ACARA Australian Curriculum Consultation Portal 5/03/2010 14
Draft Consultation version 1.0.1 Australian Curriculum locations and routes and describe and demonstrate the effects of transformations.ACARA Australian Curriculum Consultation Portal 5/03/2010 15
Draft Consultation version 1.0.1 Australian Curriculum Year 6 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Integers 1. Data representation 1. Geometry Read, represent, write, interpret and order Construct, read and interpret tables and Visualise and solve problems relating to positive and negative integers graphs including ordered stem and leaf plots, packing and stacking and construct pie charts and other simple 2. Decimals 2. Measurement data displays including using technology Recognise and represent numbers involving Solve problems involving comparison of 2. Data interpretation thousandths, read, write and order those length, area, volume and other attributes numbers, and connect them to fractions Interpret secondary data presented in the using appropriate tools, scales and metric media and elsewhere, identifying misleading units 3. Place value representations and distinguishing between 3. Metric System Justify uses of the place value system to samples and populations describe decimal numbers, and to partition Work fluently with the metric system to 3. Variation and regroup those numbers to assist convert between metric units of length, calculation and solve problems Explore concepts of variation and error by capacity and mass, using whole numbers and collecting repeated measurements commonly used decimals 4. Multiplication and division 4. Chance 4. Angles Apply multiplication and related division facts to solve realistic problems efficiently using List all outcomes for chance events and Estimate, compare and measure angles mental and written strategies and calculators quantify probabilities using simple fractions, 5. Time justifying the reasonableness of answers and decimals and percentages explaining reasoning Create, interpret and use timetables and timelines including calculating elapsed time 5. Ratio and rate 6. Measurement formulas Recognise and solve problems involving unit ratio and everyday rates and check for Understand and use the formulas for reasonableness of answers calculating perimeters and areas of rectangles, and volumes of rectangular 6. Decimals prisms Understand and work fluently with decimal 7. Transformation and symmetry numbers to thousandths, and multiply and divide numbers including decimals by whole Describe patterns in terms of reflection and numbers to solve additive problems, including rotational symmetry, and translations using technology including identifying equivalent transformations using ICT 7. Fractions 8. Location Understand and work fluently with and solve additive problems involving fractions with Describe and interpret locations and give and unrelated denominators, compare and follow directions, using scales, legends, contrast fractions using equivalence compass points, including directions such as NE and SW, distances, and grid references 8. Estimation Estimate the outcomes of calculations involving decimal numbers and justify the reasonableness of answers 9. Number properties Identify and describe properties of numbers including prime, composite and square numbersACARA Australian Curriculum Consultation Portal 5/03/2010 16
Draft Consultation version 1.0.1 Australian Curriculum Achievement standard (Year 6) By the end of Year 6, students are able to work with numbers including fractions and decimals to thousandths and apply their place value understanding to establish equivalences. They confidently solve realistic problems including those involving rate and ratio choosing appropriately written and mental strategies or calculators. They use estimation strategies to predict and check reasonableness of calculations. Students represent data choosing appropriate displays including stem and leaf plots and distinguish between sample and population data. They are beginning to quantify probability. Students can visualise and connect two- and three-dimensional shapes and objects. Their facility with maps extends to the use and interpretation of scales and legends. They are beginning to connect algebra and measurement, understanding the basis for formulas for perimeter, area and volume of simple polygons and rectangular prisms.ACARA Australian Curriculum Consultation Portal 5/03/2010 17
Draft Consultation version 1.0.1 Australian Curriculum Year 7 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Indices 1. Data measures 1. Geometry Understand and work fluently with index Determine mean, median, and range and use Describe the properties of parallel and notation and represent whole numbers as a these measures to compare data sets perpendicular lines, triangles and product of powers of prime numbers explaining reasoning including using ICT quadrilaterals to classify them and make geometric constructions including angle 2. Integers 2. Data investigation bisectors and perpendicular bisectors Order, add and subtract integers fluently and Investigate questions involving the collection 2. Measurement formulas identify patterns for multiplication and division of univariate and simple bivariate data, including using ICT including the use of back-to-back stem plots Relate the formula for calculating the area of and scatter plots triangles to the formula for rectangles and 3. Calculation parallelograms, to develop the formula for the 3. Sample space Understand and become fluent with written, volume of rectangular prisms, and use these mental and calculator strategies for all four Construct sample spaces for single-step to solve problems operations with fractions, decimals and experiments with equally likely outcomes and 3. Transformations percentages use them to assign probabilities Visualise, demonstrate and describe 4. Variables 4. Relative frequency translations, reflections, rotations and Apply the associative, commutative and Calculate relative frequencies, and recognise symmetry in the plane, including using distributive laws and the order of operations variation between results of chance coordinates and ICT to mental and written computation and experiments 4. Time generalise these processes using variables Calculate duration using 12- and 24-hour 5. Linear equations time, explain and use time zones Use symbols to represent linear relationships 5. Location and solve problems involving linear relationships where there is only one Interpret and create maps and plans, occurrence of a variable including using legends and scales, describe relative position, and plan journeys 6. Coordinates Plot points on the Cartesian plane using all four quadrants Achievement standard (Year 7) By the end of Year 7, students work fluently with index notation. They are able to use the operations to calculate accurately with integers, fractions and decimals, choosing appropriate operations when solving problems, and correctly applying the order of operations. They extend this understanding to algebraic representations, selecting and applying formulas for area and volume and begin to generalise arithmetic patterns, including linear functions, representing them algebraically and graphically. Students conduct systematic data-based enquiry using univariate and bivariate data, choosing appropriate graphs, calculating measures of spread and centre and drawing conclusions. They identify equally likely outcomes and calculate probabilities and relative frequencies from data. Students have a sound understanding of the geometric properties of angles, triangles and quadrilaterals and two-dimensional views of three-dimensional objects. They are beginning to construct logical geometric arguments about properties of triangles and quadrilaterals.ACARA Australian Curriculum Consultation Portal 5/03/2010 18
Draft Consultation version 1.0.1 Australian Curriculum Year 8 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Ratio and rate 1. Statistical measures 1. Congruence Solve problems involving use of percentages, Use a mean or median from a sample to Identify properties and conditions for rates and ratios, including percentage estimate the mean or median of a population congruence of plane figures, and use increase and decrease and the unitary and to recognise the limitations of samples coordinates to describe transformations method and judge reasonableness of results 2. Data investigation 2. Measurement formulas 2. Index laws Collect samples and construct tables and Generalise from the formulas for perimeter Understand, describe and use generalisations graphs including frequency column graphs and area of triangles and rectangles to of the index laws with positive integral indices with and without technology for grouped data, investigate relationships between the and to select and justify the choice of perimeter and area of special quadrilaterals 3. Calculation measure of centre and spread used and volumes of triangular prisms and use Solve problems involving fractions, decimals these to solve problems 3. Probability and percentages, including those requiring 3. Circles converting and comparing, and judge the Identify complementary events and use the reasonableness of results using techniques facts that probabilities range between 0 and 1 Investigate the relationship between features such as rounding and sum to 1 over the sample space to check of circles such as circumference, area, radius probabilities and diameter and generalise these to solve 4. Algebra problems involving circumference and area 4. Representing probability Generalise the distributive law to expansion 4. Congruence and factorisation of simple algebraic Use Venn diagrams or two-way tables to expressions and use the four operations with illustrate 'and', 'or', 'given' and 'not' criteria, Explain properties for congruence of triangles algebraic expressions and to calculate simple probabilities and apply these to investigate properties of quadrilaterals 5. Linear equations 5. Location Create, solve and interpret linear equations, including those using realistic contexts using Solve problems involving interpreting and algebraic and graphical techniques creating maps and plans using scales 6. Coordinates 6. Visualisation Plot graphs of linear functions and use these Create, interpret and use two-dimensional to find solutions of equations including using representations of three-dimensional objects, ICT including projections, isometric views and plans 7. Pythagoras Use Pythagoras theorem to solve simple problems involving right-angled triangles Achievement standard (Year 8) By the end of Year 8, students are able to use number, algebraic conventions and formulas and apply this understanding to problem solving with ratios and scale, percentage increase and decrease, perimeters and areas of triangles, quadrilaterals and circles and volumes of triangular prisms. Students readily connect tabular, graphical and algebraic representations of linear functions, and choose appropriate models for solving real life problems. They use numerical and graphical summaries of data, interpret these to draw conclusions and calculate probabilities. They apply mathematical reasoning including congruence and transformations to solve geometric problems and generalise formulas for the perimeter for triangles and rectangles to other quadrilaterals and develop understanding of the volumes of simple prisms. They are able to visualise three- dimensional objects from two-dimensional representations including isometric drawing and plans.ACARA Australian Curriculum Consultation Portal 5/03/2010 19
Draft Consultation version 1.0.1 Australian Curriculum Year 9 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Financial maths 1. Data investigation 1. Geometry Solve problems in financial mathematics Investigate problems requiring data-based Investigate properties of polygons and circles, including applications of simple and inquiry, collecting univariate and bivariate including lines and angles, forming compound interest including using ICT and data, including from secondary sources, and generalisations, explaining reasoning and judge reasonableness of results justify conclusions solving problems 2. Index laws 2. Sample space 2. Pythagoras Work fluently with index laws, in both numeric Calculate probabilities for two- and three-step Solve problems involving right angled and algebraic expressions and use scientific experiments with equally likely outcomes triangles using Pythagoras' theorem and notation, significant figures and which involve 'with replacement' and 'without trigonometric ratios and justify reasoning approximations in practical situations replacement' 3. Similarity 3. Linear and quadratic functions 3. Probability Apply transformations to triangles to explain Understand simplification techniques for Compare theoretical and experimental similarity and congruence, to establish linear and quadratic functions including probabilities for two- and three-step geometric properties collecting like terms, common factors, the experiments 4. Circles expansion of binomial products and simple 4. Sampling binomial factorisation Solve problems involving circumference and Evaluate non-random and random sampling area of circles and part circles, and the 4. Linear equations techniques surface area and volume of cylinders and Solve problems involving linear equations and composite solids inequalities and substitution into, and 5. Location rearrangement of formulas Interpret and create maps and plans, 5. Simultaneous equations including relative location, directions and Solve problems involving linear simultaneous bearings, and optimal paths equations, using algebraic and graphical 6. Visualisation techniques including using ICT Construct and identify elevations and cross- sections of three-dimensional objects, and explain reasoning Achievement standard (Year 9) By the end of Year 9, students are able to skilfully use number and algebra in problem-solving situations involving finance, right-angle triangle geometry and the calculation of area and volume. They have a sound understanding of linear functions and index laws, and are developing fluency with quadratic and simple non-linear functions. Students choose appropriate techniques, including sampling, in data-based inquiry and confidently represent sample spaces and use these to determine theoretical probabilities. They are confident users of maps and plans, and are developing the use of formal proofs in geometric contexts. They apply Pythagoras' theorem to the solution of right-angled triangles and have a basic understanding of trigonometric ratios.ACARA Australian Curriculum Consultation Portal 5/03/2010 20
Draft Consultation version 1.0.1 Australian Curriculum Year 10 Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Financial maths 1. Data representation 1. Geometry Solve problems in financial mathematics Construct and interpret box plots and Use formal mathematical language to classify including ones using recursive techniques, compare data sets represented by parallel shapes and objects including congruence and and extend these techniques to investigate box plots similarity growth and decay including using ICT 2. Data investigation 2. Trigonometry 2. Proportion Pose data-orientated questions, plan Work fluently with trigonometric ratios and Solve problems involving direct and inverse sampling, data collection and representation, solve problems requiring their use in right- proportion make and justify conclusions, report the angled triangles including direction and investigation and evaluate choices angles of elevation and depressions using the 3. Coordinate geometry three trigonometric ratios 3. Chance Understand and use graphical and analytical 3. Surface area and volume methods of finding distance, midpoint and Identify, whether two events of the sample gradient of an interval on a number plane space are independent or not, or mutually Solve problems involving surface area and exclusive, for one- and two-step experiments volume of pyramids, cones and spheres 4. Quadratic expressions with equally likely outcomes 4. Latitude and longitude Understand how to expand and factorise 4. Data interpretation quadratic expressions using a variety of Solve problems involving latitude, longitude, strategies Evaluate statistical reports in the media and and distances on the Earth's surface, using other places by linking claims to displays, great circles 5. Functions statistics and sampling Connect algebraic and graphical representations of functions and relations such as parabolas, circles and exponentials 6. Equations Solve non-linear equations algebraically and graphically and using technology Achievement standard (Year 10) By the end of Year 10, students are able to skilfully use number and algebra in problem-solving situations involving finance, proportion, trigonometry and the calculation of area, volume and distances on the Earth's surface. They readily interpret and connect algebraic and graphical representations of functions and use these to analyse and solve equations. Students choose appropriate numerical, technological and graphical techniques to interpret and compare data sets presented to them and confidently determine theoretical probabilities for one- and two-step experiments and understand the concept of independence. They readily interpret and construct geometric proofs involving the application of congruence and similarity. They routinely communicate solutions in appropriate formats and can judge the reasonableness of results and evaluate the strategies and techniques used.ACARA Australian Curriculum Consultation Portal 5/03/2010 21
Draft Consultation version 1.0.1 Australian Curriculum Year 10A Content descriptions Number and Algebra Statistics and Probability Measurement and Geometry 1. Surds 1. Bivariate data 1. Trigonometry Work fluently with operations with surds and Model linear relations in bivariate numerical Use the unit circle to graph trigonometric fractional indices and solve simple data sets using the least squares line of best functions and solve simple trigonometric exponential equations fit and interpret the result including using ICT equations 2. Recursion 2. Sine and cosine rule Apply recursive techniques to arithmetic Understand the sine and cosine rules and integer sequences, generalise the nth term apply these to solve problems involving non- and solve related problems right-angled triangles 3. Functions and relations Solve a wide range of quadratic equations and construct graphs of parabolas and circles Achievement standard (Year 10A) In addition to the Year 10 achievement standard, by the end of 10A students are able to reason mathematically in a wide range of contexts. Their understanding of the real number system is extended to irrational numbers including surds. They can use algebraic, including recursive, techniques to solve equations including quadratics and simple exponential equations. They can model linear relationships in bivariate data and are able to solve trigonometric equations and use trigonometric relationships to solve problems involving non-right-angled triangles.ACARA Australian Curriculum Consultation Portal 5/03/2010 22
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Essential Computer Math
9780070379909
ISBN:
0070379904
Pub Date: 1982 Publisher: McGraw-Hill
Summary: Master essential computer mathematics with Schaum'sthe high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use Scha...um's!If you don't have a lot of time but want to excel in class, this book helps you: Brush up before tests Find answers fast Study quickly and more effectively Get the big picture without spending hours poring over lengthy textbooksSchaum's Outlines give you the information teachers expect you to know in a handy and succinct formatwithout overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's lets you study at your own pace and reminds you of all the important facts you need to rememberfast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams.Inside, you will find: Detailed problems with step-by-step solutions Clear, concise explanations of the binary system, computer codes, computer arithmetic, algorithms, and much more Help with truth tables, logic gates, vectors, and matrices A solved-problem approach that teaches you with hands-on help Exercises for improving your problem-solving skillsIf you want top grades and thorough understanding of essential computer mathematics, this powerful study tool is the best tutor you can have!Chapters include: Binary Number System Computer Codes Computer Arithmetic Logic, Truth Tables Algorithms, Flowcharts, Pseudocode Programs Sets and Relations Boolean Algebra, Logic Gates, Simplification of Logic Circuits Vectors, Matrices, Subscripted Variables Linear Equations Combinatorial Analysis Probability Statistics Random Variables Graphs, Directed Graphs, Machines
Lipschutz, Seymour is the author of Essential Computer Math, published 1982 under ISBN 9780070379909 and 0070379904. Three hundred twenty nine Essential Computer Math textbooks are available for sale on ValoreBooks.com, one hundred fifteen used from the cheapest price of $3.99, or buy new starting at $117037990070379904 BRAND NEW. We are a tested and proven company with over 900, 000 satisfied customers since 1997. Choose expedited shipping (if available) for much faster delivery. [more]
0070379904 BRAND NEW. We are a tested and proven company with over 900, 000 satisfied customers since 1997. Choose expedited shipping (if available) for much faster delivery. Delivery confirmation on all US orders.[less]
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Is there anything more beautiful than an A in Algebra? Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying resources with one goal in mind: giving students all the tools they need to achieve success. With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)-new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more! Note: This is the standalone book, if you want the book/access card and DVD order the ISBN below; 0321799070 / 9780321799074...
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Key Books 5-7 and Books 8-10 are available separately, as well as the Key to Algebra Reproducible Tests. book, is what makes this book the market leader.
Kelley Wingate's Algebra helps students in grades 5 and up master the skills necessary to succeed in algebra. Aligned to the Common Core State Standards, practice pages will be leveled in order to target each student's individual needs for support. The activities cover skills such as operations with real numbers, variables and equations, factoring, rational expressions, ratios and proportions, graphing, and radicals. This well-known series, Kelley Wingate, has been updated to align content to the Common Core State Standards. The 128-page books will provide a strong foundation of basic skills and will offer differentiated practice pages to make sure all students are well prepared to succeed in today's Common Core classroom. The books will include Common Core standards matrices, cut-apart...
LessThe seventh edition of Contemporary Abstract Algebra, by Joseph A. Gallian, Provides a solid introduction to the traditional topics in abstract algebra while conveying that it is a contemporary subject used daily by working mathematicians, computer scientist, and chemists. The text includes numerous theoretical and computational exercises, figures, and tables to teach you how to work out problems, as well as to write proofs. Additionally, the author provides biographies, poems, song Lyrics, historical notes, and much more to make reading the text an interesting, accessible and enjoyable experience. Contemporary Abstract Algebra will keep you engaged and gives you a great introduction to an important subject. Study Resources to Help you Succeed Student Solutions Manual This manual contains...
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Make math matter to students in grades 6 and up using Algebra: Daily Skill Builders! This 96-page book features two short, reproducible activities per page and includes enough lessons for an entire school year. It covers topics such as number patterns, word problems, equations, tables, graphs, linear relationships, variables, contextualized problems, properties, order of operations, and exponents. Activities become more challenging as students build upon what they have learned. The book is perfect for review and practice and supports NCTM and Common Core State Standards.
ALGEBRA 2 STUDENT WORKBOOK [Paperback]AGS Secondary (Author)Take students a step further in learning algebra Specially written for low-level learners,Algebra 2 covers several methods for solving quadratic equations, such as factoring, completing the square, and graphing. The text also introduces trigonometry and exponential functions—vital concepts for real world applications. Filled with full-color illustrations and examples throughout, Algebra 2 motivates students to learn.Overall, this high
Algebra 1/2 Home Study Kit includes the hardcover student text, softcover answer key and softcover test booklet. Containing 123 lessons, this text is the culmination of prealgebra mathematics, a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include Prime and Composite numbers; fractions & decimals; order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem and more. Utilizing an incremental approach to math, your students will learn in small doses at their own pace, increasing retention of knowledge and satisfaction!
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiarundersta nding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more...
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978-0-13-400037-4 / 0134000374
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
This book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. The organization of the text draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in its approach, it is written with an assumption that the reader may have computing facilities for two- and three-dimensional graphics and for doing symbolic algebra. The book contains many figures, and encourages the reader to viszualize with the aid of hand drawings and computers, and through expositions and exercises. It introduces geometry in three-dimensional space, together with Cylindrical and Spherical Co-ordinates, anticipating their later use in connection with the Chain Rule and change of variable in double and triple integrals. It also introduces matrix notation and the rudiments of linear algebra to facilitate exposition. It also provides approximately 1200 exercises, including drills, applications, proofs and "technologically active" projects.
Hardcover, ISBN 0134000374 Publisher: Prentice Hall College Div College Div, 1997 Used - Good, Usually ships within 1 - 2 business days, Only lightly used. Book has minimal wear to cover and binding. A few pages may have small creases and minimal underlining. Our books ship from the USA and delivery time is 2 to 3 weeks. Book Selection as BIG as Texas.
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Precalculus - With CD - 6th edition
Summary: David Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Sixth Edition, focuses on teaching mathematics by using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greate...show morer emphasis. Many sections now contain more examples ...show less
Radian Measure. Radian Measure and Geometry. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
10. SYSTEMS OF EQUATIONS.
11 The Conics in Polar Coordinates. Rotation of Axes.
12. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
Fair Pages have significant wear and cover is damaged. May have writing and highlighting throughout. All pages are intact. We ship daily Monday-Friday!
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Although not so well known today, Book 4 of Pappus' Collection is one of the most important and influential mathematical texts from antiquity. The mathematical vignettes form a portrait of mathematics during the Hellenistic "Golden Age", illustrating central problems - for example, squaring the circle; doubling the cube; and trisecting... more...
For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery
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Singapore Math Curriculum
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A Brief History of Singapore Math in the United States
The 1981 curriculum focused on basic content. This curriculum was revised in 1992 to make it a problem solving curriculum. The Primary Mathematics (2nd Edition) was based on the 1992 curriculum.
The Primary Mathematics (3rd Edition) series was based on a reduced syllabus in 1994. In 1999, Singapore's Ministry of Education decided to reduce the content in the curriculum up to 30% for most subjects. In 2008. Singapore Math Inc. published in the United States is the Primary Mathematics Standards Edition. This series was designed to meet all state standards in California; a state that has written standards based on the National Council of Teachers of Mathematics (NCTM) Focal Points. While this series will continue to be supported for a few years, it has been supplanted by…
Click below to find more information on each Singapore Math Edition. The 1981 curriculum focused on basic content. This curriculum was revised in 1992 to make it a problem solving curriculum. The Primary Mathematics (2nd Edition) was based on the 1992 curriculum. The Primary Mathematics (3rd Edition) series was based on a reduced syllabus in 1994. In 1999, Singapore's Ministry of Education decided to reduce the content in the curriculum up to 30% for most subjects.
Singapore Math in the United States published in the United States is the Primary Mathematics Standards Edition. This series was designed to meet all state standards in California; a state that has written standards based on the National Council of Teachers of Mathematics (NCTM) Focal Points.
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Very good seminar. Excellent introduction into Singapore Math. I learned about Singapore years ago but this was much more helpful. Thanks!Eddie Grant, 5th Grade Teacher, Smyrna, GA
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Mathematics
Next Steps
Mathematics: Course Outlines
Math: Course Outlines
The outlines listed on this page are general descriptions of courses offered by Lourdes. For specific information regarding this semester's courses, including textbooks and schedules, please consult the Course Syllabi page. All outlines are provided in PDF format.
MTH 097: Basic Mathematics
Involves practical arithmetic: decimals, fractions, ratios, percentages; operations on numbers; introduction to Algebra. Designed to develop skills of persons with limited background in mathematics. Prerequisite: placement test. Successful completion is a C* (2.0) or better. Grades are not calculated in the G.P.A.
MTH 132: Calculus for the Managerial Sciences
Deals with functions and the mathematics of finance, and concentrates on calculus techniques used to solve business and managerial related problems. Prerequisite: MTH 122 or equivalent placement test score.
MTH 225: Mathematics for Teachers of Young Children II
This course concentrates on concepts recommended by NCTM for preparation of teachers. Topics include geometry, measurement, probability and statistics. Prerequisite: MTH 110 or equivalent placement test score. Enrollment limited to students in the Department of Education.
MTH 242: Introduction to Mathematical Reasoning
Prepares students for the study of higher mathematics by exploring the techniques and fundamentals of proving theorems. The course will include elementary logic and set theory, a discussion of the real number system, and an introduction to the basic theorems of number theory. Prerequisite: MTH 136.
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Elementary Algebra
The Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of ...Show synopsisThe Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would doReviews of Elementary Algebra
Received the book in a timely manner. It was in good condition. I don't think this will happen every time, so don't expect this, but it turned out to be an instructor's manual, which I didn't ask for, but I'm glad I got - the answers are right next to the problems; no flipping to the back to check my work anymore
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with Mathematica®: An Introduction for an Amazon Gift Card of up to £18.50, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Book DescriptionMore About the Author
Product Description
Book Description
This practical, example-driven introduction is designed for Mathematica users, new and accomplished, who wish to learn the foundations of the Mathematica programming language in order to apply it to the task of solving concrete problems in science, engineering, economics and finance, computational linguistics, geoscience, bioinformatics and so on.
About the Author
Paul Wellin worked for Wolfram Research from the mid 1990s through 2011 directing the Mathematica training efforts with the Wolfram Education Group. He has taught mathematics at both public schools and at the university level for over 12 years. He has given talks, workshops and seminars around the world on the integration of technical computing and education and he has served on numerous government advisory panels on these issues. He is the author of several books on Mathematica.
I wish that this book had been available 3 years ago, when I started programming with Mathematica®. I was not then aware of the earlier edition, but in any case that edition related to Mathematica version 5, and versions 6 and 7 introduced many significant changes that made for compatibility problems with earlier code. Indeed this edition is slightly out of date because it covers Mathematica 8 and not the latest version 9.
However, as an introduction to the essentials of programming with Mathematica, it is excellent, and is particularly helpful in explaining the differences between Mathematica® and other languages. The author also introduces new topics using full notation and avoids the Mathematica shorthand that makes code much shorter but also much more difficult to comprehend. The differences between symbolic and numerical computing are made clear and the numerous worked examples and problems are especially relevant and useful.
I also have copies of Stephen Wolfram's "The MATHEMATICA ® Book", Version 5, and Heikki Ruskeepaa's "Mathematica Navigator", Third Edition. The former is now out of date, stopping at Mathematica version 5, and Paul Wellin is much more successful than Stephen Wolfram at explaining how to actually use Mathematica. "Mathematica Navigator" is a very good general reference and covers more Mathematica features, such as the data functions, but is basically written about Mathematica version 6, with addenda to cover version 7, and is not as good at explain the fundamentals of Mathematica programming.
None of these books provides a comprehensive reference to some very important features of Mathematica, and its own documentation is also deficient in these areas. Mathematica can import and export data from a very broad range of sources and in a wide range of formats, but actually processing imported data in a Mathematica notebook, or preparing data for export, must frequently be learned by trial and error. Similarly, of the more than 3000 functions in Mathematica, only the mathematical functions are explained in more than perfunctory detail, and then on a separate website, whilst general data functions, such as Country Data, Financial Data and Weather Data, have only rudimentary descriptions. These general references, descriptions and explanations may be outside the scope of an introduction to Mathematica programming, but there is an unfulfilled need for a set of books covering the broader aspects of Mathematica, and Paul Wellin has shown that he could be ideally qualified to satisfy that need.Read more ›
This book is quite nice and it was written in Mathematica itself, so this already provides an idea of how much one can do with Mathematica. Chapter 1 begins with a tour of some of the main capabilities using eye-catching examples (there are plenty of eye-catching examples throughout the text), which was exactly what I needed to get started. However, as I went deeper, I found that the book is mostly about the Mathematica language -- its structures, lists, rules, expressions, functions, etc. -- and less about "how to do math with Mathematica", which was perhaps what I was looking for.
Nevertheless, I kept reading and actually trying out many of the examples. The author uses Mac OS, but is sufficiently careful to point out differences to other OSes whenever appropriate (I used Mathematica both in Windows and Linux, the only issue that I found was that the sound routines in Section 10.3 do not work on Linux).
Despite the focus on "programming with Mathematica" rather than "doing math with Mathematica", after reading this book I feel quite comfortable with the tool and its language. For example, I can browse through the documentation and immediately understand the syntax of all Mathematica functions and how to use them in my code.
The rich set of examples throughout the book also helps in this respect, but in some examples it would be useful to have more detailed explanations. The author is absolutely proficient with Mathematica, but the text explanations could be made more precise, especially when the examples become relatively complex.
This means that using this book for self-study can be challenging. I can imagine that it would be much easier if I would be attending classes and a teacher would walk me through through some of these examples. From a teaching perspective, the book is a wonderful resource.
One final comment, at times I found myself wondering how to type some special symbols in Mathematica, could not find it in the symbol palettes, and had to go look it up on the Web. For example, an undirected edge in a graph is written as Esc+ue+Esc. The book does not always mention how to type these special inputs.
16 of 17 people found the following review helpful
5.0 out of 5 starsgreat introduction book on programming with mathematica7 April 2013
By XX - Published on Amazon.com
Format:Hardcover
This book is an updated version of the book "An Introduction to Programming with Mathematica®". The original book is already very good: nice and clear explaination, logical organization, etc. This book introduces the usage of several new functions in Mathematica 9.0 (such as Pick). Compared with the older version, there are two noticeable updates. One is regarding the examples. The author seems put lots of considerations in selecting the examples: the topics vary from computer science subject (such as random graph), numerical analysis, to data processing in biology (protein data, etc.). The other significant change is that patterns and rules are introduced immediately after the discussion of list, before functional programming. This seems a better choice than the older version, where rule programming is put after functional programming, considering that patterns and rules play such an important role in mathematica.
This 700+ page textbook from Cambridge is pricey, but thorough. It tells the student to also reference Mathematica's own excellent explanations which are easily accessible within the program itself, but to learn Mathematica through the excellent built in reference material is like trying to drink the ocean. This book adds structure to the learning process. Don't miss the answers to the practice problems. They can be downloaded for free from the book store under this book's title and author's name ( Working through these problems at the end of each chapter is clearly intended to be a large part of the learning process. They're not a snap so you need the answers PDF file to see tricks not covered in the chapter. This book uses Mathematica version 8.
4 of 4 people found the following review helpful
4.0 out of 5 starsAn excellent source of practical information for beginners of Mathematica!4 Jun 2013
By Hector I Amadeo - Published on Amazon.com
Format:Hardcover|Verified Purchase
The book starts you with all the pertinent information to get you started. Once you are familiar with the material, it provides practical application and example on how to use the built in functions. I recommend this textbook for those who are new and intermediate users of Mathematica.
3 of 3 people found the following review helpful
5.0 out of 5 starsAn excellent introduction14 May 2013
By doodler - Published on Amazon.com
Format:Hardcover|Verified Purchase
Just a wonderful introduction to Mathematica. Gives a very precise programming introduction as well as mathematical exposure to the core elements of the program.
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concepts of mathematics and computer science, this book is about the sequences of symbols that can be generated by simple models of computation called "finite automata". Suitable for graduate students or advanced undergraduates, it starts from elementary principles and develops the basic theory. The study then progresses to show how these ideas can be applied to solve problems in number theory and physics.
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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Algebra
--------
operations on sets, Arithmetic and Geometric sequences, complex numbers and how to transform between its different forms (Cartesian,Polar,Exponential,Trigonometric) and De Moivre theorem, mathematical induction and its applications(series,recursive,divisibility,matrices,derivative and inequality problems),Graph theory,matrices and its applications(solving equations,division and the other operations),number systems(decimal,binary,ternary,octal,hexadecimal) and the transformation from each one to the other and the operations on each system, Fourier series , how to calculate it and its applications in real life.
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In In this calculus learning exercise, student solve 6 multi-step problems involving volume, intervals, acceleration, and graphing. A graphing calculator will be necessary to complete the learning exercise.
Looking for an interractive presentation for your high schoolers dealing with calculus? Then this PowerPoint is for you! Problems that cover area, volume, and other calculus-related topics are presented. Students are led through the steps necessary to solve the problems, and are given instant feedback.
In this pre-calculus learning exercise, student solve 35 multiple choice problems and then place the answers in a Sudoku puzzle form. This learning exercise would be a great warm up or fun test review.
In this calculus worksheet, students solve functions using the derivatives. They calculate the volume where the graph is revolving around the x-axis, a line, the y-axis and where x=e. There are 28 questions.
In this calculus worksheet, students observe the graph the function and identify the interval as increasing or decreasing. They identify the critical points and perform integration. There are 4 questions.
Here is a high-level, interractive presentation on calculus for your high schoolers. Parametric equations, derivatives, functions, and the Pythagorean Theorem are all part of this fine PowerPoint. Additionally, two interesting photographs of Mark Twain's homes begin the slideshow.
Learners apply the Fundamental Theorem of Calculus. In this calculus instructional activity, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.
Students graph different functions and observe the slope of the tangent line. In this calculus lesson, students identify the slope and critical points on a graph. They use the TI calculator to provide a visual of the graph.
In this calculus practice exam, students select the best answer to 28 multiple choice questions. Questions cover information from the entire year of calculus. A suggested time limit of 55 minutes is included.
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History in Mathematics Education - 1 edition
Summary: This book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. Most of the leading specialists in the field have contributed to this ground-breaking book, whose topics include the integration of history in the classroom, its value in the training of teachers, historical support for particular subjects and for stude...show morents with diverse educational requirements, the use of original texts written by great mathematicians of the past, the epistemological backgrounds to choose for history, and non-standard media and other resources, from drama to the internet. Resulting from an international study on behalf of ICMI (the International Commission of Mathematics Instruction), the book draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. Together with its 300-item annotated bibliography of recent work in the field in eight languages, the book provides firm foundations for future developments. Focusing on such issues as the many different ways in which the history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource, and on the political process of spreading awareness of these benefits through curriculum design, the book will be of particular interest to teachers, mathematics educators, decision-makers, and concerned parents across the world101.63 +$3.99 s/h
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Limits, Limits Everywhere by David Applebaum
Book Description
A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and pi, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject.
A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
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Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. This volume gathers papers from internationally renowned mathematicians, many of whom have been Stein's students.
Author Biography - David Applebaum
David Applebaum obtained his PhD at the University of Nottingham in 1984. After postdoctoral appointments in Rome and Nottingham, he became a lecturer in mathematics at Nottingham Trent University (then Trent Polytechnic) in 1987 and was promoted to reader in 1994 and to a chair in 1998. He was Head of Department 1998-2001. He left Nottingham Trent for a chair in Sheffield in 2004 and served as Head of Department of Probability and Statistics there from 2007-10
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Web Codes
Course 2
Course 2 consists of a structured approach to a variety of topics such as ratios, percents, equations, inequalities, geometry, graphing and probability.
Test Taking Strategies provide a guide to problem solving approaches that are necessary for success on standardized tests. Checkpoint Quizzes assess student understanding after every few lessons. Daily Guided Problem Solving in the text is supported by the Guided Problem Solving worksheet expanding the problem, guiding the student through the problem solving process and providing extra practice.
The Manipulatives Kit allows students to explore concepts in a hands-on way using a variety of measurement, geometry, algebra, and probability tools. The kit is designed for a class of 30 students.
Designed for use with overhead projectors, this kit helps you demonstrate concepts in a using probability tools, including algebra tiles, tangrams, a geoboard with rubber bands, a spinner, and pattern blocks.
Prentice Hall Mathematics 2008 - Course 1 - Algebra Readiness Tests
Online at PHSchool.com Personlized intervention for each student—
Assess—Students take Diagnostic Tests or Benchmark Tests online.
Diagnose—Based on assessment results, each student automatically recieves an assignment for any skills that have not been mastered.
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Key Features in Maple T.A.
Full Support for Mathematics
Maple T.A. is designed especially for courses involving mathematics, and so it is your best choice for your mathematics, engineering, science, and other courses that use math. Maple T.A. lets you ask the questions you want, the way you want, and then grades the responses just like you would.
Natural math notation is used in both the question text and student response.
Free-response questions are graded for mathematical equivalence. Where appropriate, responses do not need to be identical to the solution to be graded as correct; they just need to be equivalent. For example, if the correct answer is , Maple T.A. will also accept , and if the answer is , Maple T.A. will also accept .
Open-ended questions can have infinitely many answers. With Maple T.A. you can ask questions for which you cannot know in advance how the student will respond, and Maple T.A. can still grade their responses automatically. You can ask questions such as "Give an example of a function that has a maximum at x = 0," "List two composite numbers that have no factors in common," or "Give an example of an invertible matrix."
Adaptive questions provide students another chance when they give an incorrect response. Knowing the student is having trouble, the question can be adapted to walk the student through the problem one step at a time, allow students to try a simpler version of the same question before retrying the original, or whatever the instructor feels is appropriate.
Sophisticated visualization tools let you easily include plots in your questions by taking advantage of the over one hundred 2-D and 3-D plot types and customization options available from Maple. When appropriate, you can even allow students to see a plot of their response before they submit their work.
A wide variety of mathematical and scientific question types support free response questions, questions that require a numeric answer to fall within given margin of error, chemical formula questions, questions that handle units, multi-part questions, and more.
Flexible partial grading lets you give partial credit for mathematical responses that are not completely correct, and you can control how generous or rigorous the grading will be.
Extensive mathematical knowledge coming from Maple means Maple T.A. can automatically grade questions from virtually any area of mathematics.
Easy Content Creation
Maple T.A. is the system of choice for those who want full control over their question content. Whether you want to customize the many available questions or write your own, Maple T.A. provides the most comprehensive, easiest-to-use authoring tools available for mathematics-based content.
Step-by-step Question Designer walks you through the creation of a wide variety of questions.
Easy-to-use editor lets you add formatting, images, plots, and special characters to questions.
International language support allows questions to be written in any language.
Hints and feedback for each question lets you provide additional guidance to your students.
Thousands of built-in math commands provide coverage of virtually all areas of mathematics, so you can create questions for any course, at any level.
Powerful algorithm design tools make it easy to create sophisticated question templates which are used to generate hundreds of instances of a single question. You can vary more than one value in your question, set conditions on those variables, and even take advantage of sophisticated randomization tools found in Maple for generating mathematical objects, such as matrices, polynomials, and prime numbers.
The Maple T.A. Cloud enables easy content sharing, so you can access questions created by other Maple T.A. users and share your own content with the community from within Maple T.A. Searching for and using publicly shared questions is as easy as working with content you wrote yourself. Questions from the Maple T.A. Cloud can be copied into your own class, used immediately, or modified to better suit your needs.
Thousands of questions, many of which have been extensively field tested, are freely available for you to use and customize for your own classes. Topics include calculus, precalculus, physics, chemistry, engineering, differential equations, statistics, and more.
Everything else you want in a testing and assessment system
Of course, Maple T.A. has all the features you would expect in any testing and assessment system, in addition to all the features that make it ideal for math-based testing, including lots of different question types, control over numerous aspects of the assignments, and a gradebook that is second to none in terms of its flexibility and analytical tools.
Over 15 question types, including mathematical free response, multiple choice, fill-in-the-blank, matching, clickable image,essay, and numeric with margins of error, cover all your needs for both technical and non-technical subjects.
The Maple T.A. Proctored Browser, an optional testing environment, requires students to stay inside Maple T.A. until the test or assignment is completed, so they cannot access other web sites or programs.
Flexible assignment properties determine start and end times, how much feedback the student gets during the assignment, passing score, number of attempts, restrictions on where they can take the assignment, and more.
An intuitive assignment editor makes it easy to construct assignments and set assignment properties.
flexible gradebook provides all the tools you need to track and analyze your students' progress. It captures student results for individual assignments and questions within an assignment and allows you to set up grading schemes that include work done outside of Maple T.A., import and export grades, and more. Its unsurpassed statistical analysis tools provide in-depth insight of the results from the student, assignment, and question point of view, so you can get the information you want in the form you need.
Administration
Maple T.A. can be seamlessly integrated into all your institutions' systems and routines, ensuring a smooth experience for students, instructors, and administrators alike.
Content can easily be shared between instructors, making multi-section courses simple to administer.
Single sign-on for all classes provides a convenient starting point for students and instructors.
Maple T.A. can be incorporated into virtually any course management system, making for a seamless experience for instructors and students. Learn more about integrating Maple T.A. with course management systems.
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You are here
Mathematical Analysis: A Concise Introduction
Publisher:
John Wiley
Number of Pages:
562
Price:
95.00
ISBN:
9780470107966
This is the Greatest Hits version of mathematical analysis. It covers all the high points of real and abstract analysis, but doesn't go into depth on anything. The treatment is rigorous and error-free. Roughly half the book deals with real analysis theorems, and half with abstract analysis and function spaces (including multivariable calculus). There is also a short section on physical applications, dealing mostly with differential equations.
The book skimps on worked examples. Most of the illustrative examples are in the exercises, often with hints. Many traditional analysis topics appear only in the exercises, for example, Stirling's formula for n!, Riemann-Stieltjes integrals, Lagrange multipliers, and the Stone-Weierstrass Theorem,
It may seem peculiar to subtitle a 562-page book "concise", but that is an accurate summary of the approach. The book manages to cover an enormous amount of material in those pages.
As I was reading I was continually puzzling over where the book would fit in the curriculum. The author used the draft in a two-quarter course at his university, but it must have been a struggle to get through all the material in that time. In some ways the book looks like a text for an introduction to proofs course, but it also includes a number of topics that would normally be in graduate courses, and everything in between. Is this "The Only Analysis Book You'll Ever Need"? Probably not — there's no complex analysis, for example, and Fourier analysis is only touched on briefly.
My big gripe with this book is that it is uninspiring. It never shows you why people get excited about analysis. The history of real analysis is largely a history of pathological cases and counterexamples, and how analysts prevailed over these difficulties to create a beautiful theory. This book shows you the theory but not the beauty.
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.
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Problem Solving Through Recreational Mathematics [NOOK Book] Each chapter contains ...
More About
This Book
Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers' appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition.
Related Subjects
Table of Contents
Preface; To the Reader; Acknowledgments
1. Following the Clues; Sample problems; Which chart or Diagram to Choose; Presenting a Solution; Some Steps in Problem Solving;
Tree Diagrams; The Multiplication Principle; Simplification; The Chapter in Retrospect; Exercises
2. Solve It With Logic; Sample Problems; Statements; Variables and Connectives; Negation; "And"—Conjunction; "Or"—Disjunction; Conditional and Biconditional Statements;
Drawing Conclusions; Compound Statements; Logical Implication and Equivalence; Arguments and Validity; The Chapter in Retrospect; Exercises
3. From Words to Equations: Algebraic Recreations; Sample Problems; Introducing Variables; The Chapter in Retrospect; Exercises
4. Solve It With Integers, Some Topics from Number Theory; Sample Problems; Diophantine Equations; Divisibility; Prime Numbers; The Infinitude of Primes; The Sieve of Eratosthenes; More About Primes;
Linear Diophantine Equations; Division With Remainders; Congruence; Casting Out Nines; Solving Linear Congruences; Solving Linear Diophantine Equations; The Chapter in Retrospect; Exercises
5. More About Numbers: Bases and Cryptarithmetic; Sample Problems; Positional Notation; Changing Bases; Addition and Multiplication in Other Bases; Cryptarithmetic; The Chapter in Retrospect; Exercises
6. Solve It With Networks: An Introduction to Graph Theory; Sample Problems; Graphs; Eulerian Paths and Circuits; Odd and Even Vertices; More Than Two Odd Vertices;
Directed Graphs; Hamiltonian Circuits; The Knight's Tour; Other Applications; Coloring Graphs and Maps; The Chapter in Retrospect; Exercises
7. Games of Strategy for Two Players; Sample problems; Chance-Free Decisionmaking; Games of Perfect Information; Finiteness; The Existence of Winning Strategies; Position--State of the Game;
The State Diagram of a Game; How Do We Find a Winning Strategy?; Finding a Winning Strategy by Working Backward; Finding Winning Strategies by Simplifying a Game;
Finding Winning Strategies With a Frontal Assault; How Many Possibilities Need Be Considered?;
Symmetry as a Limiting Factor; Déjà Vu—We've Seen it Before; The Game of Nim; Pairing Strategies; Variations of a Game; The Chapter in Retrospect; Exercises
8. Solitaire Games and Puzzles; Sample Problems; The Tower of Brahma; Dissection Problems; Polyominoes; Soma; Peg Solitaire; The Fifteen Puzzle; Even and Odd Permutations;
Coloring and the 15 Puzzle--A Second Approach; Colored Cubes; Colored Cubes--A Second Approach; The Chapter in Retrospect; Exercises
9. Potpourri; Decimation; Coin Weighing; Shunting; Syllogisms; Grab Bag; The Book in Retrospect
Appendix A. Some Basic Algebraic Techniques
Appendix B. Mathematical Induction
Appendix C. Probability
Bibliography; Hints and Solutions; Answers to Selected Problems 26, 2005
Excellent introduction to a variety of math methods
This book has opened up so many doors for me. Each section gradually works its way through a topic, giving a variety of problems to explore the ideas. Lots of solved or answered problems to help with the concepts. Excellent introduction to number theory, game theory, logic, and more. All discussed in an easy manner that disarms any math phobia. Thoroughly enjoyable.
1 out of 1 people found this review helpful.
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In an introductory trignometry course, there are many options for introducing trigonometric functions:
As ratios of sides of right triangles
As coordinates (or ratios of coordinates) of intersections of the unit circle with rays from the origin
As graphs that are periodic (and wavelike in the sin/cos case)
I was taught #1 first in high school, and then graphs. I saw #2 in college.
I feel that #1 is the traditional secondary-education method of introducing trigonometric functions, which has the benefit of coming a year or two after Euclidean geometry in the United States.
I feel that #2 is traditional in more rigorous textbooks used in University level courses, where radians are used.
Method #3 has the advantage that many students benefit from graphing calculators and visualize a function based on its graph.
Which of these three methods (or another unmentioned method like power series) would be best to introduce a college freshman with no math past algebra to trigonemetric functions with the goal of eventually covering the other two methods?
1 Answer
1
Physics approach (recommended, if the students have physics background or are simultaneously educated in the relevant physics):
Introduce the operations as the coordinates of a point ($\sin$ and $\cos$) resp. slope of the lines ($\tan$ and $\cot$) moving in a uniform motion along a circle of radius 1. Best example: Earth moves (nearly) uniformly along a (near) circle of radius 1 (AU). Give them other examples as well (car going in a curve, clock hand going around the clock).
Reason: Circular motions usually have more real life connection to the students than ratios of sides of triangles.
Afterwards, introduce the functions via harmonic mechanical oszillations. That way, you keep to the context of motions.
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I'm having some serious troubles with Calculus 3 (Multivariable Calc).
My grades in my previous math classes were high C's, and I just barely missed getting a B in Diff EQ. I've completely hit a wall with Calc 3. To me, it's all just alphabet soup.
One thing that complicates matters is that I am an "older" student with a 50-60hr/week job and a family. I could probably put 100 adderall-fueled hours a week into this class, and probably still not pass.
Now, I'm sure some will say "you've got to put the time in to pass". I know that, however, I just don't have the time, or stamina to just brute-force this class. I also can't risk losing my job over having my calc book out at work.
Where things fall apart for me in this class are tests. I score in the B range on homework and project assignments. During tests, the relevant formulas just fall apart in my head. No, we aren't allowed a note sheet.
The professor provides practice exams, and I can work through those with similar results as homework, but as stated above, when it comes to the actual test, everything falls apart.
Any advice/strategies/tips/hacks would be appreciated. No, using a TI-89 isn't an option.
I would suspect that the downvotes are more a consequence of where you posted this, as opposed to where it probably fits better - in /r/learnmath or /r/cheatatmathhomework . Reddit is a finnicky machine, some days are particularly downvote heavy.
Anyway, if you're doing well on the homework, the problem could be that you just aren't doing enough problems to be able to regurgitate the information quickly on an exam. For that I'd recommend doing some odd-numbered exercises in your book (the ones with solutions in the back) beyond your assigned load. It sucks staying up a little later or waking up a little earlier to accomplish it, but math isn't a spectator sport and really requires learning by doing.
Also, when learning new concepts, I highly recommend you really think about each and every step and why it all makes sense. If something isn't clear, you should think about it and ask for help until it is clear to you. To aid in clarification, I also recommend you check out other sources, like Paul's Online Math Notes. Sometimes different wording can make all the difference.
One thing that I didn't realize until after I took Calc 3 (multivariate calculus, right?) is that you're really doing calculus on a vectorspace.
Instead of thinking of f(x, y) as "a function of two reals", think of it as "a function of one vector in R2".
You can ignore direction derivatives and instead use direction derivatives. These (to me) seem more obvious. You define:
df/dv = lim h -> 0 of (f(x + hv) - f(x)) / h
Where v is the direction vector (usually a unit vector) respect to which you are taking the derivative.
Note now that the partial derivative with respect to x is just the direction derivative with v = (1, 0) and the partial derivative with respect to y is the directional derivative with v = (0, 1).
Along the same lines as above, whenever you are studying a new technique, keep in mind the domain and codomain of the operations and functions you're learning about. It helps!
In calc 1, almost all the functions you talk about in class are R -> R (that is, they take a real, and they return a real).
In calc 1, the derivative is an operation that acts on functions of type R -> R and returns a function of type R -> R. Put it all together and you get that the derivative is of type (R -> R) -> R -> R.
The anti-derivative is a bit funny (that +C comes from the fact that the anti-derivative is a relation, not an single-valued operation). But pretending it is, it's also (R -> R) -> R -> R.
In multivariate calculus, you have to start dealing with more complicated spaces. A scalar function of two variables is a fancy way of saying R2 -> R. An example of a scalar function is f(x, y) = x2 + y2.
If you haven't seen that, R2 just means an ordered pair of real numbers. You can add them component-wise, meaning (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2). You can also multiply them by scalars: a (x, y) = (ax, ay).
You can also picture the graph of these things. Instead of a 2-dimensional graph with an x-axis and a y-axis, you have a 3-dimensional graph: the x- and y- axes tell you what the input is, and the z-axis tells you what the value at that (x, y) value is. A handy way of thinking about scalar graphs is "how tall a mountain is at this point on a map".
The (directional) derivative on a scalar function takes a scalar function as input (R2 -> R), a direction v that the derivative respects (R2), and it returns another scalar function (R2 -> R).
There are other kinds of functions. You have parametric functions which take a number and return a point in 2d space: R -> R2. There are vectorfields, which take vectors to vectors: R2 -> R2.
I had troubles in multivariate for time commitment reasons also. Looking back, the reason I was able to get through the class was because of my friends. They were able to help me out with concepts and problems I got stuck on; sometimes I was able to help them.
Study with friends, look for resources outside the classroom. It's the same material regardless of who teaches it. I'm sure you could find YouTube videos that explain things in other ways which may appeal to your mental wiring a bit better.
Regarding test-taking: Make a note card with the equations. Sometimes professors allow the on the exam, usually not. Even if you cannot use a note card, making one forces you to find the meat-and-potatoes equations and processes. Don't just copy down the variables and steps though... Take the time to understand the equations, look for geometric interpretations of things, try to attach some sort of meaning to the mess of equations. Try to find where the complicated problems break down into simpler problems from differential and integral calculus. Try to understand what it MEANS to have a vector equation, etc.
I find drawing helps, but I'm not certain if you're already doing that for your stuff. Multivariate calculus is just multidimensional shape drawing in my head. When you draw what you think the spaces should look like, missing pieces become apparent. This may cause difficulty for N>3 (but it shouldn't).
A vector equation means that I'm changing this many in that direction, this many in that other direction. 2D is like hills and valleys for differentiable things, 3d is like balloons and cubes and such.
Are you taking only 1-2 courses/semester? If not, and even if you are, I think one of the best advice I could give you is to cut down on job hours. That would help tremendously, not only for additional hours in the week but being less fatigued and stressed will help you understand the material better. Otherwise it may be wise to give up on school. University in a major that requires that type of technical mathematical understanding simply is not easy enough to do with a full time+ job.
How much time are you putting in the class? Putting time into it isn't about "brute forcing" it, it is about understanding the material. For an average university class in the first year that is about 6 hours a week outside of lecture, for multivariable calc it may be 9-12.
I'm sure the folks at /r/learnmath will be more than willing to help. Give khan academy a shot as well. Another great resource for math is PatrickJMT.
I'm in 9 cr/hrs this semester. Cutting down on job hours isn't an option. No better job prospects without a 4yr/degree, and this is the last math class I need to graduate. (I'm in my last scheduled semester).
112 credits in towards a 4 year degree, so "quitting" is kind of a bullshit suggestion, no offense.
As for /r/learnmath , and khan academy, I'll have to take a look at them.
I understand there's no "easy" mode for math, but for some reason this material just isn't sticking. With math, you either get it, or you don't.
Calc1 and Calc2 just seemed to flow. DiffEQ was work, but the class was mostly practical application, so again it stuck.
No worries. Because of my non-traditional status, I've had to jumble up the courses a bit to fit them into my work schedule. The courses for my specialization only required Calc1/2 and Physics 1/2. DiffEQ and Calc3 are required though for the degree.
I certainly COULD take it by itself, but I'd kind of like to graduate with a 4 year degree in less than ten years.
Understand why things work and be able to put them together yourself. One way to check this is to see if you know the material well enough to explain it to someone else (and have them understand it). The parts you can't explain are the parts you probably need to work on.
I am currently taking Calc. 3 myself and am an older student. About half of my class (myself included) have taken Linear Algebra and I have found that the basic concepts learned in that class has made it a lot easier to understand some of the more complex concepts. I'm not sure if you've taken a linear algebra class but some of the basic lessons have really helped me with multi-variable calc.
When you do the homework and practice exams, are you constantly referring to formulas or the answers? If you are you need to stop and try to reproduce exam conditions as much as possible.
Line equations are often made easier by finding a good parametrisation. I like to do this by imagining a point that moves through the plane with a certain velocity, tracing out the line/contour. The parametrisation is simply the function that describes the position of the point as a function of time.
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A comprehensive review of trigonometry, this book covers topics like the inverses, trigonometric identities, trigonometric ratios, the law of sine, and the law of cosine. The book contains 487... More > questions that are convenient to practice. Each chapter has an explanation, practice questions, and answer keys. The content is high qualityA calculus companion book for Calculus I, II and III (3D Vector Calculus). Addressed to Science/Premed majors, not math majors. VERY unusual for its coverage of Calc III. Several chapters are... More > designed to work also as a Liberal Arts overview of calculus, although in general the book is more technical and practical than philosophical.< Less
By enrolling in this self-study course, you have demonstrated a desire to improve yourself and the Navy. Remember, however, this self-study course is only one part of the total Navy training program.... More > Practical experience, schools, selected reading, and your desire to succeed are also necessary to successfully round out a fully meaningful training program. COURSE OVERVIEW: The objective of this course is to enable the student to: a. Apply logarithms to the solution of problems encountered in mathematics and the sciences. b. Apply trigonometric techniques as tools in the analysis of mathematical, physical, and scientific problems. THE COURSE: This self-study course is organized into subject matter areas, each containing learning objectives to help you determine what you should learn along with text and illustrations to help you understand the information. The subject matter reflects day-to-day requirements and experiences of personnel in the rating or skill area.< Less
Students who need practice performing subtraction can use this short worksheet that provides immediate feedback as it is self-checking. While having fun decoding a secret message (and getting... More > immediate, satisfying feedback) young students will complete fifteen subtraction problems. Similar PUZZLE MATH worksheets and books on subtraction and later math topics are available at including, "PUZZLE MATH: Subtracting a Single Digit", "PUZZLE MATH: Adding, Subtracting, Multiplying, and Dividing Fractions", "PUZZLE MATH: Trigonometry and Logarithms", and "PUZZLE MATH: Mixed Derivatives".< Less
McCaulay's Practice Exams for the ACT* Mathematics Test contains four complete 60-question, 60-minute sample tests for a total of 240 practice questions with answers and explanations designed to... More > measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade. The math content covered includes 23% Pre-Algebra, 17% Elementary Algebra, 15% Intermediate Algebra, 15% Coordinate Geometry, 23% Plane Geometry, and 7% Trigonometry. The questions on each exam are ordered by level of difficulty, from basic math problems to very challenging problems where one must plan an approach to solve them.< Less
This worksheet provides immediate feedback for students as it is self-checking. It is fun and satisfying for students because the answers correspond to letters that decode a secret message. First... More > it provides clear examples of evaluating exponential expressions with negative, fractional, and negative fractional exponents. It also has clear examples of solving equations with these three types of exponents as well. Then it gives students plentiful opportunities to practice these skills. The variables in most of the equations are exponents. You may also be interested in "PUZZLE MATH: Mixed Derivatives" and "PUZZLE MATH: Trigonometry and Logarithms".< Less
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What does e + π mean and how can we evaluate it? What is the difference in the meaning of the equals sign between x2 −1 = 0, x2 −1 = (x−1)(x+1), (x2 −1)/(x−1) = x+1 and √x2 = x? What does it mean for a line to be straight? Are there lines that are not straight? In Math 499 we will be addressing these questions and more!
In this class we will explore the foundations of mathematics and how we acquire and process mathematical knowledge. We will revisit K-12 mathematics from the point of view of a mathematician. We will explore the roles of metaphors, models, and definitions. We will discuss the use of symbols and see that even in mathematics their meanings are often contextual. We will compare and contrast proofs and convincing arguments and think about the roles they play in developing and understanding mathematics. We will discuss the relationship between mathematics and our physical world and how we use mathematics to understand the physical world. We will consider various algorithms common in K- 12 mathematics and discuss why and how they work. We also will read and discuss the literature on how K-12 mathematics is taught and how we learn and process that knowledge. Throughout the semester, you will also the opportunity to observe and participate in classes at AUGUSTUS HAWKINS High School. This is a new school with a modern curriculum implementing an initiative called the Algebra Project.
This class has no prerequisites. In particular, it is not necessary to have taken any college level math classes; you are only expected to know how to count (albeit fairly well!). However, students must be willing to engage with the material at a mathematically sophisticated level. There will be very little lecturing. There will be a lot of discussion, group work, and both oral and written presentations. This class will be valuable for math majors, anyone with an interest in teaching mathematics, and sociology and psychology majors interested in the science of learning.
Tired of trying to translate your research experiences into a CV? Bring your laptop with your current CV or résumé. USC SACNAS Chapter will provide best practices and tips, then graduate students and USC staff will help you write it! This is a working workshop!
Sponsored by the USC SACNAS Chapter, this workshop features a panel of USC researchers explaining the importance of research in society and sharing their paths into the sciences. This is the first of a series of professional development workshops called Careers in Research designed to expose students to research.
SACNAS, the Society for the Advancement of Chicanos and Native Americans in Science, is an inclusive organization for all people and all disciplines dedicated to promoting academic excellence and mentoring students to advanced degrees in STEM fields. The goal of the USC SACNAS Chapter is to create a community at USC for all students in all disciplines interested in research Dornsife Environmental Studies Program Catalina Sustainability Semester is a situated learning experience for students that are majoring and/or minoring in either environmental studies or biology. Recommended preparation includes completion of ENST 100 or BISC 120L. Students will learn about coastal ecology and management through scientific diving, laboratory and field studies, and personal interaction with marine managers and scientists, while simultaneously gaining a better understanding and appreciation for the Southern California coastal environment.
Students enrolled in the Catalina Sustainability Semester will live and study at the USC Wrigley Marine Science Center for the entire semester (weekend transportation to the mainland is generally available). Rates for room and board are comparable to those on the University Park Campus. Courses are offered in a block format in which a single class meets on a daily basis (i.e., Monday through Friday, although participation in some weekend activities may be required). Each course will run for approximately four weeks,after which another class will take its place (four courses total; see below for details).
Course participants are expected to become scientific diver certified in accordance with the standards of the American Academy of Underwater Sciences (AAUS). As part of this training, the USC Dive Safety Officer or his designee will require each student to submita completed medical history and dive physical examination. Students will be assessed for water safety and ability to perform ecosystem measurements underwater
3 paid URAP internships: Seeking 3 talented undergrads (biology/pre-med, math/engineering, and computer science/engineering) for a multidisciplinary cancer simulation team. The team will work to make powerful 3-D computer models of cancer user friendly enough for diverse research teams, while testing and refining simulations of invasive breast cancer, stem cell biology, and chemotherapy. Publication and indepdendent study opportunities available. Applications due May 10, interviews May 13-17, and project to run summer 2013-spring 2014. See details in the attached flyer or at MathCancer.org, and apply as instructed to [email protected].
Requirements: Should be a junior or advanced sophomore with a 3.5+ GPA. One position in biology, pre-med or related. One position in math or engineering or related. One position in computer science or engineering or related. Same flyer for all 3 positions
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Biological Sciences
Biology: One Equation at a Time (Full)
John Berges, Associate Professor
Course: BIO SCI 194, SEM 001
Class Number: 52257
Credits: 3 NS
Time: R 3:00 - 4:50 PM
Place: LAP 258
Course Description:
Biology has been described as "the ideal major for the scientifically-inclined but mathematically-challenged", but paradoxically, many of the most exciting recent discoveries in biology have relied on application of mathematical techniques. This seminar is intended to develop mathematical literacy among biology students, but also to introduce students of more mathematically-oriented sciences to the important applications of mathematics in biological sciences,
ranging from medicine to marine biology.
Work Involved:
The seminar explores critical biological questions using relatively simple equations (e.g. why do smaller organisms often lack circulatory systems? how can the effectiveness of drugs be improved?, why is predicting climate change so difficult?). Seminars involve interactive problem-solving and discussion, with some use of computers and a weekly online discussion/tutorial session. Only basic mathematical skills and biological background are assumed.
Goals of the seminar include: developing an appreciation of the critical importance of mathematics in all areas of biology, improving understanding of the application of specific mathematical approaches in biology, increasing confidence in quantitative problem-solving skills.
About the Instructor:
John Bergesis a Professor in the Department of Biological Sciences and an affliliate in the School of Freshwater Sciences.He holds degrees in Marine Biology and Oceanography and has studied marine and freshwater ecosystems ranging from the Canadian High Arctic to the Great Barrier Reef in Australia.In Canada, N. Ireland and the U.S., he has tried to convince biology students that mathematics can be fun; his ten-year old son and his cat remain skeptical. John has mixed mathematical abilities: he does his own taxes and has memorized many biologically-important mathematical constants, but struggles to program his MP3 player and has trouble remembering his cell phone number.
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Senior High Math League
Rules for Senior High Math League
1. Each school may enter a team of one to four
eligible students in each of five groups. (Those schools
which only offer Algebra II and Geometry in alternate
years may still enter teams for the group which includes
the subject not currently being taught. In this case,
the team members must have been enrolled in the course
the last year it was taught.) See the
TOPICS page for a more detailed list of topics covered
and eligibility.
2. One or two students from each of the five
teams will work each of two sets of problems, Set A
and Set B. No more than two students per team will work
on any given set. Twenty minutes will be allowed for
each set, with a short break between each set. Each
set of problems will be worth 20 points.
3. Two group competitions will take place after
completion of both sets of problems. A four member Bonus
Relay and a three member group Bonus Question. These
competitions will begin at the same time.
A. Four Member Bonus Relay: Each four member
relay team will submit one solution to the bonus relay.
The relay will have a maximum value of 7 points. The
score will be added to the total school score. Each
school may enter one team for the relay. See Bonus
Relay page.
B. Three Member Group Bonus Question: Each
group of three members will work together on a bonus
question. There will be a ten minute time limit after
which each team will submit one answer. The bonus
question is worth up to 5 points. The score will be
added to the total school score. Each school may enter
one team for the bonus question.
4. Calculators are permitted (in fact encouraged)
in all tests and bonuses.
5. Two complete sets of awards will be presented:
one for the 1A/2A schools, another for the 3A/4A schools.
In each of the five subject groups, a trophy will
be awarded to the school with the highest total points.
Certificates for 2nd, 3rd, 4th, and 5th place schools
in each subject group will also be given. In addition,
trophies will be given for 1st, 2nd, and 3rd places
in overall point totals, as well as certificates for
4th and 5th place in overall point totals.
Procedures for Breaking Ties
I) Breaking any ties within a particular
group competition:
The Bonus question will be used by first comparing
the number of points received on the question, then
by comparing the finish number for those teams who
have tied.
II) Breaking any ties within the Grand Prize
division.
The Bonus Relay question will be used by comparing
the number received on the Relay, then by counting
the number of parts the team has gotten correct, and
finally by taking the order of finish on the Relay.
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MERLOT Search - category=2526&sort.property=overallRating
A search of MERLOT materialsCopyright 1997-2014 MERLOT. All rights reserved.Fri, 25 Jul 2014 02:21:58 PDTFri, 25 Jul 2014 02:21:58 PDTMERLOT Search - category=2526&sort.property=overallRating
4434Population Modeling Applet
In this applet, the user applies Euler's Method to modeling population growth using the Malthus exponential model and the Verhulst constrained growth model. After finding the Euler solution, the user can check the solution with the Adaptive Euler Approximation or with a slope field. Also, the user can enter an exact solution obtained from separating variables (or whatever) and again check the Euler solution graphically.Math Warehouse
This site has has interactive explanations and simulations of math from alegrbra to trigonometry. Just click the "interactive" tab on the top left menu and you can choose different simulations. It includes, the complete definition of parabolas, reaching beyond the ability to graph into the realm of why the graph appears as it does. It also has vivid descriptions of angles including circle angles for geometry. It also has calculators for principal nth roots, gdc, matrices, and prime factorization. It's definitely worth checking out. Quote from site: "A parabola is actually a locus of a point and a line. The point is called the focus and the line the directrix. That means that all points on a parabola are equidistant from the focus and the directrix. To change the equation and the graph of the interactive parabola below just click and drag either the point A, which is the focus, or point B, which controls the directrix." This is an interactive site that allows people to change the graph to understand why directrix and focus dictate parabolic graphs. Cyberkidz educational games
Cyberkidz is an educational platform for boys and girls in the age of 4 till 12 years. By playing the educational games, children will practice subjects they learn in elementary school (Preschool, Kindergarten, Grades 1-5). of Planet Earth
More than a hundred scientific societies, universities, research institutes, and organizations all over the world have banded together to dedicate 2013 as a special year for the Mathematics of Planet Earth.Our planet is the setting for dynamic processes of all sorts, including the geophysical processes in the mantle, the continents, and the oceans, the atmospheric processes that determine our weather and climates, the biological processes involving living species and their interactions, and the human processes of finance, agriculture, water, transportation, and energy. The challenges facing our planet and our civilization are multidisciplinary and multifaceted, and the mathematical sciences play a central role in the scientific effort to understand and to deal with these challenges.Matlab-based Numerical Methods in Engineering course
This web page shows links to lectures for a course on Numerical Methods in Engineering taught by the author in the Spring Semester of 2009. Click on the lecture links for class notes, Matlab scripts and functions, and assignments. Subjects covered: vectors and matrices in Matlab, graphics in Matlab, programming, numerical linear algebra, solution to equations, numerical integration, data fitting, and ordinary differential equations. Measuring Biodiversity across North America
Through this series on measuring biodiversity students will conduct investigations based on their own questioning, they will develop a methodology, collect and analyze data, test hypotheses, and communicate results. Each example given is a model for analysis with step-by-step procedures for investigating categories of questions on biodiversity and the inherent value of the different landscapes of North America.Goals: As a result of completing an investigation into the biodiversity of North American Mammals, all students should develop an understanding of the following. The concept of biodiversity, and ways to measure the diversity of organisms The role of taxonomy in assessing biodiversity Associations between the distribution of organisms and environments How to plan and conduct an investigationIn addition, students should become more familiar with the mammal communities and ecoregions in their residential areas, the biomes and ecoregions across North America, and practice independent inquiry about the natural world.A+Click Math Skill Self-Study Tests for Grade 1 to 12
A+Click Math Self-study Tests and Skill Assessment for Grade 1 to Grade 12. It includes more than 1000 challenging problems and answers and tons of illustrations. The practice tests adapt to student ability. This website has a graduated set of problems, starting from very simple, to quite difficult. To progress to a new level, you have to answer five consecutive questions correctly. The questions are appropriate to elementary students; almost any second grader could answer the easiest. This is a good assessment test without being insulting or frustrating.Adding apples and oranges
To calculate the value of an apple and an orange from 2 purchases.About mental arithmetic, with a pre-algebra tool introducing the Gaussian elimination.In the mirror site, there's the Android 2.2 (and up) version of this program.Adding apples oranges and pears
To calculate the value of apple, orange, pear from 3 purchases.About mental arithmetic, with a pre-algebra tool introducing the Gaussian elimination.
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{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":14.69,"ASIN":"0691149925","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":3.99,"ASIN":"0486270785","isPreorder":0}],"shippingId":"0691149925::X%2FsjXHPADHphRf6TcuKA7qanAlpynKoJI0%2FKNc1f9xYz%2BRXZyykTS1abcuarKyE9UV%2FpIbKQxI4nXHUp8cssE2wfVdDhJDNSBQdDeXk8%2FDm%2Bn%2BHPhFHqNA%3D%3D,0486270785::HN3bCgSrJcockkRgCHjQ%2FQ1uHp7E8VAxnvlx2LXJ%2FS%2F4FOQj1%2BqZ1WrVfbH9DAcALICoTxCQ1pMSD%2BQXP2GHhg9U08M%2BC3pGHZc%2BcQ1mGSM are many books that include ideas or instructions for making mathematical models. What is special about this one is the emphasis on the relation of model- or tool-building with the physical world. The authors have devoted themselves to making wood or metal models of most of the constructions presented; 33 color plates nicely show off their success in this area."--Stan Wagon, American Scientist
"The question posed by this book turns out to be a real toughie, but nevertheless the authors urge you to answer it. This gem of a book tackles several such questions, revealing why they are crucial to engineering and to our understanding of our everyday world. With a nice emphasis on practical experiments, the authors do a refreshing job of bringing out the mathematics you learned in school but sadly never knew why. And they show just how intuitive it can be."--Matthew Killeya, New Scientist
"Mathematics teachers and Sudoku addicts will simply be unable to put the book down. . . . Part magic show, part history lesson, and all about geometry, How Round Is Your Circle? is an eloquent testimonial to the authors' passion for numbers. Perhaps it will spark a similar interest in some young numerophile-to-be."--Civil Engineering
"This is a great book for engineers and mathematicians, as well as the interested lay person. Although some of the theoretical mathematics may not be familiar, you can skip it without losing the point. For school teachers and lecturers seeking to inspire, this is a fantastic resource."--Owen Smith, Plus Magazine
"This book is very clearly written and beautifully illustrated, with line drawings and a collection of photographs of practical models. I can strongly recommend it to anyone with a bit of math knowledge and an interest in engineering problems--a terrific book."--Norman Billingham, Journal of the Society of Model and Experimental Engineers
"This book has many gems and rainbows. . . . The book will appeal to all recreational mathematicians . . . not just because of the way it is written, but also because of the way puzzles, plane dissections and packing and the odd paper folding or origami task are used to bring a point home. . . . More than one copy of this book should be in every school library. . . . It should help to inspire a new generation into mathematics or engineering as well as be accessible to the general reader to show how much mathematics has made the modern world."--John Sharp, LMS Newsletter
"This book can be dense, but it is great for dipping into, a rich resource of interesting thinking and project ideas. Bryant and Sangwin, the engineer and the mathematician, must have had a great time putting this book together. Their enthusiasm and humor shine through."--Tim Erickson, Mathematics Teacher
"The book is very nicely printed and contains many nice figures and photographs of physical models, as well as an extensive bibliography. It can be recommended as a formal or recreational lecture both for mathematicians and engineers."--EMS Newsletter
From the Inside Flap
"This book is a mine of exploration and information. I would recommend it to anyone with an interest in how things work and in how mathematics can help make sense of the world. Budding engineers and mathematicians will find it an inspiration."--John Mason, The Open University
"Truly impressive. This book builds a bridge across the ordinarily huge chasm separating how engineers and mathematicians view the world. Its innovative approach will be refreshing to readers with an engineering bent, and an eye-opener for many mathematicians. The audience for this book includes just about anyone who has any curiosity at all about how mathematics helps in explaining the world."--Paul J. Nahin, author of An Imaginary Tale
"I learned a lot from this book. I think it will have wide appeal, including with those readers who are interested in mathematics and those who are interested in building models. I was up until midnight the other night making a hatchet planimeter out of a coat hanger and washers!"--David Richeson, Dickinson College
--This text refers to an out of print or unavailable edition of this title.
This book is in the tradition of the famous book "Mathematical Models," by H. Martyn Cundy and A. P. Rollett. It shows how to create models that illustrate particular mathematical laws, and in fact Cundy was consulted, while he was still alive, by the author. It is a worthy successor to Cundy & Rollett's book, concentrating mainly in two areas: linkages to draw straight lines and curves, and constant-breadth shapes, though entering a few other areas.
An example of the type of problem this book considers is: How would you construct "the first" protractor or ruler, if there were none already existing?
The spirit of the book is the kind of practical thinking that is thought of as engineering, but the mathematics discussed is fundamental. This is a highly recommended book.
What this book shows you is that you can really understand Mathematics, when you try to build things, even something simple, like cutting a good circle from wood. Many areas of mathematics are discussed that people instinctively feel they understand, such as the roundness of a curve or circle, dividing an angle into 3 equal parts and other interesting Objects De Mathematica. You will find fascinating ways to really model the pythagorean theorem, or gather the sectors of a circle to make an equivalent triangle. There is much to discover between these pages, and Mathematics becomes concrete, objectified, and deeply understood. As another example: "what would a 3 dimensional object that has constant width throughout (based on the tetrahedron) Look like? You can see what this object looks like, when you read the work, and see the model. To add to your understanding, the Authors have constucted Models of the various mathematical principles and ideas, that you can see with your own eyes: such as "two-tip" polyhedrons, and summing the squares of numbers from 1 to n. Reading this book will improve your grasp of mathematics, as well as inspire you to study Engineering, if you havent already. Future Engineers, will be much smarter for having read this great book. Richard H. Pratt, Ph.D.
This fascinating book flags the spot where engineering and mathematics meet. Each chapter essentially covers a different subject: from linkages to vernier scales to slide rules to balancing dominoes to suspension bridges and so much more. The authors combine the rigidly theoretical approach of mathematics to the very real, practical and physical problems faced in engineering. The result is an amazing romp through various subject areas where the two meet. Very few mathematical derivations are presented here; instead, appropriate references are given throughout (but the reader may feel the urge to attempt some of the derivations him/herself). Some of the results are truly amazing, e.g., stacking a leaning tower of dominoes; some are very ingenious, e.g., the vernier scale and the slide rule; and some chapters I found rather disappointing, e.g., the chapter on suspension bridges - a subject dear to my heart that somehow I felt was lacking. The writing style can be a model of clarity for many chapters while, unfortunately, others seem rather cloudy by comparison; for example, I would place the first (Hard Lines) and seventh (Follow My Leader) chapters in the second category. But overall, the reader is bound to find this book very much worth the read. Those who are likely to relish this book the most would include mathematicians, engineers and serious science buffs. This book could also be used as a supplementary text for related university courses.
I am an engineer interested in recreational mathematics so it is not surprising the book appealed to me. However, I believe the book will be more than just interesting for a wider technical oriented crowd.
I found the topics to be handled with extreme clarity. The examples are abundant and most important of all, the book just makes you want to put it down, jump out of the sofa to the nearest hardware store and build the models described, by yourself. My favorite by far was the chapter on mechanical linkages.
The review in American Scientist said it beautifully and also included a few of the gorgeous photos of demonstrations created by the two authors. There are blocks that can be piled up so they balance with their tops not over their bottoms. There is a planimeter made from a coat-hanger wire with which to find the area of a plane figure. There is a drill bit that can drill a square hole. Terrific fun at every level from the logo chief to the graduate engineer.
All I wanted to point out is you need the right device for the Kindle version. I have 3 devices with which to compare this book: Microsoft Surface 2 running Win 8.1 update 1 (10.6", 1920 x 1080, 208ppi), Nexus 10 (10.1" 2560×1600, 300ppi) and Nexus 7 2013 (7", 1920x1200, 323ppi) both running Android 4.4.2.
1. Text. The Windows 8.1 version of the Kindle app shows text in two columns in landscape, whereas on both Nexus the book is displayed in one column in landscape. Works fine on the smaller screen Nexus 7, harder to read on Nexus 10. No settings I can find to change this. In Portrait mode, they are all one column. The Nexus definitely have sharper looking text but both Nexus and Surface are readable.
2. Diagrams and formulas. This book depends heavily on illustrations and formulas for explanations. Unfortunately, those items do not scale on the Nexus device, i.e, no way to enlarge the diagrams or the formulas. On both Nexus, the diagrams got rendered way too small due to the high PPI. In fact, on both Nexus, the diagrams are exactly the same physical size. The rendered diagrams have labels of inside angles of triangles that are small so it very hard to read. On the Surface 2, it is sized appropriately (about 50% bigger measured physically), so even though the resolution of the device is lower, it is easier to read.
Moral of the story: High PPI <> readability. Whether this book should be a Kindle or physical book will depend on what device you have.
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Introductory Algebra Through Applications, Books a la Carte Edition
KEY MESSAGE: Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that ...Show synopsisKEY MESSAGE: Presented KEY TOPICS: Whole Numbers; Fractions; Decimals; Basic Algebra: Solving Simple Equations; Ratio and Proportion; Percents; Signed Numbers; Basic Statistics; More on Algebra; Measurement and Units; Basic Geometry MARKET: for all readers interested in introductory algebra.Hide synopsis
Description:Good. Introductory Algebra through Applications, Books a la...Good. Introductory Algebra through Applications, Books a la Carte Edition (2nd Edition) This book is in Good condition. Buy with confidence. We ship from multiple location.
Description:Good. Looseleaf. May include moderately worn cover, writing,...Good. Looseleaf. May include moderately worn cover, writing, markings or slight discoloration. SKU: 978032165564655646
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Introductory Algebra - With Access (11TH 11 - Old Edition)
by Marvin L. Bittinger Publisher Comments
This package consists of the textbook plus an access kit for MyMathLab/MyStatLab. The Bittinger Worktext Series changed the face of developmental education with the introduction of objective-based worktexts that presented math one concept at a... (read more)
Mathematical Reflections (97 Edition)
by Peter Hilton Publisher Comments
A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful... (read more)
Statistical Analysis with Excel for Dummies (For Dummies)
by Joseph Schmuller Publisher Comments
You too can understand the statistics of life, even if you're math-challenged! What do you need to calculate? Manufacturing output? A curve for test scores? Sports stats? You and Excel can do it, and this non-intimidating guide shows you how. It... (read more)
Discrete Algorithmic Mathematics 3RD Edition
by Stephen B Maurer Publisher Comments
Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos... (read more)
Calculus I With Precalculus : a One-year Course (3RD 12 Edition)
by Ron Larson Publisher Comments
Carefully developed for one-year courses that combine and integrate material from Precalculus through Calculus I, this text is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them... (read more)
Discrete and Combinatorial Mathematics (5TH 04 Edition)
by Ralph Grimaldi Publisher Comments
This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it... (read more)
Elementary Statistics - With CD (10TH 06 - Old Edition)
by Mario F. Triola Publisher Comments
Addison-Wesley is proud to celebrate the Tenth Edition of Elementary Statistics. This text is highly regarded because of its engaging and understandable introduction to statistics. The author's commitment to providing student-friendly... (read more)
Schaum's Outline of Precalculus (Schaum's Outlines)
by Fred Safier Publisher Comments
Schaum's has Satisfied Students for 50 Years. Now Schaum's Biggest Sellers are in New Editions! For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates... (read more)
Ez 101 Statistics 2ND Edition
by Martin Sternstein Publisher Comments
Books in the EZ-101 Study Keys series are intended as brush-up reviews for a variety of college-101 courses. They are designed as a set of classroom "notes" that reflect typical lecture material presented in a classroom over the course of a semester. As... (read more)
Statistics Unplugged (4TH 13 Edition)
by Caldwell Publisher Comments
Learn statistics the easy way with STATISTICS UNPLUGGED! Written in a friendly, easy-to-understand style, this practical book takes the intimidation out of statistics and helps you understand the relevance of statistics to your own life. Interesting
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Author(s): David Halliday; Robert Resnick; Jearl Walker
Note:
This eResource includes the publisher's eTextbook. When you use the eResource after purchase, enter the Course Code provided by your instructor to get full access to the eTextbook for your course.
Price Information
eResource Digital Rental:
Your WileyPLUS Course will be active for the length set by your instructor.
Important:
To use this product you will need course-specific information from your instructor. Please check with your instructor before purchasing.
Additional product details
eText:
ISBN-10 0470524723, ISBN-13 9780470524725
Print:
ISBN-13 9780470524725
Author(s): David Halliday; Robert Resnick; Jearl Walker
Publisher: John Wiley & Sons
Description
WileyPLUS combines the complete, dynamic online text with a valuable suite of teaching and learning resources in one easy-to-use system. It provides a very robust collection of high-quality problem sets, offering immediate and meaningful feedback to students, along with varying levels of question assistance. In addition to offering the end-of-chapter problem sets, WileyPLUS provides the support instructors need to efficiently and effectively manage their classroom and improve student performance.
* A Math Skills Module – essentially a Chapter Zero – gets students up to speed with a comprehensive review of the algebra and calculus required in the course. * Guided Online (GO) Tutorials – these step-by-step tutorials, written by Jearl Walker, start with the key idea then break the problem down into steps, providing hints along the way. As he wrote these, Jearl imagined what he would say to a student in his office who was stuck on a problem. The result is a friendly, clear explanation that helps students along the way. The ninth edition features over 500 GO Tutorials! * Additional interactive simulations, animations and video mini-lectures accommodate a variety of learning styles. Through the videos, Jearl Walker teaches students how to read technical content. Extra help material (not in the printed text) is available through hypertext links for those students who need or want it.
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selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.
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An Introduction to Knot Theory
"This essential introduction to vital areas of mathematics with connections to physics, while intended for graduate students, should fall within the ken of motivated upper-division undergraduates."—CHOICE
Most Helpful Customer Reviews
The level of detail in this book is just right. It provides complete and rigorous proofs without getting bogged down in too much detail. In addition to some other knot theory standards, it has an excellent section on 3-manifold invariants arising from the Temperley-Lieb algebra. This book is appropriate for those who have a knowledge of algebraic topology.
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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Course
4 Unit 4 - Counting Models 1st Edition
Students have learned
concepts and methods for solving counting problems in previous courses
of the Contemporary Mathematics in Context program, but not as
explicit instruction. This unit from the discrete mathematics strand
pulls
together and formalizes this work. (See the descriptions of Course 4
Units.)
Unit Overview
Counting Models
extends student ability to count systematically and solve enumeration
problems. The unit also develops student understanding of and ability
to do proof by mathematical induction.
Unit Objectives
To develop the skill of careful counting in a variety of contexts
To understand and apply a variety of counting techniques,
including the Multiplication Principle of Counting, tree diagrams,
systematic lists, and combinatorial reasoning
To understand and apply the General Multiplication Rule for
probability
To understand and apply the Binomial Theorem and Pascal's
triangle
To develop the ability to prove statements using combinatorial
reasoning and the Principle of Mathematical Induction
Sample Overview
This sample material
consists of the two investigations of Lesson 2, "Counting Throughout
Mathematics."
In the first investigation, students use counting methods developed in
Lesson 1 to solve probability problems. In the second investigation,
the
focus shifts to algebra as students learn about the connections among
combinations, the Binomial Theorem, and Pascal's triangle.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design.
View Sample
Material
Contact
Adobe with any technical questions
about their software or its installation.
How the Discrete Mathematics Strand Continues
The counting and
reasoning skills developed in this unit will be applied in future
units.
For example, combinations are required in Unit 5, Binomial Distributions
and Statistical Inference, for the binomial probability formula,
and counting arguments related to binary strings are used in Unit 9, Informatics
(the final discrete mathematics unit). Pascal's triangle is revisited
in Unit 10, Problem Solving, Algorithms, and Spreadsheets.
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Find a Hayward, CA Algebra 2They have so far known and used different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compou
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Mathematics Principles On Your Mobile [NOOK Book] For easy reading, a comprehensive list of hundreds of topics each with a graphic image and explanatory text ...
More About
This Book
For easy reading, a comprehensive list of hundreds of topics each with a graphic image and explanatory text condensed to note form act as a useful exam revision reminder or reference tool for professionals.
The accompanying software which brings all these images to life can be downloaded at no extra charge thereby providing an additional computer based interactive learning resource as an easy and enjoyable way to study.
NOTE: Includes Mathematics V10 interactive software download to accompany this eBook title which is fully activated with the eBook payment receipt. See Additional Notes at the back of the eBook for the download
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Pre-Algebra Homework Practice Workbook
The Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of ...Show synopsisThe Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve word problems.Hide synopsis
Description:Very Good. 0078907403 No excessive markings and minimal...Very Good. 0078907403 No excessive markings and minimal highlighting. CD Roms, access cards/codes, and other supplemental materials may or may not be included based on availability.Description:New. The Homework Practice Workbook contains two worksheets for...New. The Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve
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WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of...
see more
WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics. Includes a video and teacher resources.
A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution...
see more
A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution portals -״The Question Locker" and "Beyond H2 maths״which are relevant to the general high school and early college maths student.
PUMAS (poo' • mas) -- is a collection of brief examples showing how math and science topics taught in K-12 classes can be...
see more
PUMAS (poo' • mas) -- is a collection of brief examples showing how math and science topics taught in K-12 classes can be used in interesting settings, including every day life. The examples are written primarily by scientists, engineers, and other content experts having practical experience with the material. They are aimed mainly at classroom teachers, and are available to all interested parties via the PUMAS web site
A computational tool that runs the one-way ANOVA by the user inputing individual data or by copying and pasting a delimitted...
see more
A computational tool that runs the one-way ANOVA by the user inputing individual data or by copying and pasting a delimitted data set. This reference also includes description of what the ANOVA is and how it compares to the t-test.
This website was created by a Harvard student to offer free SAT-prep materials for impoverished high school students. The...
see more
This website was created by a Harvard student to offer free SAT-prep materials for impoverished high school students. The site offers sixty "engaging lessons in math, reading, and writing that infuse pop culture into learning to make prep accessible; 800+ challenging practice exam questions that simulate the SAT and provide full explanations; and unique features like a score projector to show" students how they are predicted to score on the actual exam.
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Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":71.2,"ASIN":"08218478130821847813::yUvlI6oTDR8%2F2yOrveHzEOfwdrIWD9dHHJkleoKo0sm2fti0LGhceyiJLlhULM4R7y3WOleUPxp7Zc2Klp2iMhUNAsaDN6hI%2FaPMs0OMpb%2BVKnUi3IRuAQ%3D%3D,0471433349::2vbB%2BNYET1SuGlo6YuiJxh%2B8FlrHwTi2nWVQ9hQ0HQPTqqfZCyAXKnLH7CiVwlfCkzte09bcTYacjZ9FhE3JNyRw59%2B6Vms6k9JJ325nPrU%3D,007054235X::0d3Im6CaDbGU7TlMfEaLNbBRxsg2EtWTV28V0P4XBE27XAZymw75cwqmnEpdWY6yDpwqbsHBiIX1Tm0w2dvmu4Nt67%2BpSCkdjKrGWpvalThis self-contained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme. ---- SciTech Book News
More About the Author
Paolo Aluffi was born in Italy, and studied mathematics in Torino under the direction of Alberto Collino, and then at Brown University, obtaining a Ph.D. with a dissertation in algebraic geometry under the supervision of William Fulton. He has held postdoctoral positions at the University of Chicago and Oklahoma State University, and joined the department of mathematics at Florida State University in 1991. He is currently professor of mathematics at FSU. Paolo Aluffi has visited many universities and mathematics institutes for extended periods of time. Among these are the Max-Planck-Institut in Bonn, Germany; Harvard University; the Institut des Mathématiques in Luminy, France; the Mittag-Leffler Institut in Stockholm, Sweden; the Mathematical Sciences Research Institute in Berkeley, California; and the California Institute of Technology.
Beside `Algebra: Chapter 0', he has published more than 40 research papers in algebraic geometry. He has also published a book of mathematics for the `general public' in Italian, `Fare Matematica'.
Most Helpful Customer Reviews
I should first mention that I, along with about twenty of my fellow first-year mathematics graduate students, scoured this book from beginning to end. We completed nearly every exercise, and discovered a number of errata (there is quite a large list available on the author's website, but this book shines in spite of it all).
I've experienced Fraleigh, Artin, Dummit and Foote, and Aluffi's texts on abstract algebra. While each has it's place, I have to say that Aluffi is my favorite. His writing style is phenomenal (and humorously pretentious at times). This text is not intended to be a reference, but instead read from start to finish, and Aluffi monopolizes this to its full effect. The content is spot on for the intended audience. His exercises cover important, relevant topics to important fields I and my fellow graduate students intend to pursue. These include, but are not limited to: algebraic geometry, commutative algebra, homological algebra, and Lie theory.
This book is the best I have encountered for transitioning from an elementary understanding of abstract algebra to a mature perspective, backed by the might of category theory. That being said, I can see how the book may go more smoothly if one has had some initial exposure to algebra before Aluffi. This text does an excellent job synthesizing my understanding, but the organization could be confusing for a beginner.
My only real disappointment with the book is in the final chapter on homological algebra. By the last two or three sections, the content is almost prohibitively confusing. It could be the case that there are errata that have confused me (indeed, the listed errata on his website sharply fall in this chapter, and I believe it's because most students don't get this far).Read more ›
This is a well organized and clearly written book. Professor Aluffi must be an excellent teacher. He guides the reader through the material and shows the beauty of the subject. His use of category theory- particularly universal properties- reveals the underlying unity of seemingly disparate notions.The chapters on Field Theory and Homological Algebra are superb. He always provides useful comments to place topics in context. I hope Professor Aluffi will write more texts.
I attended a course in abstract algebra using Fraleigh's book. Then I sorta just stumbled across this one (which I should add covers a lot more than Fraleigh). With experience from Fraleigh's book (which is good) I can say this one is absolutely brilliant. It is well organized, covers a lot of ground in a (not too) leisurly pace, and the exercises are interesting. The best part about this book, however, is the way it seamlessly and naturally uses and demystifies category theory -- a subject I thought I'd not be able to understand for years -- to unify a great deal of the topic that is undergraduate/graduate algebra.
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Intermediate Algebra : Text/ Workbook - 8th edition
Summary: The sixth edition of this text/CD-ROM package for use in a traditional lecture class or for self-paced instruction features early coverage of graphing and functions, new material incorporating the use of graphing calculators, spreadsheet programs, and computer graphing, and new chapter openings, application problems, and projects. Other learning features include chapter summaries, chapter and cumulative reviews, and tests. Coverage progresses from basic properties an...show mored definitions through equations and inequalities, quadratic functions, and conic sections. The companion CD-ROM contains five hours of video instruction, plus problems and solutions02 +$3.99 s/h
Good
southbrooklyntexts New York, NY
0495826758
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Editorial Reviews
From the Back Cover
This book provides an introduction to the basic ideas, computational techniques, and applications of linear algebra. Introductory Linear Algebra with Applications Sixth Edition emphasizes the computational and geometrical aspects of linear algebra, while keeping abstraction to a minimum and illustrating every idea with examples. It provides three different types of exercises. Exercises contains routine exercises. Theoretical Exercises includes exercises that fill in gaps in some of the proofs and can be used to challenge the more capable and interested reader. The third class consists of MATLAB exercises connected to the available MATLAB disk. In addition, the end of every chapter contains a summary of Key Ideas for Review, a set of Supplementary Exercises, and a Chapter Test. The sixth edition of Introductory Linear Algebra with Applications has been revised to incorporate recommendations from The Linear Algebra Curriculum Study Group on developing ways to improve instruction in linear algebra. A valuable reference book on the basic of linear algebra and its applications for any reader seeking information on the subject.
--This text refers to an alternate
Hardcover
edition.
This book is a fabulous resource... explains things in as clear a way as Linear Algebra can be. If you want deeper understanding, many concepts are described in more depth, and most proofs are given in detail. It's not filled with cartoons and useless pictures like some textbooks, but clear, concise explanations of what turns out to be an interesting and fairly simple area of mathematics.
This isn't the easiest linear text I've scene. This also isn't the hardest. The book has a ton of applications, which is good if you're an applied math, engineering, or science major. If your interests are in pure math the applications are still a nice little side note. The book's explanations are explained as clearly as possible without giving up any rigor. At first I didn't like the book, but after looking at several other linear textbooks I realized that these authors did a good job of explaining a difficult topic.
I am teaching myself linear algebra from this book before I go to college, and the text is very accessible. I am glad that I picked this text in particular. Starts out with basic things like linear systems with 3 variables, then introduces meatier subjects.
This is an OK book. Not bad for a first introduction to linear algebra and good enough for self studying. There are plenty of exercises with answers for the odd numbered questions at the back. There are a few chapters with various applications of the material but I mostly skipped over those. In addition, each section includes not only computational exercises but also theoretical exercises where you have to prove things and also MATLAB exercises. I think the main problem with this book is that it is repetitive and not well organized.
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A book of mathematicians by nationality the mathematics of gauss introduction cornell university mathematic worksheet, this trick resolve, the recent development of variation methods of mathematic formulation to resolve this book of mathematicians by nationality the mathematics of gauss introduction cornell university question. With the book of mathematicians by nationality the mathematics of gauss introduction cornell university mathematicworksheet you can obtain vision to workout some mathematic work, with an endless supply of printable mathematic worksheets. These worksheets are provided in PDF format. Browse the best completion in the mathematic fact, book of mathematicians by nationality the mathematics of gauss introduction cornell university and knowledge, search and sort the match formulation, in the case about your mathematic question with comprehensively solution.
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More About
This Textbook
Overview
Numerical ability is an essential skill for everyone studying the biological sciences but many students are frightened by the 'perceived' difficulty of mathematics, and are nervous about applying mathematical skills in their chosen field of study. Having taught introductory maths and statistics for many years, Alan Cann understands these challenges and just how invaluable an accessible, confidence building textbook could be to the fearful student. Unable to find a book pitched at the right level, that concentrated on why numerical skills are useful to biologists, he wrote his own. The result is Maths from Scratch for Biologists , a highly instructive, informal text that explains step by step how and why you need to tackle maths within the biological sciences.
Features:
* An accessible, jargon-busting approach to help readers master basic mathematical, statistical and data handling techniques in biology
* Numerous end of chapter problems to reinforce key concepts and encourage students to test their newly acquired skills through practise
* A handy, time-saving glossary
* A supplementary website with numerous problems and self-test exercises
Related Subjects
Meet the Author
Alan Cann has worked in both the UK and USA, and in addition to teaching undergraduate and postgraduate biologists and medical students, he runs an active research laboratory at the University of Leicester, UK, studying the molecular biology and pathogenesis of viruses. He has been awarded numerous grants for educational research and was the inaugural winner of the Society for General Microbiology UK Wildy prize for Education
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4.3 Pie charts, bar charts, histograms and line graphs Interpreting percentages Reading data from tables Reading articles for mathematical information Reflecting on your mathematical history Reflection on mathematics.1 Using a site map8.1 Changing your settings.1 Internet Explorer (IE) What is a PDF? Frightened of the internet? This unit will help you make effective use of the internet, giving you the basic skills required for using web-based resources. Useful tricks1 What is a computer virus Are websites reliable Favourite sites Searching the web How to recognise links Distance between two points in the plane Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics Defining
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Pre-Algebra - 06 edition
Summary: A new way of thinking about Algebra readiness! Focused, organized, and easy to follow, Glencoe Pre-Algebra shows your students how to read, write, and understand the unique language of mathematics, so they'll be prepared for every type of problem-solving and assessment situation.
All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780078704246-5-0
$4566.97 +$3.99 s/h
VeryGood
AlphaBookWorks Alpharetta, GA
007870424397.30 +$3.99 s/h
New
PaperbackshopUS Secaucus, NJ
New Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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Concepts are more important in mathematics because they can lead to accuracy and better understanding. I prefer for my students to give many solutions for a small group of problems than trying to work superficially on a greater group.
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Common Core Standards for High School Mathematics: A Quick-Start Guide (EBOOK)
Shifting your high school's math program to new Common Core standards is much easier when teachers and leaders have this handy guide. Getting a copy for every staff member involved in the process ensures everyone knows
How the six conceptual categories throughout the math standards are connected and reinforced.
How the modeling standards bring math content to life through real-world applications.
How the mathematical practices standards are an integral part of the Common Core.
To jumpstart your standards implementation, the standards are provided in easy-to-read narrative form, and there's a lesson design template based on Classroom Instruction that Works, 2nd Edition with three sample lessons, so you and your colleagues can see the implications and advantages of teaching the Common Core.
(ASCD E-Book, 2011) PDF e-book accompanied by bonus MOBI and EPUB files for use on e-book readers like the Kindle and the Nook. See the e-book FAQ link for information about device compatibility.
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Mathematics
General Math MAT1001 - Full Year A two-semester course designed to review the basic operations of whole numbers, fractions, decimals, and directed numbers. Problem solving, rates, percents, statistics, and basic geometry are also discussed. If a student takes this course a subsequent year, mathematics life skills will be emphasized.
Pre-Algebra MAT1002 - Full Year Pre-Algebra is a two-semester course for students who need additional time to prepare for Algebra I. It reviews fundamentals of mathematics, reviews algebraic concepts previously introduced in other math courses, and introduces new math concepts. Topics covered include the four fundamental math operations, order of operation, fraction, decimals, percents, ratio, proportion, exponents, scientific notation, perimeter, area, volume, solving equations and inequalities, graphing and translating real life problems into mathematical sentences.
Algebra 1 MAT1003 - 9th Grade - Full Year A two-semester course in Algebra designed to give the student a complete foundation in algebraic structure and method. The course covers work in the areas of real numbers, simple and complex equation and problem solving, polynomials, fractions, factoring, graphing, rational and irrational expressions, and quadratic equations and the inequalities.
Algebra 2* MAT1004 - 10th/11th/12th Grade - Full Year This elective course is designed to give the student an in-depth study of algebraic concepts. The course covers a review of Algebra I, rational and irrational numbers, radicals, quadratic equations, complex numbers, graphing, exponents, logarithms, permutations, and combinations. Prerequisite: Algebra I and Geometry
Geometry* MAT1005 - Any Grade - Full year This two-semester course is designed to help students understand the basic structure of geometry, develop powers of special visualization while building their knowledge of the relationships among geometric elements, and grow in the understanding of the deductive method and in an appreciation of the need for precision of language. Students will also strengthen their algebraic skills, gain some knowledge of the methods of coordinate geometry and the way in which algebra and geometry complement each other, and experience the stimulation and satisfaction that comes from clear and creative thinking. Prerequisite: Algebra I
AP Calculus* MAT2004 - 12th Grade - Full Year Calculus is an advanced branch of mathematics that is concerned with limits of function models and with differentiation (slope dy/dx) and integration (area) of the function models and their applications to the functions they model. These topics will help to understand and model some of the wonders of our almighty God. The course is designed for a full year course in calculus I that follows advanced mathematics (pre-calculus) and precedes higher levels of calculus. The skills and objectives will empower you to model and study physical sciences, economics, business, engineering, statistics, or many other problem-solving applications. Prerequisite: B or higher in Advanced Math
Statistics* MAT1013 - 11th/12th Grade - Full Year This course is designed to provide the student with a comprehensive treatment of introductory statistics and probability in such areas as business, sociology, ecology, economics, education, medicine, psychology, and mathematics as well as in our everyday life as consumers. Students in these courses must frequently demonstrate a knowledge of the language and methods of statistics. Methodology and applications have been integrated throughout the course. Prerequisite: Algebra I and Geometry
Basic Algebra MAT1016 - 12th Grade - Full Year This is a two-semester course, which is designed for the student who has completed Algebra 1 and or Geometry, but it is not a requirement. This math course will connect experiences with comprehensive mathematics. The course will use algebra, geometry, trigonometry, linear programming, and optimization techniques to solve problems. This course will show students mathematics is a vital, relevant, flexible tool for interacting with their world in many ways and at many levels, from the commonplace setting of everyday life and work to the frontiers of science and technology.
Honors Pre-Calculus & Trigonometry* MAT2002 - 11th/12th Grade - Full Year A two-semester course designed to prepare the student for modern courses in calculus, abstract algebra, and probability. Topics covered are logic, properties of the complete ordered field, mathematical induction sequences and series, algebra of vectors, plane analytical geometry of points and lines, linear and polynomial functions, exponential and logarithmic functions, and circular and trigonometric functions and their properties. Prerequisite: Algebra II
Consumer Mathematics MAT1006 - 12th Grade - Full Year This course begins with an extensive look at federal and state income tax forms and filing procedures. Other items covered are auto ownership, purchasing goods, personal income, various areas of banking and banking services, investments, insurance, and housing cost.
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How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications)
9781420082609
ISBN:
1420082604
Edition: 2 Pub Date: 2010 Publisher: C R C Press LLC
Summary: Allenby, Regnaud B. J. T. is the author of How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications), published 2010 under ISBN 9781420082609 and 1420082604. Three hundred fifty nine How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications) textbooks are available for sale on ValoreBooks.com, one hundred three used from ...the cheapest price of $54.65, or buy new starting at $71.80.[read more20082609
ISBN:1420082604
Edition:2nd
Pub Date:2010 Publisher:C R C Press LLC
ValoreBooks.com is the top book store for cheap How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications) rentals, or new and used condition books for purchase.
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math911 contains step by step tutorials in Introductory Algebra, Intermediate Algebra, PreCalculus and Introductory...
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math911 contains step by step tutorials in Introductory Algebra, Intermediate Algebra, PreCalculus and Introductory Statistics. The given link is to the setup file. After setup, you should see a math911 icon on the desktop. Click on the icon to run math911. Vista, Windows 7, Windows 8 users might need to right click and in the drop down list select 'Run As Administrator.'To set up a grade report file you will be asked to enter your name, birth date (or any other date) and select a course.A grade report file will be created (FLmmdd.mdb where F=first initial, L=last initial, mmdd= month and date). Grades are saved AUTOMATICALLY to this file..Select a chapter, then a lesson and a problem will appear.For a tutorial: You can step through the solution (click See Solution, See All Steps, See Next Step, etc.)To answer: Type the answer and press ENTER Only correct answers count. Wrong answers are ignored !If your answer is incorrect: Click on See All Steps, See Next Step, etc.Use the up/down arrows to enter exponents and move between the numerator and denominator of a fraction. There are up to 8 levels for each lesson and all the types of problems for you to master AlgebraIMPORTANT. math911 is activated for Introductory Algebra. For full activation to other courses, RIGHT click on the ABOUT button and enter the code: essex.Once fully activated you can switch back and forth to the other courses.Math911 is continuously updated. For technical help please call Professor Martin Weissman 347-528-7837
Old Egyptian Fractions at MathCats(Web and android version)Old Egyptian Math Cats knew fractions like 1/2 or 1/4 (one piece...
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Old Egyptian Fractions at MathCats(Web and android version)Old Egyptian Math Cats knew fractions like 1/2 or 1/4 (one piece of a pie).But to make fractions like 3/4, they had to add pieces of pies like 1/2 + 1/4 = 3/4.Old Egyptian Math cats never repeated the same fraction when adding.They never wrote: 1/4 + 1/4 + 1/4 = 3/4How it works:Choose puzzles from the list on the top. ( * = easier, **** = very hard.)Add 2 or 3 fraction pieces below.After you find one solution, the puzzle is marked "Solved." Can you find more solutions? (Click to see them listed on the bottom.)There's the android version in the mirror site link
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Mathematics with Business Applications
Glencoe "Math with Business Applications" is a comprehensive text that covers all the skills students need to manage their personal finances and ...Show synopsisGlencoe "Math with Business Applications" is a comprehensive text that covers all the skills students need to manage their personal finances and excel at their first jobs and in everyday life. "Math with Business Applications" is a three-part program that takes students from basic math concepts to sophisticated financial strategies. Basic Math Skills reviews the fundamental math operations, Personal Finance teaches money management skills, and Business Math provides a thorough primer on launching and running a business. "Math with Business Applications" contains lessons, workshops, features and activities that comprise a well-rounded program.Hide synopsis
Description:Fair. Creased cover and spine, previously a schoolbook Obviously...Fair. Creased cover and spine, previously a schoolbook Obviously well-worn and handled but no text pages are missing, however, it may be without endpapers or a title page. There might be markings, but they do not interfere with readabilityGood. Mathematics with Business Applications, Student Edition....Good. Mathematics with Business Applications, Student Edition. This book is in Good condition. Buy with confidence. We ship from multiple location
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Authors Wayne Winston and Munirpallam Venkataramanan emphasize model-formulation and model-building skills as well as interpretation of computer ...Show synopsisAuthors Wayne Winston and Munirpallam Venkataramanan emphasize model-formulation and model-building skills as well as interpretation of computer software output. Focusing on deterministic models, this book is designed for the first half of an operations research sequence. A subset of Winston's best-selling OPERATIONS RESEARCH, INTRODUCTION TO MATHEMATICAL PROGRAMMING offers self-contained chapters that make it flexible enough for one- or two-semester courses ranging from advanced beginning to intermediate in level. The book has a strong computer orientation and emphasizes model-formulation and model-building skills. Every topic includes a corresponding computer-based modeling and solution method and every chapter presents the software tools needed to solve realistic problems. LINDO, LINGO, and Premium Solver for Education software packages are available with34359645-5Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780534359645Very Good. Very good condition-Has cover, edge, corner or page...Very Good. Very good condition-Has cover, edge, corner or page wear and may have mild highlighting/writing. TEXT ONLY! No supplemental materials
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More About
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Overview
Introductory Mathematics for the Life Sciences offers a straightforward introduction to the mathematical principles needed for studies in the life sciences. Starting with the basics of numbers, fractions, ratios, and percentages, the author explains progressively more sophisticated concepts, from algebra, measurement, and scientific notation through the linear, power, exponential, and logarithmic functions to introductory statistics. Worked examples illustrate concepts, applications, and interpretations, and exercises at the end of each chapter help readers apply and practice the skills they develop. Answers to the exercises are posted
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This is not necessarily true. Having a graphing calculator for calculating rref of matrices greatly reduces the time necessary to calculate the inverse of a matrix. I'm also taking statistics theory and methods and differential equations and find having a calculator very comforting, even if I don' use it. Like a safety blanket. Not everything needs a calculator, but when in a time crunch, it helps a lot.
well, if I think the answer is fishy, I go check what I put into my ti-84. I was just talking about a petty annoyance, since we can use our calculators in physics and checking it simply involves moving your eyes
When the difference is large it's easier to realize it is fishy. But when the answer you got looks right, it's hard to know there was a mistake made at all. I always double check my calculator specifically for this reason.
You could do that? We were not allowed to use a calculator at all. It all had to be done by hand and we could not use a calculator to check. Our calculus sequence and linear algebra no calculators were allowed. There were a couple exceptions on some test but we were usually not allowed to use them.
Wow. I don't NEED a calculator luckily, but having one lets the students put more emphasis on concepts and understanding as opposed to stressing about making simple algebra mistakes, or at least that's what I believe. My stats class in particular could not be done without a calculator. It would be impossible.
Yeah. Most of my mistakes on all of my tests have been simple arithmetic/algebra errors. A lot of people didn't like it because if you made an algebra mistake such as maybe getting a wrong eigenvalue or something simple will mess up your problem completely. It has made me more careful but it's stressful not to make a simple mistake in the duration that we have for tests.
Oh I'm aware - computers are very good at repetitive methods, that's why I haven't calculated any of this stuff by hand since my undergraduate days. My point is that undergraduate mathematics is 90% about understanding how things work and why - calculators don't really help with that, which is why they aren't necessary (or aren't allowed) for 90% of the material.
Once you understand how and why you'll do very little by hand ever again, a few fields excepted - we have MATLAB for linear algebra, for instance.
I'm just really surprised that a teacher would not allow a calculator in a test situation at all. I have never experienced this in my classes in university. I've used MATLAB in differential equations class briefly. I'm glad all this will be over this week though. Finally graduating. No more class! At least until grad school in a couple years...
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constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
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More college students use Amos Gilat's MATLAB: An Introduction with Applications than any other MATLAB textbook. This concise book is known for its just-in-time learning approach that gives students information when they need it. The new edition gradually presents the latest MATLABThis book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of…
The magnum opus of one of the world's leading origami artists, the second edition of Origami Design Secrets reveals the underlying concepts of origami and how to create original origami designs. Containing step-by-step instructions for 26 models, this book is…
A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, readers…
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Give your Saxon Math 5/4 students support and reinforcement! Comprehensive lesson instructions feature complete solutions to every practice problem, problem set, and test problem with step-by-step explanations and helpful hints. These user-friendly the 3rd Edition. Four Lesson CDs and 1 Test Solutions CD included.
Does the Teacher CD-ROM contain a 10 - 15 minute presentation of the new concept at the beginning of each new lesson?
[The descriptions for the D.I.V.E. CD and Teacher on DVD both specifically state that the new concept is presented in a 10 - 15 minute presentation - with or without actual use/demonstration of a specific problem from the book and with or without additional problems demonstrated for their solutions, depending on the product. However, the description for the teacher CD did not seem to include the presentation of the concept, so I was curious.] Thank you!
asked 2 months, 3 weeks ago
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answer 1
These do have an introduction of the concepts at the beginning of each lesson. The length will vary based on how long the lesson is in the book. The CD follows the text of the book pretty closely, with some deviation for further explanation. It will use the same example problems used in the textbook.
Saxon Teacher 5/4 CD-ROM- Mac Compatibility?
We use a Macbook with OS 10.6.8. Your site says the following for Mac compatibility: Mac OS 10.3.9-10.4.x Is this outdated information (since it was published in 2005) or will this CD work with 10.6.8 as well?
asked 1 month ago
by
ARose
on Saxon Teacher for Math 5/4, Third Edition on CD-Rom
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answer 1
You should be able to use it with Mac OS 10.6. However anything 10.7 and above will not work.
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Description
This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books à la Carte also offer a great value–this format costs significantly less than a new textbook.
Ratti and McWaters have combined years of lecture notes and firsthand experience with students to bring readers a book series that teaches at the same level and in the style as the best math instructors. An extensive array of exercises and learning aids further complements the instruction readers would receive in class and during office hours.
Table of Contents
P. Basic Concepts of Algebra
P.1. The Real Numbers and Their Properties
P.2. Integer Exponents and Scientific Notation
P.3. Polynomials
P.4. Factoring Polynomials
P.5. Rational Expressions
P.6. Rational Exponents and Radicals
P.7. Topics in Geometry
Chapter P. Summary
Chapter P. Review Exercises
Chapter P. Practice Test
1. Equations and Inequalities
1.1. Linear Equations in One Variable
1.2. Applications of Linear Equations
1.3. Complex Numbers
1.4. Quadratic Equations
1.5. Solving Other Types of Equations
1.6. Linear Inequalities
1.7. Equations and Inequalities Involving Absolute Value
Chapter 1. Summary
Chapter 1. Review Exercises
Chapter 1. Practice Test A
Chapter 1. Practice Test B
2. Graphs and Functions
2.1. The Coordinate Plane
2.2. Graphs of Equations
2.3. Lines
2.4. Relations and Functions
2.5. Properties of Functions
2.6. A Library of Functions
2.7. Transformations of Functions
2.8. Combining Functions; Composite Functions
2.9. Inverse Functions
Chapter 2. Summary
Chapter 2. Review Exercises
Chapter 2. Practice Test A
Chapter 2. Practice Test B
Cumulative Review Chapters. P-2
3. Polynomial and Rational Functions
3.1. Quadratic Functions
3.2. Polynomial Functions
3.3. Dividing Polynomials
3.4. The Real Zeros of a Polynomial Function
3.5. The Complex Zeros of a Polynomial Function
3.6. Rational Functions
3.7. Polynomial and Rational Inequalities
3.8. Variation
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Practice Test A
Chapter 3 Practice Test B
Cumulative Review Chapters P-3
4. Exponential and Logarithmic Functions
4.1. Exponential Functions
4.2. The Natural Exponential Function
4.3. Logarithmic Functions
4.4. Rules of Logarithms
4.5. Exponential and Logarithmic Equations
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Practice Test A
Chapter 4 Practice Test B
Cumulative Review Chapters P-4
5. Trigonometric Functions Angles and Their Measure
5.1 Right Triangle Trigonometry
5.2 Trigonometric Functions of Any Angle; Unit Circle
5.3 Graphs of the Sine and Cosine Functions
5.4 Graphs of the Other Trigonometric Functions
5.5 Inverse Trigonometric Functions
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Practice Test A
Chapter 5 Chapter Test B
Cumulative Review Chapters P-5
6. Trigonometric Identities
6.1 Verifying Identities
6.2 Sum and Difference Identities
6.3 Double-Angle and Half-Angle Identities
6.4 Product-to-Sum and Sum-to-Product Identities
6.5 Trigonometric Equations I
6.6 Trigonometric Equations II
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Practice Test A
Chapter 6 Practice Test B
Cumulative Review Chapters P-6
7. Applications of Trigonometric Functions
7.1 The Law of Sines
7.2 The Law of Sines: Ambiguous Case
7.3 The Law of Cosines
7.4 Area of a Triangle
7.5 Vectors
7.6 The Dot Product
7.7 Polar Coordinates
7.8 Polar Form of Complex Numbers; DeMoivre's Theorem
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Practice Test A
Chapter 7 Practice Test B
Cumulative Review Chapters P-7
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Systems of Nonlinear Equations
8.4 Systems of Inequalities
8.5 Linear Programming
8.6 Partial-Fraction Decomposition
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Practice Test A
Chapter 8 Practice Test B
Cumulative Review Chapters P-8
9. Matrices and Determinants
9.1 Matrices and Systems of Equations
9.2 Matrix Algebra
9.3 The Matrix Inverse
9.4 Determinants and Cramer's Rule
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Practice Test A
Chapter 9 Practice Test B
Cumulative Review Chapters P-9
10. Conic Sections
10.1 Conic Sections: Overview
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Practice Test A
Chapter 10 Practice Test B
Cumulative Review Chapters P-10
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences; Partial Sums
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles
11.7 Probability
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Practice Test A
Chapter 11 Practice Test B
Cumulative Review Chapters P-11
Answers to Selected Exercises
Credits
Index of Applications
Index
This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.
| 677.169 | 1 |
Beginning Algebra
The Lial series has helped thousands of readers succeed in developmental mathematics through its approachable writing style, relevant real-world ...Show synopsisThe Lial series has helped thousands of readers succeed in developmental mathematics through its approachable writing style, relevant real-world examples, extensive exercise sets, and complete supplements package. The Real Number System; Linear Equations and Inequalities in One Variable; Linear Equations and Inequalities in Two Variables: Functions; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Applications; Roots and Radicals; Quadratic Equations For all readers interested in Beginning Algebra.Hide synopsis
Description:Very good in very good dust jacket. Glued binding. Paper over...Very good in very good dust jacket. Glued binding. Paper over boards. 740 p. Contains: Illustrations. Audience: General/trade. Has "Used" sticker on back of cover but inside is perfect
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Get ready to master the principles and operations of calculus! Master Math: Calculus is a comprehensive reference guide that explains and clarifies the principles of calculus in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, the book helps clarify calculus using... more...
Suitable for those concerned with multiple integral variational problems and with elliptic partial differential equations, this book presents a comprehensive treatise of the theory of multiple integral variational problems. more...
The treatise De Rationis Sectione by Apollonius of Perge, which deals with a unique and difficult problem, is a remarkable, complex example of the study of the necessary pre-conditions for the existence of a solution. This volume presents the editio princeps of the text, which has only survived in an Arabic version. It is made accessible in the form... more...
its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps... more...
This new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content-driven, it provides an intermediate-level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics... more...
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GeoGebra is a learning app for all the students, teachers and people who work with mathematics on a daily basis, offering everyone comprehensive tutorials, powerful tools and flexibility that is unmatched by any similar program. The basis of the GeoGebra is a complete support for all the aspects of the mathematical fields of arithmetic, geometry, algebra and calculus, with tools that enable work with points, vectors, lines, conic sections and more. You can directly manipulate formulas, equations and coordinates, ability to investigate parameters by working with sliders, finding of symbolic derivatives, and work with many complex commands, such as root or sequence.
Main interface of GeoGebra is clearly focused to provide mathematic enthusiast easy access to all its tools that can be used by both high school students tall the way up to worldwide experts. This was precisely goal of GeoGebra' s creator Markus Hohenwarter, who released first version of this app in 2001. After more than decade of feature expansions and new tools, this extremely useful open source app is currently under leadership of Michael Borcherds, who led the mission to successfully port GeoGebra on many modern devices such as iPad, Android and Windows Phone. All versions of this Interactive geometry software support core features (dynamic geometry environment, built-in CAS, scripting, spreadsheet support) and secondary tools that enable any mathematician to extract everything from their own knowledge without being restricted by tools and need to spend a lot of time on manual calculations.
If you have firm grasp of mathematic, and you need to be in contact with daily for your studies, work or projects, then GeoGebra is a perfect freeware app for you.
GeoGebra Quick Facts:
Graphics, algebra and tables are connected and fully dynamic
Easy-to-use interface, yet many powerful features
Authoring tool to create interactive learning materials as web pages
Available in many languages for our millions of users around the world
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Starting at $46.67 7th edition with a publication date of 1/26/2006 Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. New! Side-by-side Example Solutions for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles. New! Checkpoints after each Example/Solution refer students to similar drills in the Section Exercises, allowing students to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book. New! Vocabulary Checks open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts. Exercise Sets have been carefully analyzed and revised to improve the categorization of problems from basic skill-building to challenging; improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications. New! Make a Decision applications--presented throughout the text at the end of selected exercise sets--are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format. Eduspace, powered by Blackboard, Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the College Algebra text. This content is paired with the recognized course management tools of Blackboard. For copyright 2007, two titles have been added to the Precalculus Series: Precalculus with Limits and Precalculus: A Concise Course. These titles enhance the scope of the series, making it even more flexible and adaptable to a variety of learning and teaching styles.
Table of Contents
Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving
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Math software
Listed below is the math software installed on the public computers in Bruno, Gorgas, Hoole, McLure, and Rodgers libraries. Click on the desired software to find its location, version, and any plugins.
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IIT Foundation MATHEMATICS Class 9IT Foundation MATHEMATICS Class 9 Description
About the Book :
A child with a strong foundation takes much less time to understand a subject as compared to other students. MATHEMATICS FOUNDATION CLASS 9 aims at providing the right foundation to the students as they enter class 11. This book will prove to be a stepping stone to success in higher classes and competitive exams like Olympiads, IIT-JEE etc. The book covers a very broad syllabus so as to build a strong base. The USP of the book is its style and format. The book is supplemented with "Do You Know," "Knowledge Enhancer," "Checkpoints," and "Idea Box." Another unique feature is the Exercise Part which is divided into 2 levels. The broad variety of questions covered are Short, Very Short, Long, Fill in the Blanks, True/ False, Matching, HOTS, Chart/ Picture/ Activity Based, MCQ's - one option correct, multiple options correct, Passage based, Assertion-Reason, Multiple Matching etc. Solutions to selected questions has been provided at the end of each chapter.
Discussion : IIT Foundation MATHEMATICS Class
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More About
This Textbook
Overview
This book introduces the fundamentals of 2-D and 3-D computer graphics. Additionally, a range of emerging, creative 3-D display technologies are described, including stereoscopic systems, immersive virtual reality, volumetric, varifocal, and others.
Interaction is a vital aspect of modern computer graphics, and issues concerning interaction (including haptic feedback) are discussed. Included with the book are anaglyph, stereoscopic, and Pulfrich viewing glasses. Topics covered include: - essential mathematics, - vital 2-D and 3-D graphics techniques, - key features of the graphics, - pipeline, - display and interaction techniques, - important historical milestones.
Designed to be a core teaching text at the undergraduate level, accessible to students with wide-ranging backgrounds, only an elementary grounding in mathematics is assumed as key maths is provided. Regular 'Over to You' activities are included, and each chapter concludes with review and discussion
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Intermediate Algebra - 2nd edition
Summary: This student-focused text addresses individual learning styles through the use of a complete study system that starts with a learning styles inventory and presents targeted learning strategies designed to guide students toward success in this and future college-level courses.
Students who approach math with trepidation will find that Intermediate Algebra, Second Edition, builds competence and confidence. The study system, introduced at the outset and used c...show moreonsistently throughout the text, transforms the student experience by applying time-tested strategies to the study of mathematics. Learning strategies dovetail nicely into the overall system and build on individual learning styles by addressing students' unique strengths. The authors talk to students in their own language and walk them through the concepts, showing students both how to do the math and the reasoning behind it. Tying it all together, the use of the Algebra Pyramid as an overarching theme relates specific chapter topics to the 'big picture' of algebra94 +$3.99 s/h
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Springfield, VA PhysicsThis material involves motion under constant acceleration and can involve application and manipulation of a set of non-linear equations. In principle, Algebra 1 and some modest extensions are all the math background that is needed for this part of physics. I find however, that some students - e served for two years on the executive committee of my fraternity. Once as the Vice President of Operations and once as the Vice President of Professional Programming. In both positions I gave frequent presentations to large groups (50 to 100) people.
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Computers are playing an increasing role in education. Write a program that will help an elementary school student learn multiplication. Use Math.random to produce two positive one-digit integers. The program should
Math Program - Java Beginners Math Program The greatest common divisor of two integers 16 and 24 is 8.
Develop the algorithm for finding the greatest common divisor of two numbers. Write a program that prompts the user to enter two integers and calculates
Summary: Math Class
Java Summary: Math Class
In this section we will study about the Match class of Java API.
Some basic math functions can be found in the Math class...;
double ar; // angle in radians.
x is any of int, long, float, or double.
Math
Summary: Math and java.util.Random Classes
Java Summary: Math and java.util.Random Classes
In this section we will discuss Math and java.util.Random classes.
Both these classes can be used for generating the random numbers.
Some basic math functions can be found in the Math
Java - Math class in Java
Java - Math class in Java
In this example you will learn about Math class. This example explains how you can use functions provided by the
Math class like E,
PI, round, abs
Introduction To Math Class In Java
Introduction To Math Class In Java
In this tutorial we will read about.... Math class is created inside the java.lang
package and the classes created inside... the application.
Class Declaration
public final class Math extends Object
Constant
JavaScript exp method
by using the Math object reference. In Math object we have some very
useful.... The exp() method of Math object returns the value of ex
, where "e"
Methods - OOP
.
A good example of a static methods in Java is the Math or Character... in the Math class. Cosine takes only one
(primitive) parameter, and it doesn't work
TeXlipse
closing of acrobat on Windows, smartkeys, reference hovers
and math commands... also. Some of the new things: more command completions, more math
modes, syntax
XML Interviews Question page9
, if the document type you use provides for math, and your users' browsers... other DTDs, such as ISO 12083 Math, or OpenMath, or one of your own making. Browsers which display math embedded in SGML existed for many years (eg DynaText
Randomizer
by using the random() method of the Math class and change them
into different... by the randomFloat() method by
using the round() method of the Math class. Now we
Intro Java help with Double
Intro Java help with Double I have to evaluate a math expression using double in Java. I can input the code fine for the expression, but I don't know how to view the answer that it gives me. help
Question in Java ??
Question in Java ?? Welcome every One ,I have Q in Java :
Write aprogram that print the falewing table using SQRT method in the Math Class?
Number squrfoot
java - Java Beginners
java i have to make a programm in java to multiply any number with 100 without using any math operator. To multiply with 100 no need of mathematical operators.
int result=Integer.parseInt(String.valueOf(num)+"00
Random in jsp
.
random() is
a method of Math class which extends java.lang package. The Math... we are going to make a use of random()
method of the Math class. We are using
For Loop/PHP
For Loop/PHP Write a class called math. It is to have one property called num. It also has one method called factorial. This method is to start...;Here is a java example that finds the factorial of a number.
public class math
how to write the program - Java Beginners
how to write the program WAP to create the report card user input Name, Class, Division, Roll no., Marks obtained in following subjects
Lang
Hindi
History
Geography
Math
Phy
Chem.
Bio
Eve
CSTA
Also has a back up
java
java write a complete java application to prompt the user for the radius of a sphere,and call method sphereVolume to calculate and display the volume of the sphere.use the Math.pow(radius)method and Math.PI constant of Math
Java - Java Beginners
Java How to make a multiple choice quiz in java,
1- Quiz program that answers questions about Math, Science and Arts.
2- Student selects the topic, the program presents a series of questions.
3- Student should answer
Java - RMI
Java Write and deploy a simple, Java RMI-based Client/Server application, in which the (multithreaded) Server serves requests of remote Java Clients for mathematical operations. This is a simple Math Service, which we'll refer
| 677.169 | 1 |
Mathematics: A Practical Odyssey - 7th edition
Summary: MATHEMATICS: A PRACTICAL ODYSSEY, 7E demonstrates mathematics' usefulness and relevance to students' daily lives through topics such as calculating interest and understanding voting systems. Well known for its clear writing and unique variety of topics, the text emphasizes problem-solving skills, practical applications, and the history of mathematics, and unveils the relevance of mathematics and its human aspect to130.53148.93 +$3.99 s/h
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May contain some highlighting. Supplemental materials may not be included. We select best copy available. - 7th Edition - Hardcover - ISBN 9780538495059
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I'm looking to work through "How to Solve it: Modern Heuristics" by David B. Fogel and Zbigniew Michalewicz. I need someone experienced in machine learning, data science, applied mathematics, or mathematical analysis.
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College Algebra Essentials-Text Only - 4th edition
Summary: Bob Blitzer has inspired thousands of students with his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations. Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical...show more183365166.5971.70 +$3.99 s/h
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Has minor wear and/or markings. SKU:9780321833655-3-0
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Reviews basic math skills and demonstrates their application to real estate. Each question is worked out in detail and has the corresponding answer keys, which cross reference the user back to the text.
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Publisher Comments:
Whether you're new to fractions, decimals, and percentages or just brushing up on those topics, CliffsQuickReview Basic Math and Pre-Algebra can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as
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CliffsQuickReview Basic Math and Pre-Algebra acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. Here are just a few ways you can search for topics:
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Jerry Bobrow, PhD, is an award-winning teacher and educator. He is a national authority in the field of test preparation. As executive directory of Bobrow Test Preparation Services, Dr. Bobrow has been administering the test preparation programs for most California State Universities for the past 27 years. Dr. Bobrow has authored more than 30 national best-selling test preparation books including Cliffs Preparation Guides for the GRE, GMAT, MSAT, SAT I, CBEST, NTE, ACT, and PPST. Each year he personally lectures to thousands of students on preparing for these important exams.
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MathematicsPc Calculator is a clever note and formula editor combined with an advanced and strong scientific calculator. Being an editor it is extremely user-friendly allowing all possible typing and other errors to be easily corrected and fast recalculated
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...(View More) by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)...(View More) engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
This simple example shows how algebra can be useful in the real world by exploring the question: Should Grandpa start receiving his Social Security benefits at age 62 or should he wait until age 65? This resource is from PUMAS - Practical Uses of...(View More) Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
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Prealgebra - 4th edition
Summary: Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. In this thorough review of arithmetic and geometry, the authors also introduce the fundamental algebraic concepts needed by students who intend to take an introductory algebra course. Tussy and Gustafson build the strong mathematical foundation necessary to give students confidence to apply their newl...show morey acquired skills in further mathematics courses, at home, or on the job39044317 -used book - book appears to be recovered - has some used book stickers - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front ...show moreor back ...show less
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As students progress in their educational endeavors, more knowledge and skill will be required for each level.This course will foster a development and understanding of functions and their graphs. Students will acquire skills in utilizing the Pythagorean Theorem to solve real-world problems.Students solve multi-step equations involving real numbers.Problem solving in the course includes modeling consumer applications with systems of equations.It develops other important mathematics topics including patterns, functions, geometry, measurement, and statistics.It provides remediation for students who are below grade level as well as enrichment for advanced students.
Text and Required Materials:
Mathematics Grade 8 published by Holt McDougal and corresponding workbook.
**This schedule may need to be adjusted depending on the needs of the students, testing schedule for MAP and PASS.
Evaluation of Student Progress:
Students will be assessed through teacher observation, class work, homework, quizzes, tests, and exams. Grades will be determined each quarter in the following manner.
• Homework will count as 10% of the grade. Home work will receive a grade of 100 if the student has put forth the effort to complete the assignment and make any corrections in class.
•Class work, Activities and other minor assessments count as 40% of the grade. This includes quizzes.
• Tests count as 50% of the grade. Tests will be given at the end of a unit in most cases. Some units will be broken into parts and tested individually.
• Showing work: Seeing student's steps is an important part in assessing their progress. It is through their work that I am able to find areas of strengths as well as their weaknesses. Students that do not show the necessary work will not receive credit for assignments. This policy also applies to quizzes and tests.
• Notebook: Each student should keep an organized notebook. These are checked periodically and recommendations are made for improvement.
Grading scale
93 – 100 A
85 – 92 B
77 – 84 C
70 – 76 D
Below 70 F
Teaching Methods and Strategies:
Students will be given challenging real-world application projects and assignments.High quality work is expected.Classroom activities will include authentic hands-on-activities, problem solving, projects, content based games and research.Students will work in cooperative groups and pairs, but will be expected to complete individual assignments in relation to the cooperative work.Formal assessment methods will include written exams, tests, and projects with rubrics, quizzes, and written reports.Informal assessment will include class content games, student response, and group discussion. Instructional activities are designed based on our district curriculum guide, state standards, and the Common Core Standards. Standards can be found at:
Presentation of Rules and Procedures:
A letter was posted on the teachers' web page the first week of school. This letter contains information regarding expectations, procedures, grading, materials needed, and behavior. The classroom rules are also posted in the front of the classroom and were discussed during the first week of school. Rules and procedures will be reviewed and discussed as needed.
Rules for Student Behavior
·I expect students to follow the school and district policies.
·Students will stay seated during class unless given permission otherwise.
·Students should have pencil, textbook, homework, and notebook on their desks at the beginning of class.
·It is the student's responsibility to make up missed work due to absences.
Proceduresfor Non-Instructional Routines:
Students are expected to be on time and to have all assignments and materials needed for the class. Attendance is taken at the beginning of the class period.As students enter the room, they should get their materials needed for the day, sharpen their pencils, be seated, and begin completing the assigned bell work. Roll is taken at the beginning of the class. Tardies are recorded in our attendance system and addressed through administration. Students are asked not to go to the restroom unless it is an emergency. Instructional time is very important.
All quizzes and class work/home work taken up for grades will be returned as soon as possible. Teacher generated tests will be returned to students. They must be signed by parents if the grade is below a "C". Students are to keep all returned tests, quizzes, and assignments in their math notebook. District level generated tests will not be sent home. Students will be given these tests back in order to assess their progress and mistakes, but these tests will not be sent home. Parents are welcome to look at these tests by making an appointment.
Extra help will be given as needed. In some cases I will let a student know that it would be in their best interest to arrange a time with me for extra help. If a student feels they are having some difficulties in a particular area, they need to sign up for a day on the sheet next to the door. Extra help time is usually scheduled before school at 07:45 on Tuesdays and Thursdays. If they cannot come before school due to transportation problems, then they need to speak with me so we can meet from 3:15 – 3:45 after school. Students staying after school need to make prior arrangements for transportation.
Homework Policy
Doing homework is essential to learning mathematical concepts. It gives students the opportunity to work independently, as well as reinforce and extend previously learned skills. Homework is checked daily at the beginning of class. The student is given points based on the work completed. All work must be shown.
Make-Up Policy:
Provisions for the make-up of school work missed during excused absences will be worked out with the teacher(s) concerned and should not exceed five (5) school days after the student returns to school.
Provision for the make-up of school work missed during unexcused absences may be approved only with permission of the principal. It is the responsibility of the student to make this contact prior to the absence.
There will be no make-up of school work missed due to out of school suspensions unless specified by an administrator.
Consequences For Violating Class and School Rules / Policies:
Positive consequences: caught doing good passes and other rewards
Negative consequences: Depending on the severity and number of occurrences the following consequences will be used - warning, student/teacher conference, sent to another classroom for time out, phone call to parent, detention, writing assignment to address the behavior, sent to guidance counselor, parent conference, or referral.
Severity Clause: For blatant misbehavior (fighting, extremely rude or crude behavior, etc.), a student will be sent immediately to the office with a referral.
Beginning of the year letter: A letter was posted on the web page during the first week of school regarding classroom rules and procedures.
Progress Reports: These will be sent home during each quarter for all students. Updated reports will be sent at others times that might be necessary. (Students grades suddenly dropping or a marked improvement in grades.) Updated progress reports will also be sent home with parent requests.
Report Cards: These will be sent home at the end of each quarter. (See information concerning the agenda below.)
Agenda: Student agendas will be used for daily communication when the parents and teacher have agreed that it is in the student's best interest. All parents are encouraged to use the agenda to communicate with the teacher. Parents are also encouraged to check their child's agenda on a regular basis for homework assignments and notes from the teacher. There is a calendar located in the front of the agenda which contains dates for progress reports and report cards.
Web Site: Students and parents may access my web site through the district at This site will have updated information about classes as well as weekly assignments.
E-mail: You may contact me via e-mail at [email protected].
Conferences: Conferences can be scheduled through the team leader, Ms. Robison, at the request of the parent. The teacher will also request conferences as the need arises.
Phone calls: Please feel free to call at any time with questions or concerns. (355-7022) If I am not available, leave a message. I will return your call as soon as possible.
| 677.169 | 1 |
Understanding Elementary Algebra With Geometry A Course for College Students
9780534999728
0534999727
Summary: Dr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York.
Hirsch, Lewis is the author of Understanding Elementary Algebra With Geometry A Course for College Students, published 2005 under ISBN 9780534999728 and 0534999727. Six hundred fifty Understanding Elementary Algebra With Geometry A Course for College Students te...xtbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $34.24, or buy new starting at $240.21.[read more]
Ships From:Ventura, CAShipping:StandardComments: 0534999727 Your purchase benefits those with developmental disabilities to live a better quality... [more] 05.[less [more business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[ALTERNATE EDITION: Missing components. Instructor Edition: Same as student edition with additional notes or answers. May include moderately worn cover, writing, markings or slight discoloration. SKU:9780534999810 Hirsch and Goodman offer a mathematically sound, rigorous text to those instructors who believe students should be challenged. The text prepares students for future study in [more]
ALTERNATE EDITION: Hirsch and Goodman offer a mathematically sound, rigorous text to those instructors who believe students should be challenged. The text prepares students for future study in higher-level courses by gradually building students' confidence without sacr.[less]
| 677.169 | 1 |
DVD Features:
Rated: G
Run Time: 20 minutes
Released: June 9, 2009
Originally Released: 2008
Label: am productions, llc
Encoding: Region 1 (USA & Canada)
Audio:
Dolby Digital 2.0 Stereo - English
Product Description:
This easy-to-follow teaching aid for algebra teachers explores the fundamental concepts of functions and relations with the use of a graphic calculator. The program leads viewers through a series of lessons, demonstrating the keystrokes involved in each example, and uses animations to illustrate ideas
| 677.169 | 1 |
Discrete Mathematics and Its Applications
The goal of this text is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, ...Show synopsisThe goal of this text is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The fifth edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the fourth edition, the text specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. This text is designed for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite6311631154.
Beware of international editions. The one my son received did not have the same questions in it as the american one and therefore we had to buy the american edition as his instructor required these questions be anwsered as part of his assignment
| 677.169 | 1 |
0768917 SAT Math Workbook, 1st ed (Peterson's Master Math for the SAT)
Peterson s New SAT Math Workbook provides targeted test preparation for the new SAT I exam that will be introduced in March 2005. This title is designed as a self-teaching text to prepare for the mathematics sections of the SAT. At the beginning of each chapter, there is a ten-question diagnostic test to guide the student s preparation throughout the book. At the end of each chapter is a retest that is similar to the diagnostic test. It also includes hundreds of practice problems covering geometry, algebra, fractions, and more, as well as expert test-taking strategies, flexible study planning, user-friendly design geared to the high school student, and answers with comprehensive explanations for all test items in an easy-to-use workbook format.
| 677.169 | 1 |
More About
This Textbook
Overview
People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.
Related Subjects
Table of Contents
Preface; Series foreword; 1. What is street mathematics?; 2. Arithmetic in the streets and in schools; 3. Written and oral arithmetic; 4. Situational representation in oral and written mathematics; 5. Situational and mathematical relations: A study on understanding proportions; 6. Reversibility and transfer in the schema of proportionality; 7. Reflections on street mathematics in hindsight
| 677.169 | 1 |
...
More About
This Book
stresses the use of both traditional and alternative arithmetic algorithms. The latter are introduced so as to provide the teacher with a means to enhance performance in the area of whole number arithmetic in such a way that the difficulties of the student are circumvented. Providing a range of arithmetic activities useful in both the general education and special education settings, the book addresses needs of students in both general education and special education.
Related Subjects
Meet the Author
John F. Cawley emeritus professor, Department of Educational Psychology, University of Connecticut and emeritus professor, Department of Learning and Instruction, State University of New York at Buffalo. Anne Hayes dean emeritus, University of Hartford Teresa E. Foley Instructor of Mathematics, Asnuntuck Community College, Enfield,
| 677.169 | 1 |
Express/Lin Equat/Inequal
This course provides a conceptual study of problems involving linear expressions, equations, and inequalities. Emphasis is placed on solving contextual application problems. Upon completion, students should be able to distinguish between simplifying expressions and solving equations and apply this knowledge to problems involving linear expressions, equations, and inequalities
| 677.169 | 1 |
Now in its eighth edition, this text masterfully integrates skills, concepts, and activities to motivate learning. It emphasises the relevance of ...Show synopsisNow in its eighth edition, this text masterfully integrates skills, concepts, and activities to motivate learning. It emphasises the relevance of mathematics to help students learn the importance of the information being covered. This approach ensures that they develop a sold mathematics foundation and discover how to apply the content in the real
| 677.169 | 1 |
This course is primarily
for students in mathematics, engineering the sciences and other areas requiring
strong mathematical backgrounds. The purpose is to give students a basic
understanding of the concepts of calculus of several variables.
| 677.169 | 1 |
Walter Zimmermann
I see mathematics as multifaceted, including concepts and principles, deductive reasoning, computational skills, visualization skills, and applications. Through problem solving, I endeavor to develop all of these aspects of the discipline in a balanced way. I try to proceed systematically from simple problems to more challenging ones and from concrete questions to more abstract ones. My approach to teaching is lecture-based, interspersed with opportunities for questions, discussion or short periods of individual work. I give frequent short quizzes, which I see as a valuable learning tool. I use graphing calculators where appropriate.
Most of my courses are calculus or calculus-based. I see these as a sequence in which each course should build on the previous ones and develop a foundation for the courses which follow. Students should gradually achieve a coherent grasp of calculus and advanced topics.
I've worked with other colleagues to develop the major in Applied Mathematics. My more advanced courses especially are designed to serve the goals of this major, which are to develop the concepts and tools used.
| 677.169 | 1 |
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