text
stringlengths 8
1.01M
|
|---|
Students are reminded that for those classes requiring a calculator, they need to purchase a TI-84+ (preferred)or a TI-84 Silver Edition Graphing Calculator. Now is the time to watch for back-to-school sales of these products! Please also know, the Pius XI Math Department participates in Texas Instruments' Rewards Program to get technology into the classroom. As such, students are asked to submit the TI Technology Rewards Points Symbol to their teacher this fall.
While the physical world we live in is finite, bounded, limited and measurable, the realm of mathematics is the opposite – infinite, unbounded, limitless and immeasurable. Because students arrive at Pius XI at many different levels of understanding, different skill levels and abilities, the mathematics department offers a full range of courses from Pre-Algebra to Advanced Placement Calculus. While a comprehensive four-year program is recommended for all students, those at a higher level are encouraged to participate in a unique peer-tutoring program to foster strong bonds among all levels of ability.
Students are introduced to both the historical and cultural roots of mathematics, as they learn to communicate this knowledge in oral and written form using mathematical vocabulary and symbols. In addition, skills in analysis, social interaction and decision-making are developed through the discovery process. On a technical level, graphing calculators and computers are integrated into select classes, and Geometry students can expect to use computers on a regular basis. The classroom environment overall promotes intellectual curiosity and a desire to become lifelong learners.
Incoming freshmen are placed in one of two levels of algebra, or accelerated geometry or PreAlgebra based on their placement score and the recommendation of the middle school teacher. Prospective students are invited to participate in the Eighth-Grade Math Competition.
Students will learn to:
Understand numbers and the important and powerful ways in which they are used, thus developing their numerical literacy skills.
Organize work and present mathematical procedures and results clearly, concisely, and correctly.
Communicate using numeric, algebraic and geometric approaches, deciding which is most appropriate given the specific information.
Select appropriate problem-solving strategies and apply them to a variety of situations.
Interpret theoretical and real-world data, make predictions and assess the validity of their predictions. |
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined... more...
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finiteComprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: "to present the mathematical analysis underlying probability results" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra... more...
In the past 50 years, discrete mathematics has developed as a far-reaching and popular language for modeling fundamental problems in computer science, biology, sociology, operations research, economics, engineering, etc. The same model may appear in different guises, or a variety of models may have enough similarities such that same ideas and techniquesPresents the mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. more... |
Precalculus: Concepts Through Functions, A Unit Circle Approach to Tr text embodies Sullivan/Sullivanrs"s hallmarks accuracy, precision, depth, strong student support, and abundant exerciseswhile exposing students early (Chapter One) to the study of functionsand taking a unit circle approachto trigonometry."IT WORKS"for instructors and students because it focuses students on thefundamentals:preparingfor class,practicingtheir homework, andreviewing. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function. |
Develop your knowledge and understanding of the learning of geometry particularly at Key Stages 2–4. This course integrates development of the core ideas of geometry with relevant pedagogical constructs and principles, and will extend your awareness of how people learn and use geometry. There is no formal examination: assessment is based on three tutor-marked assignments and an end-of-module assessment. To complete these assessments, you'll need access to learners of geometry at Key Stages 2–4, which could include adult learnersYou will learn
Entry
The course is open to everyone, though it particularly has in mind teachers, teaching assistants, home-school parents and special educational needs co-ordinators.
Your own knowledge of geometry should be at or above the level of a B on GCSE maths, or you could have studied Mathematical thinking in schools (ME620) or the discontinued courses ME624 or MEXR624.
It is recommended that you study ME620 before this course as it provides a useful background in mathematics education and you are more likely to successfully complete this Level 3 course.
If you are considering taking ME627 alongside another OU course, please bear in mind that the workload for ME627 alone is around 12 hours a week.
In order to complete the course assessments, you will need regular access to at least one other learner of geometry with whom to work on two tasks a week study materials are available in Adobe Portable Document Format (PDF). Components may not be available or fully accessible using a screen reader and mathematical, scientific, and foreign language materials may be particularly difficult to read in this way.
There are many diagrams in both the course book and the printed material to provide help with visualising aspects of geometry – these diagrams may present a challenge if you have impaired sight, so diagram descriptions can be made available. In addition, the computer element of the course requires manipulation of interactive geometry files such as those referred to in the National Curriculum for school mathematics. For students who find difficulty accessing these files, the course team has prepared alternative material in the form of 'imaginings'. The imaginings are available both in audio format and as printed transcripts course text book (with CD-ROM), two teaching units, a course guide, bookmark and a website.
You will need
You require access to the internet at least once a week during the course to download course resources and to keep up to date with course news. Access to interactive geometry software, such as Cabri Geometre or Geometer's Sketchpad will be helpful, but not compulsory There will be individual telephone tutorials rather than face-to-face group tutorialsThe end-of-module assessment takes the form of a 3000-word tutor-marked assignment. You will be given more detailed information when you start the courseI did this module after MEXR624 and ME624 (now replaced by ME620). The earlier modules were useful preparation.
The module ..."
Read more
"A great course for teachers and good resources for the pupils. Encourages rich tasks and ticks most of the boxes |
Math
Program
The math curriculum at Drew is designed to prepare our students for advanced math courses in college. Our core curriculum addresses the need for students to see problems algebraically, graphically, and verbally. We strongly feel that students not only need to be strong in the algorithmic side of math, but also feel comfortable with word problems. Thus applications are covered throughout the year. In addition, the department feels that students learn math best by doing math in the classroom. Most of our class time is spent working on new problems and reviewing older problems. We stress the importance of constant review and that mathematics is a never ending cumulative subject. We want all of our students to see the connections between math and other subject matters, and to be able to work comfortably in any situation requiring math.
Courses
Algebra 1
This course is an intense study of algebraic concepts with an introduction to functions. Particular areas of focus include linear and quadratics, solving equations of one and two variables, exponents, simplifying roots and radicals, as well as the property of numbers. The emphasis is on mastery through the repetition of topics throughout the year.
Geometry
This course covers the study of geometry from both a deductive and inductive approach. Students will learn geometric proofs as well as applications of geometry. The subject is rich in word problems, and the goal is to expose students to the usefulness of geometry in the real world. The course covers coordinate geometry and the connections with algebra as well.
Algebra 2
This course extends a student's prior knowledge of algebra. The course covers more advanced functions including rational, exponential, logarithmic and trigonometric. Matrices and vectors are also studied as they help students prepare for more advanced science classes.
Precalculus
Precalculus is primarily concerned with the study of functions and trigonometry. Mathematical notation, which was learned in the earlier core classes, is refined and expanded. Concepts such as domain and range are stressed. All of the basic functions are further entwined with applications – hence the students are constantly seeing how functions relate to the world around them. The goal is to prepare students for calculus.
Calculus
This is an introductory course into the subject of calculus. Limits and derivates are the main topics for the first semester, whereas the second semester will expand into the subject of integration. The pace of the course is much slower than the AP Calculus class and most of the class is devoted to applications. Because this is not an AP course, we can spend time making sure that the concepts are clearly understood before moving on to new material.
AP Calculus - AB
The AP Calculus course is modeled on the College Board AP curriculum and moves at a much faster pace than the Calculus course. This is a more theoretical class than the regular Calculus class, and hence there is more mathematical rigor. The topics included are limits, derivatives, and integrals. Upon successful completion of this course, students will be prepared to sit for the AP exam in May.
Statistics...and beyond
Although this course covers extensively statistics or "the science of data", it is also an in-depth look at Mathematical literacy in today's world. Students who wish to pursue humanities and the social sciences are strongly recommended to take this course as an elective. The pace is designed so that students can focus their energies on understanding the material and in turn appreciate the functionality of Mathematics in the world around them. Topics include probability, the Mathematics in voting and social choice, game theory, coding and cryptography, management science, finance and the economics of resources, and a glimpse into chaos theory. Students will gain not only a working knowledge of some very practical Mathematics but also a newfound appreciation of the integral role Mathematics plays in their lives. |
Mathematica
As the progress of scientific discoveries are being pushed further and further with the aid of computational power, it is becoming more and more apparent that computational and programming skill are something scientists in general have to equip themselves with. Thus, starting at the implementation of Integrated Science Curriculum in 2010, Mathematica became a compulsory lesson (taught in SP2171 Discovering Science) to all SPS students. Of course, Mathematica is not the only technical computation software available in the market. There are other softwares, e.g. Matlab, LabView, Maple, etc that you have probably heard and used before. Well, you may then ask particularly, "Why Mathematica?". Well,…
First of all, any NUS Faculty of Science students are entitled a FREE licensed copy of Mathematica (available for PC, Mac or Linux user) throughout their candidature. Please follow the instruction given here, to get your copy installed. Other softwares do not come FREE.
Secondly, apart from being a very good technical computation software, Mathematica supports excellent animated graphics, interactive user-interface and intuitive command lines, making it an excellent visually-engaging pedagogical tool, for instance (installation of CDF Player or Mathematica required): |
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Readership
Undergraduates, graduate students, and research mathematicians interested in mathematics.
Reviews
"This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. It is appropriate for either It could also be used as a starting point for undergraduate research topics or a place to find a short undergraduate seminar talk. This is a wonderful book that is not only fun to read, but gives the reader new ideas to think about."
-- MAA Reviews
"Summarizing, this is a "desert island book", a "coffee table book", a book to share with friends, colleagues and students, a gift for beginner and expert alike--in short, a wonderful addition to our personal, school and university libraries." |
A rigorous introduction to group theory and related areas with applications as time permits. Topics include proof by induction, greatest common divisor, and prime factorization; sets, functions, and relations; definition of groups and examples of other algebraic structures; and permutation groups, Lagrange's Theorem, and Sylow's Theorems. Typical application: error correcting group codes. |
K12 CURRICULUM REVIEWS, the best online traffic school palm beach traffic school
traffic school game
online automotive courses
pharmacy school courses
regional accreditation online schools
online business school programs
affordable online mba
how to become a home based travel agent
locksmiths courses
about online colleges
learning how to take pictures
child online learning
"CK-12 FlexBooks on Probability explains whether an event will or will not occur. Using the laws of probability, we can find the likelihood
of two events occurring together, not occurring, or a large variety of other combinations."
"In statistics, there are many discrete probability distributions. The binomial distribution is a discrete probability
distribution that describes the probability of success in a binomial experiment. Learn more with CK-12 Flexbooks"
"CK12 Flexbooks on Operations with polynomial explains Monomials and polynomials can contain numbers, variables, and exponents. They can be added, subtracted, multiplied,
divided, and factored, just like real numbers. There are a few special products of polynomials that are important to
know, such as the product of two binomials." |
interactive tutorial CD-ROM provides algorithmically generated practice exercises that are correlated at the objective level to the exercises in the textbook. Every practice exercise is accompanied by an example and a guided solution designed to involve students in the solution process. Selected exercises may also include a video clip to help students visualize concepts. The software provides helpful feedback for incorrect answers and can generate printed summaries of students progress. |
I don't know anything about your math background so I can't recommend anything for certain. However, if you have never taken calc, then I would def take math 103. Many students struggle with econ simply because they don't have the math background/skills so I think 103 would be helpful if you have absolutely no calc experience. I definitely think stat 101 is more applicable in science/business/other areas in general so I would take that if you feel that you already have a solid math background. I have no idea about the stat 101 curve but I believe that the math 103 curve is decent despite what many others may say. I started with math 114 (which is also part of the undergraduate series) and I remember that over 50% of students got some form of an A. I think that the 103 curve is prob a little harsher than that but still decent overall.
Stat 101 is a Wharton course. The College equivalent would be Stat 111. Both are intro stat courses, though Stat 101 claims to have a more business-focus. Both Stat 101 and 111 fulfill the same Quantitative Analysis requirement.
Math 103 is probably more useful because it's a pre-req for 104 which is a pre-req for 114. If you're going to minor in Econ, you'll need 114.
A lot of people take both Math 103/104/114 and Stat 111 in the College to fulfill the formal reasoning requirement and the quant. analysis requirement.
if you wanna take stat101 (wharton's intro to business stat) then you need math104 as a prerequisite. But if you wanna take stat111, CAS's intro to statistics, then you don't need any college level math as a prereq
So.....Math 103, then Math 104, then Math 114+Stat 101/111 to take more advanced econ?
Basically, yes. But keep in mind that taking Math 103, then 104, then 114 (or 115) is not optional if you're going to minor or major in Econ; it's a requirement.
Whether you take Stat 101 or Stat 111 is really your choice. They both fulfill the same requirement and are more similar than they are different (case in point, I took Stat 101 and my professor advised us to consult the Stat 111 textbook occasionally to review some concepts). People generally tend to agree that Stat 101 is a little more challenging, if only because of the curve, though.
I would say that it is a good idea to take Stat 101 instead of 111 if you're planning on dual degreeing or transferring to Wharton. If you don't end up getting in or decide against that plan, then at least it still fulfills your quant. requirement. If you do end up getting into Wharton, then you've already completed one of Wharton's requirement. The only disadvantage to taking 101 rather than 111 is that 101 is a little tougher. I wouldn't say it's much tougher, though. Stat is stat. |
Linear Algebra by Georgi E. Shilov Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, and moreChallenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.Products in Algebra
Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problemsOur Price: $11.95
On Sale!$8.96
Algebra by Larry C. Grove This graduate-level text is intended for initial courses in algebra that proceed at a faster pace than undergraduate-level courses. Subjects include groups, rings, fields, and Galois theory. 1983 edition. Includes 11 figures. Appendix. References. Index.
Our Price:$19.95
The Algebra of Logic by Louis Couturat In an admirably succinct form, this volume offers a historical view of the development of the calculus of logic, illustrating its beauty, symmetry, and simplicity from an algebraic perspective. 1914 edition.
Our Price:$37.50
The Algebraic Structure of Group Rings by Donald S. Passman "Highly recommended" (Bulletin of the London Mathematical Society) and "encyclopedic and lucid" (Bulletin of the American Mathematical Society), this book offers a comprehensive, self-contained treatment of group rings. 1985 edition.
Our Price:$29.95Our Price:$25.95Our Price:$16.95
Boolean Algebra by R. L. Goodstein This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
A Course in Linear Algebra by David B. Damiano, John B. Little Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter features multiple examples, proofs, and exercises. Includes solutions to selected problems. 1988 edition.
Our Price:$26.95
Elementary Matrix Algebra by Franz E. Hohn This treatment starts with basics and progresses to sweepout process for obtaining complete solution of any given system of linear equations and role of matrix algebra in presentation of useful geometric ideas, techniques, and terminology.
Our Price:$49.95Our Price:$12.95
Foundations of Galois Theory by M. M. Postnikov A virtually self-contained treatment of the basics of Galois theory. This 2-part approach begins with the elements of Galois theory and concludes with the unsolvability by radicals of the general equation of degree n is greater than 5. |
Summary of Content: The module introduces students to many concepts and techniques of mathematics that will be used in subsequent modules. Firstly the basic concepts of complex numbers, vector algebra and matrix algebra are established. Then these ideas are extended to vector spaces, linear transformations and inner product spaces. Throughout the emphasis is on developing techniques that are widely applicable.
Method and Frequency of Class:
Activity
Number Of Weeks
Number of sessions
Duration of a session
Lecture
22 Two lectures per week plus problem classes and tutorial support.
Method of Assessment:
Assessment Type
Weight
Requirements
Exam 1
80
2 hour 30 min written examination
Inclass Exam 1 (Written)
10
Inclass test 1
Inclass Exam 2 (Written)
10
Inclass test 2
Convenor:
Dr R Tew Professor I Dryden
Education Aims:
To give a concrete introduction to linear mathematics and associated techniques.
To develop skills, competency and confidence in using the range of techniques.
To consolidate pre-university knowledge of the techniques of linear mathematics.
Intellectual skills
apply complex ideas to familiar and to novel situations;
work with abstract concepts and in a context of generality;
reason logically and work analytically;
perform with high levels of accuracy;
transfer expertise between different topics in mathematics.
Professional skills
select and apply appropriate methods and techniques to solve problems;
justify conclusions using mathematical arguments with appropriate rigour;
communicate results using appropriate styles, conventions and terminology.
use appropriate IT packages effectively.
Transferable skills
communicate with clarity;
work effectively, independently and under direction;
analyse and solve complex problems accurately;
make effective use of IT;
apply high levels of numeracy;
adopt effective strategies for study. |
Welcome to your first taste of high school math. So what is algebra? Essentially its getting comfortable with our favorite number: X! No, that's not a typo! X is a number, you just need to find out what it is and algebra is what we use to solve for it!
It's more fun with our good friend, X and learning more tricks to utilize X. We also start to take a dip into calculus. Yep, that's right, we are going to learn a little bit about college math! Be proud and brave!
Geometry is essentially an analysis of shapes and angles. We will live in Euclidean Geometry, which means that the dimensions will make sense and could be constructed in our world. Warning, objects may not be drawn to scale! Play Geometry Jeopardy and you will have a blast!
Its time to put all the stuff you learned in Algebra I and II and Geometry to the test as we take on Pre-calculus. We will go head to head with parabolas, asymptotes and much more. Hunker down for a fight because we are taking this head on like a Spartan into battle! |
Discrete Mathematics and Its Applications
9780072930337
ISBN:
0072930330
Edition: 5 Pub Date: 0014 Publisher: Glencoe/McGraw-Hill
Summary: Discrete Mathematics and its Applications 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 r...elevance 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.The book is appropriate 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 prerequisite |
Calculus: an Overview - Paul Pollack
Written by a 16-year-old, this site-in-progress contains brief summaries of topics for the advanced high school student. Available pages include: Functions: a review; Limits: what they mean and how to find them; Integration practice problems; Taylor and
...more>>
Calculus Applets - Thomas S. Downey
These pages present interactive Java applets for teaching and learning single variable calculus. They use graphs and tables to illustrate concepts in calculus and allow the user to dynamically change the functions involved or the point on the graph that
...more>>
Calculus-Based Physics - Jeffrey W. Schnick
Calculus-Based Physics is a free (in electronic form) 2-volume physics textbook designed for an introductory college course. The book itself is provided in pdf and MS WordTM format. Calculus-Based Physics is also available in hard copy at LuLu.com at
...more>>
Calculus Ideas - Charley Hoye
A calculus course for the Web designed partly for those who have a hard time remembering 7X8, and partly for those who have finished a calculus course and are beginning to wonder what it was all about. It's plain…no programming wizardry…an invitation
...more>>
Calculus in Context - Five Colleges, Inc.
These calculus textbooks draw on computer technology to emphasize concepts over techniques, geometry over algebra, graphs over formulas, brute force over elegance, and numerical solutions over closed-form solutions. The authors of these calculus textbooks, Math - Kees Couprie
Algorithms for converting dates from one calendar to another and for calculating the dates of (religious) events. Also an Excel Add-In available for download.
The Calendar Zone - Janice McLean
A collection of links about calendars, organized by topic: celestial, cultural, geographic, historic, etc. Includes an extensive list of calendar software for a 3000 Years Calendar (look through Julian, Gregorian, Hebrew and Islamic calendars to see conformity
...more>>
California Mathematics Council (CMC)
A professional organization of educators dedicated to improving classroom instruction in mathematics at all levels. Goals: to foster excellence in school mathematics curricula and instructional programs, including assessment and evaluation; to promote
...more>> |
The Skills Check is a short survey which should take you no more than 3 minutes to complete. Once you have completed the Skills Check we provide you with a personal learning plan targeted to your personal study needs and goals.
More advanced help with maths
If you are studying at level 2 or 3, you might struggle with the level of skill assumed by your module material. The 'Maths for Science and Technology' booklet covers some of the most common areas of difficulty, namely indices, solving equations, scientific notation, units, significant figures, basic trigonometry and logarithms. It follows on from the 'Sciences Good Study Guide' (which is available from the OU WorldWide online shop) and assumes that you have read this.
Spend about 20 minutes working on the area that gives you most trouble, making sure to complete the activities to check your understanding.
The OU booklet 'Maths for Science and Technology' gives you further information on this subject. |
Short description (Read more) • Number and Algebra • Geometry and Measures • Handling Data In addition, there exists a Publications Guide. Our mathLoci Constructions and 3D Co-ordinates is a module within the Geometry and Measures principle section our Grades 6, 7 & 8 publications. It is one module out of a total of six modules in that principle section, the others being: • 2D Shapes and 3D Solids • Angles, Bearings and Scale Drawings • Transformations • Pythagoras' Theorem, Trigonometry and Similarity • Measures and Measurements (Less) |
Algebra Problem Solver
1.00 (1 votes)
Document Description
Get answers to all Algebra problems Solver online with TutorVista. Our online Algebra tutoring program is designed to help you get all the answers to your Algebra word problems giving you the desired edge in excelling in the subject.
To
Online Algebra Questions
Our
FromAdd New Comment
Mathematics is a subject that is included in every stream of education and its
problems gets tougher as student moves further in his studies. That's why proper
assistance in solving math problems is ...
The current market trend, inflation and job scarcity is at its peak. It is a good idea
to choose alternative career option and earn more money for a safe future. If you
are looking for peaceful yet ...
Get answers to all Algebra word problems online with TutorVista. Our online Algebra tutoring program is
designedBefore talking about linear programming, I would like to tell you the meaning of
"linear". Linear is a Latin word which means pertaining to or resembling a line.
In mathematics, linear equation means ...
In mathematics algebra plays very important role or we can say that the general
math that we use in our day to day life is all about algebra. Algebra, and
important math part consists of several ...
Content Preview
Algebra Problem Solver Get answers to all Algebra problems Solver FromThe digit can be arranged in 3 ways or 6 ways. We have already investigated 2 of these ways. We can now try one of the remaining 4 ways. One of these are n = 95 100n + 70 + 8 = 693 - 99n 199n = 615 After solving, we get n = 3 Answer: The unknown digit is 3. College Algebra Word Problem Solver Back to Top College Algebra problems Solver help students to solve the word problems step by step. They teach students how to understand the data given in the statement and solve for the value to be found out. The online Algebra tutors serve as Algebra Solver who would help students in interpreting the word problems. Let us go over a few important Math equivalents of English for numbers and algebra word problems so as to make the interpretation of word problems easier. * Add---- sum, total of, added to, together, increased by * Subtract-difference between, minus, less than, fewer than * Multiplication-of times, by a factor * Division-per, out of, ratio of, percent The above words are suggestive of the operations associated with them. Students can learn more in depth
about them on understanding Algebra problems Solver and tke the help of online Algebra Solvers. Thank You TutorVista.com |
Algebra I provides a formal development of the algebraic skill and concepts necessary for students who will take other advanced college-preparatory courses. In particular, the instructional program in this course provides for the use of algebraic skills in a wide range of problem solving situations. Topics include: properties of real numbers, solution sets, basic operations with polynomials, solving quadratic equations and systems, use of exponents, and introductory topics from statistics and probability. Students must earn a minimum C–average for each of the two semesters of Algebra I to qualify for Geometry. At the end of this course, the students will be prepared to take the Algebra I End-of-Course Assessment administered by the state of Indiana. |
Elementary Linear Algebra
9780132296540
ISBN:
0132296543
Edition: 9 Pub Date: 2007 Publisher: Prentice Hall
Summary: This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof. |
Information About:
Department of Math News
Kent State Dedicates New Math Emporium
Posted Sep. 19, 2011
Members of the Kent State University community celebrated the opening of the new Kent State Math Emporium on Tuesday, Sept. 13. The Math Emporium, a state-of-the-art computerized learning center, is located on the second floor of the University Library and is designed to help students learn math.
Robert G. Frank, Kent State provost and senior vice president
for academic affairs, cuts the ribbon dedicating the Math
Emporium. Among those helping is Andrew Tonge (far left),
chair of the Department of Mathematical Sciences at Kent State.
"The university has developed a specialized learning experience to equip students with the mathematical knowledge they will need on their path to graduation," says Robert G. Frank, Kent State provost and senior vice president for academic affairs. "The students will learn math by interacting with a team of instructors and the Web-based math software called ALEKS. The Math Emporium promises to make a significant impact on our first-year retention. For some students, it will give them confidence in their math skills to pursue careers that require math, such as nursing and finance."
At the Math Emporium, students will learn through an innovative, engaging and easy-to-use program designed to help them become comfortable and proficient in basic mathematics. The Math Emporium serves as the classroom for four classes: Basic Algebra 1, 2, 3 and 4. Prior to the beginning of school, students take a placement assessment to determine which math courses they need. Students who need additional math preparation to succeed in college will be matched with the appropriate course of study in the Math Emporium.
"Students will focus on learning exactly what they need to know at their own pace while their instructional team provides individualized coaching," says Andrew Tonge, chair of the Department of Mathematical Sciences. "The Math Emporium uses an adaptive software program, ALEKS, to determine what students already know. It then offers each student an individualized choice of paths forward. This enables them to complete the curriculum efficiently by always studying only material they are ready to learn. All students can then manage their study time to focus on actively learning precisely the information they need, with the aid of online help tools and an interactive e-book, together with one-on-one assistance from an instructional team."
"The Math Emporium's potential effect on student success is very exciting," Frank says. "In addition to this Math Emporium on our Kent Campus, we will have similar facilities on our Regional Campuses."
The Math Emporium features state-of-the-art technology with 247 computer stations in an 11,154-square-foot space. The facility also features bright, vibrant colors and comfortable furniture, making it an attractive and appealing environment.
The Math Emporium is staffed from 7:30 a.m. to 9 p.m. Monday through Thursday; 7:30 a.m. to 6 p.m. on Friday; 10 a.m. to 6 p.m. on Saturday; and noon to 8 p.m. on Sunday. Students also can access the program from any Web browser. |
You are here
Mathematics Secondary Media
Algebra 2 lesson: By developing a function to describe the annual cost of a refrigerator and given a function describing concentration of drug in the body, students relate the behavior of the graph of a rational function with the phenomenon it describes. Asymptotes and particular points become important information about the application.
Algebra 2 lesson: Using the CBL and the graphing calculator, students work in groups to collect data describing the freefall of an object over time. The data collected includes data not relevant and that must be eliminated, and data is shifted near the y-axis to make the intercept meaningful. The students describe the meaning of the coefficients. The experiment is run again with an object that has drag (like a hat) and a model is found. The follow-up problem works with the football data from the lesson: Football and Braking Distance: Model Data with Quadratic Functions.
Algebra 2 lesson: Using the definition of complex numbers and operations with complex numbers, students add, multiply, and graph with complex numbers using some sample items from the NC Algebra II Indicators. Once familiar with the operations and graphing, students iterate complex numbers in functions to determine whether the iteration stabilizes. With some experimentation, rules are developed that show patterns in stabilization that carry into graphs by special coloring schemes. The result is a fractal. Examples from the Julia Set and the Mandelbrot Set are shown.
Algebra 2 lesson: Concepts of composition are used to develop functions that describe volumes of pyramids with specific bases and combinations of special discounts when purchasing a car. The connection between study time and number of courses leads to a function using inverse function that can help students determine the number of courses to take for available weekly study time.
Algebra 2 lesson: Using rulers, students measure distances on a diagram to find a shortest path. They create ordered pairs and a scatterplot. With the motivation that the scatterplot has a clear message, the students develop a function that measures the distances using the distance formula. Based on the function, the shortest distance can be estimated and then considered on the diagram. A follow-up problem involving determining the best place to put a new Post Office is included.
Algebra 2 lesson: Data representing the period of a swinging pendulum versus the length of the pendulum can be best modeled by a square root function. Data and an appropriate model are both given to the students. Questions from the NC Algebra II Indicators require students to solve equations involving radical expressions. Solutions are also investigated from both a graphical and an analytical point of view.
Algebra 2 lesson: Students are given data to describe the trajectory of a football tossed from the tallest bleachers of a stadium. The data is fit with a quadratic function using least squares criteria. Given data extracted from page 288 of Glencoe's Algebra II book, students investigate braking distance versus speed of a car. Using quadratic least squares, the student finds a best-fit function for the data. Data is given on reaction distance versus speed of the car. When reaction distance is added to braking distance to find total stopping distance, students fit another quadratic function. A Follow Up Problem relates number of sides of a polygon with the number of vertices to create a quadratic function. |
Course Descriptions
Mathematics Course Descriptions
MAT-designated courses (with the exception of MAT101 and MAT102) qualify as Liberal Arts or Mathematics electives.
MAT101
Elementary Algebra with Lab - 3 Credits
This course develops the fundamental processes of algebraic thinking and provides students with the skills for further study in higher level algebra based courses. This course is integrated with an online mathematics program and mandatory computer lab sessions designed to further enhance the classroom experience. Topics include a study of the real number system, solving and graphing linear equations and inequalities in one and two variables, exponents, scientific notation, operations on polynomials, ratios, proportions, and basic factoring in a problem solving context. Course requires subscription to a supplementary online program. Graphing calculator will be provided for occasional use in class.
Prerequisite: Department recommendation.
MAT102
Intermediate Algebra - 3 Credits
This course builds upon algebraic skills learned in MAT101 or a similar experience and provides students with additional skills needed for further study in higher level algebra based courses. This course is integrated with an online mathematics program designed to further enhance the classroom experience. Topics include further development of the study of linear functions, solving absolute value equations and inequalities, solving linear systems for break-even analysis, working with polynomial functions, and further development of factoring skills, applications of quadratic functions, and simplifying rational and radical expressions. Course requires subscription to a supplementary online program.
Prerequisite: C or better in MAT101 or Department PermissionMAT106
Business Mathematics (elective offered in Spring of 2013) - 3 credits
This course, intended for the business major, surveys topics in elementary algebra, personal finance, probability, and statistics and is integrated with an online homework and tutorial program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics focus on real-life situations, decision making skills, and problem solving. Topics include solving algebraic equations, solving ratio and proportion problems, and applications involving percentage, simple interest, simple discounts, consumer credit, compound interest, future and present value, applied probability, descriptive statistics, investments, mortgages, and taxes. Some working knowledge of elementary algebra is expected. Course requires subscription to a supplementary online program. Scientific or graphing calculator strongly recommended.
A survey of mathematics topics all students need to meet with success in today's society. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics include a study of number systems, essential algebraic & geometric principles, sets and logic, counting principles, statistics, graphing, and data analysis. Optional topics may include networks, money, and voting principles. Course requires subscription to a supplementary online program. Scientific calculator recommended. Course is designed to prepare students for success on standard workplace competency assessments.
MAT120
College Algebra - 3 CreditsPrerequisite: C or better in MAT102 or Department Permission.
MAT130
Pre-Calculus and Trigonometry - 3 Credits
This course is a study of functions deeply embedded with real-life activities and integrated with an online mathematics program designed to further enhance the classroom experience. Topics include an overview of algebraic, exponential, logarithmic, rational, radical, and trigonometric functions as they are applied to daily life experiences. Course requires subscription to a supplementary online program. Graphing calculator required.
Prerequisite: MAT120, or MAT102 with Department Permission, or Department Recommendation.
MAT220
Statistics - 3 CreditsMAT223
Statistics II - 3 credits
This course is a continuation of introductory statistics with applications. Topics covered include inferences involving two populations, analysis of variance, linear regression analysis, multiple regression, forecasting, time series analysis, and elements of nonparametric statistics. This course is integrated with a state of the art online program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. Scientific or graphing calculator and access to a spreadsheet program is recommended.
Prerequisite: MAT 220 or Department permission.
MAT230
Quantitative Analysis - 3 CreditsPrerequisite: MAT120 College Algebra or MAT130 Pre-Calculus.
MAT250
Calculus I - 3 Credits
This course introduces differential and integral calculus of one variable. Topics include analytic geometry, functions, limits, derivatives, applications of derivatives, and anti-derivatives. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program.
Prerequisite: MAT130 Pre-Calculus or Department permission.
MAT251
Calculus II - 3 Credits
This course is a continuation of MAT250. Topics include the definite integral, the Fundamental Theorem of Calculus, exponential and logarithmic functions, techniques of integration, and applications. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. |
2011-11-02 11:00 - 11:45
Location: Ämnestorget för matematik - rum 1
Lecturers: Emmanuel Schanzer.
Description
Researchers and educators have viewed algebraic functions as a foundational concept in mathematics since the turn of the century, but many students struggle to master the concept. Starting in the 1960s, some have viewed computer programming as a vehicle for exploring functions, but the results have been mixed at best. This talk will use current research in the field of mathematical education and cognitive science to analyze previous attempts, and discuss the novel approach taken by Bootstrap, a curriculum that teaches children to program their own videogames using an algebraic programming language and mathematical activities to drive their learning. |
Basic calculus of one variable from an intuitive point of view. Topics include limits, continuity, derivatives and integrals of the elementary functions, Fundamental Theorem of Calculus, and applications. The focus is on understanding basic concepts and gaining basic computational skills. |
Complex Number Calculator Precision 45 - The Complex Number Calculator Precision 45 application was designed to be a complex number calculator and works with complex numbers, but also can be used as a real number calculator, that is a scientific calculator.The Complex Number Calculator...
MathCalc - The MathCalc calculate mathematical expressions. The expressions entered, you can save into formula lists. You can plot 2D charts by means tabular data, importing the data from files, or using Cartesian, polar or parametric functions.MathCalc run |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Engineering Problem Solving With C+ An Object Based ApproachChapter 5 Functions1FunctionsA program can be thought of as a collection of sub parts or sub tasks: input data analyze data output resultsIn C+ these sub tasks are called functions.2Funct
Kerry Is Criticized for Church DriveOctober 13, 2004 By DAVID D. KIRKPATRICK Liberal religious groups criticized Senator John KerryyestK M erday as politicizing religion by campaigning inAfrican-American churches. A spokesman for Americans United
Democrats Criticize Denial of Communion by BishopsMay 20, 2004 By LAURIE GOODSTEIN Forty-eight Roman Catholic members of Congress who areDemocrats have signed a letter to the cardinal archbishopof Washington, D.C., saying the threats by some bishops
Sampling of continuous-time signalsChap: 4.1-4.8; Pages: 140-201Jont AllenECE-310Allen April 19, 2004 p.1/45Periodic symmetryEvery function may be made -periodic with an overlap and add OLA operation and integer, the periodFunctions periodic in
Active Galactic Nuclei and Super-Massive Black Holes1 Units to be used throughout this Lab:Because dierent kinds of units are needed in this Lab Exercise, some conversions are listed below: 1 astronomical unit = 1 a.u. = average Earth to Sun distance =
AE 430 - Stability and Control of Aerospace VehiclesAircraft Equations of MotionDynamic StabilityDegree of dynamic stability: time it takes the motion to damp to half or to double the amplitude of its initial amplitude Handling quality of an airplaneO
Computational Geometry - Divide and Conquer Closest Pair In computational geometry, two well-known problems are to find the closest pair of points and the convex hull of a set of points. The closest-pair problem, in 2D space, is to find the closest pair o
Chapter 5Decision MakingManagement, by Williams South-Western College Publishing Copyright 2000Blast From The PastRational decision making can be traced back to Benjamin Franklin's "moral algebra" Frederick W. TaylorGscientific study of work Gscienti
70IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 5, NO. 1, JANUARY 2008RivWidth: A Software Tool for the Calculation of River Widths From Remotely Sensed ImageryTamlin M. Pavelsky and Laurence C. SmithAbstractRivWidth is an implementation in ITT Vis
HTMLI. Basics of HTML a. HyperText Markup Language i. HyperText 1. Connectedness of the internet 2. Notice this when "surfing" the net 3. Any page on the internet can link to any other page on the internet ii. Markup Language 1. Markup = Tags 2. Markup i
CWR 4101 HYDROLOGY 2nd TEST FALL 2004Administrative Instructions:1. There are 5 questions, do all 52. All work must be your own; cheating will result in a grade of "F" for the course and could result in addition action. All work must be done on this te
Report Lab Practice 3 Edge DetectionAuthor: Jay MehtaEdge DetectionIntroductionEdges in images are areas with strong intensity contrasts a jump in intensity from one pixel to the next. Edge detection of an image reduces significantly the amount of dat
Report Lab Practice 2 Image FilteringAuthor: Jay MehtaImage FilteringIntroductionDigital images can be processed in a variety of ways. The most common one is called filtering and creates a new image as a result of processing the pixels of an existing
ECE 4970 Homework Solutions 2.23a ( We want to find out the pre-envelope of g(t ) = ) . There are many ways to do this. I chose to do the problem in the frequency domain. Remember, G+ ( ) is the positive side of G(f). G(f) 2 G+(f)-1/21/21/2Question is
Calculus Review Definition - Derivative: The derivative of a function, F(x), is the instantaneous change of the function with respect to the instantaneous change in the variable(s). Another way of saying this is that the derivative is the slope of a tange
SENSORY PANEL METHODS I. INTRODUCTION A. What is Sensory Evaluation? Scientific discipline through which the sensory analyst evokes, measures, analyzes and interprets human responses to stimuli as perceived through the senses. B. How is Sensory Evaluation
CSES History and MotivationThe Climate Dynamics Group: 1988: Sarachik came to UW and headed the Experimental Climate Forecast Center (ECFC). 1988-1995: Research Proposals by Sarachik and then Battisti and Sarachik from the ECFC: 1993-The infrastructure g
Operating Systems2/18/2004Recap of the Last Class: DeadlocksBasic Memory ManagementnDeadlocksqFour characterizationsnHandling deadlocks:qqIgnore the problem and pretend that deadlocks would never occur. Ensure that the system will never enter
Memory [email protected] KuhnsApplied Research Laboratory, Department of Computer Science and Engineering, Washington University in St. LouisWASHINGTON UNIVERSITY IN ST LOUISWashingtonThe Big PictureCPU DRAMLow Address (0x00000000)
April 3, 2002Review - 1An independent source establishes voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit. The value of the voltage or current supplied is specified by the value of the independent source a
CHE 656 A ReviewSpring 2000 1. Overview of Model Predictive Control Model-based dynamic optimization, formulated on a moving time window, solved at each sample time after a feedback update of the model. Replaces, generalizes, and systematizes various ad
Tuesday, September 4, 2007 Maple Introduction Chad AwtreyCalculus with Analytic Geometry II MAT 271Maple IntroductionCommon Maple CommandsHere are a few Maple commands that are commonly used for calculus problems, with an explanation of what they do.
Maple Assignment 2Fall 2000 MTH 169 Due: Thursday, October 19, 2000, at the beginning of the problem session. Put your Name and the assignment number (in Text) on the top of the rst page. Clearly label each problem. You can discuss the assignment with yo
Quiz 1 for CSC 432: Database Management 100 points25 September 1996, 10:1511:05 AM June 20, 2000InstructionsIf you finish early, please try to remain seated or move out discreetly so as not to disturb others. This quiz is closed-book. However, a one-pa |
Calculus 2
MTH 2410
Basics
Office Hours
Textbook
Stewart, Essential Calculus, 1st edition, Brooks/Cole, 2007.
Computers and Calculators:
You will need either
a Laptop Computer, with TI-Interactive software (similar to a TI-83 calculator), or
a Graphing Calculator with function tables ( a TI-83 Plus or TI-83 is a good choice, especially if you will be taking a statistics course later; some other suitable calculators are TI-86, TI-89, TI-92).
General Information:
In this course we will cover the traditional material for a second semester including techniques of integration, applications of integration, series and sequences, parametric and polar equations, etc. We will often work in small groups in class. There will be several (3?) "hour-exams" and a final exam, as well as weekly quizzes to see how things are going. There will also be dialy assignments to hand in or to be done online. There will also be 3 mathematica assignments.
Grading
Tests will be worth 100 points each, Quizzes will be worth 100 points total, Homework and inclass assignments will be worth 100 points total, the Mathematica assignments will be worth 100 points, and the final will count for 20 percent of the total grade. Grading will then be on a 90-100 is an A, 80-90 is a B, etc |
Math Lab
Math Lab
About the Math Lab
What We Do
The COS Math Lab is a drop-in tutorial service staffed by a math instructor and student tutors. We can provide help for you in your math class, and are able to help with some questions from science courses as well.
How It Works
Bring your questions to the Math Lab staff! Or you can study in the Math Lab and ask questions as they arise. The goal of the Math Lab is to help you better learn and understand mathematics. This requires your active participation, so whoever is helping you will stop and discuss a topic with you instead of just working the problem for you.
How To Become Eligible To Receive Help In The Math Lab
To use the Math lab, students must enroll in EDUC 0670. That's it! There is only a $5 fee for the EDUC 0670 class (per semester) to cover costs of printing, but the tutoring and help is free.
Video
Weed Location/Contact
The Weed Math Lab is in the "loft" of the Academic Success Center (ASC) in the Learning Resources Center building (same general area as the Writing, Reading , and Computer Labs). For those not familar with the COS campus, see Math Lab Locations and maps. |
MATH 1012: Mathematics I
This course is a continuation of MATH1009. This course provides the student with advanced algebraic techniques and an introduction to trigonometry. Among the various topics presented are trigonometric functions and graphs, vectors, oblique triangles, exponents, radicals, complex numbers, and exponential and logarithmic functions.
Credits:4.5
Overall Rating:3 Stars
B
Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
Mathematics
This subject is required each year through tenth grade, or longer if
theModern Curriculum Press Mathematics: Level D
Subject: Arithmetic
Course Number: 56340
Suggested Grade Level: 4th
Authors: Richard Monnard and Authors: Royce Hargrove
Number of Pages: 351
Publisher: Pearson Education, Inc.
Academic Credit: None
Copyright: 1994
Elective Fee: None
Prerequisites: None
Course Materials: Workbook, teacher's guide, and 15 tests*
* Item published by Christian Liberty Press
Course Description: This course begins by reviewing facts regarding addition and subtraction and then presents topics such as multiplication of whole numbers, division by a one-digit number and by whole numbers, and working with decimals and fractions. Students are also introduced to measurement, graphing, probability, and geometry. A number of word problem sets are included.
Course Description: This course re-teaches and then reviews many of the concepts presented in Arithmetic 3 including the four basic arithmetic operations and multiplication and division of two-digit numbers. Area measure, estimation, elementary geometry, writing decimals as fractions, and solving equations are also taught. Fractions receive considerable attention, as do "proper and improper," finding the least common denominator, adding, subtracting, and multiplying. |
Summary: A text for a precalculus course for students who have completed a course in intermediate algebra or high school algebra II, concentrating on topics essential for success in calculus, with an emphasis on depth of understanding rather that breadth of coverage. Linear, exponential, power, and periodic functions are introduced first, then polynomial and rational functions, with each function represented symbolically, numerically, graphically, and verbally. Contains many ...show moreworked examples and problems using real world data. Can be used with any technology for graphing functions.
From the Calculus Consortium based at Harvard University, this comprehensible book prepares readers for the study of calculus, presenting families of functions as models for change. These materials stress conceptual understanding and multiple ways of representing mathematical ideas |
Basic College Mathematics - With Early Integers - With Cd - 07 edition
ISBN13:978-0132227490 ISBN10: 0132227495 This edition has also been released as: ISBN13: 978-0132230483 ISBN10: 0132230488
Summary: Basic College Mathematics with Early Integers is a new addition to the Martin-Gay worktext series. This text is designed for a 1-semester basic math courses in which an early introduction of integers is desired. Integers are introduced in chapter 2, and students continue to work with them throughout the text. This gives students ample opportunity to practice operations with integers and to become comfortable with them, prior to being introduced to algebra in chapte...show morer 7, Equations. |
the Laws of Logarithms
Once you have gone through the laws of logarithms, you can spend five minutes working a couple of problems on the board, like:
log5(x)=log5(3)log5(x)=log5(3)
and then
log5(x+1)+log5(x-1)=log5(8)log5(x+1)+log5(x-1)=log5(8)
The first establishes that if you have
log(this)=log(that)log(this)=log(that), then this must equal that. The second shows how you have to use the laws of logs to get into that form. (The OK students will answer 3. The better students will answer ±3. Only the very best will get ±3 and then realize that the −3 is, after all, invalid! But all of that is a detail, of course.)
Anyway, then there is the worksheet full of problems like that, which also gives good review of a number of old topics.
The thing is, this really isn't a whole day. Sneak it in when you have 15-20 minutes left in class. It doesn't matter whether it comes before, after, or in the middle of the next topic |
Book Description: Focuses on word problems to demonstrate practical applicability of algebra skills to real-world problems and standardized test problems. Each chapter covers one important concept, with the emphasison hands-on learning for problem-solving and mastering algebra skills. |
Unit specification
Aims
The aim of this lecture course is to introduce the basic ideas of calculus of several variables.
Brief description
Functions of several variables were briefly considered in first year calculus courses when the notion of
partial derivative was introduced. Although there are some similarities with the familiar theory of one real
variable, the theory for functions of several variables is far richer. For example, for functions of several
variables, the critical points might be maxima, minima or saddle points (which are minima in one direction and
maxima in another direction). A key idea is to generalize the definition of the derivative at a point to the
the derivative of a map f: Rn → Rm at a point a of
Rn. This is the Fréchet derivative, which is a linear map
df(a): Rn → Rm (often represented by a matrix whose entries are partial
derivatives) which gives the best approximation to the function at the point a. This derivative is used
in a number of very elegant and useful results, in particular the Inverse Function Theorem and the Implicit
Function Theorem, and is a key notion in the study of the critical points of functions of several variables.
The Fréchet derivative is an example of a differential 1-form on Rn and so naturally leads
on to an introduction to the basic ideas of differential k-forms. Differential k-forms are
fundamental in the integral calculus of functions of several variables and this is briefly considered.
Intended learning outcomes
On the successful completion of this lecture students should:
understand the notion of the limit of a function of several variables at a point and be able to find simple limits;
understand the notion of a continuous function of several variables;
understand the directional derivatives, the partial derivatives and the Fréchet derivative of a function of several
variables at a point; be able to find these; and understand the relationship between these notions;
be able to find the critical points on a real-valued function of several variables and determine the nature of non-degenerate
critical points using the Hessian matrix;
understand and be able the use the Chain Rule, the Inverse Function Theorem and the Implicit Function Theorem;
be able to apply the method of Lagrange multipliers to simple extremum problems with a constraint;
understand the notion of a differential k-form on an open subset of Rn; be able to evaluate
such forms at a point; be able to evaluate the wedge product of two forms and the derivative of a form; be able to evaluate line
intgrals of 1-forms and surface integrals of 2-forms over a surface parametrized by a rectangle.
Future topics requiring this course unit
The ideas in this course are used in many areas of pure and applied
mathematics. A natural follow on course unit is the level 3 Calculus on Manifolds.
Learning and teaching processes
Two lectures and one feedback tutorial class each week. Attendance at a weekly tutorial class is an essential part
of the course. A weekly problem sheet will be issued and other problems will be discussed in the tutorial classes.
Students should expect to spend at least four hours each week on private study for this course unit.
Assessment
A coursework test in first week after Easter (to be confirmed - Easter is very late next year so it may be before Easter): weighting 15%; |
Peer Review
Ratings
Overall Rating:
This is a tool to multiply two matrices. It also evaluates any polynomial in 2 variables where the variables represent two matrices or their inverses.
Learning Goals:
To multiply two matrices without having to perform any calculations.
Target Student Population:
Linear algebra students or college algebra students who are working on matrix multiplication.
Prerequisite Knowledge or Skills:
An understanding of matrices and the basics of matrix algebra.
Type of Material:
Simulation
Recommended Uses:
It can be used as a tool to quickly multiply matrices during in-class presentation or as a part of a homework assignment.
Technical Requirements:
Requires a "Java-enabled" browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This is part of a larger WIMS site that includes specialized calculators from several areas of mathematics. This learning object primarily calculates the product of two matrices. Other polynomials where the variables are the matrices or their inverses can also be evaluated. The learning object also has the ability to send the result to a companion learning object called Matrix Calculator that can further examine the result. The companion site gives the rank, determinant, eigenvalues, etc.
Concerns:
When there are fractions in the inverse matrix, the numbers overlap, making it difficult to read the actual numbers. There is a small typo in the instructions.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This calculator quickly produces the product or the evaluated polynomial. It can be used as a tool to quickly multiply matrices, so that the arithmetic does not get in the way of the learning. The site has links to Wikipedia explanations of the terms related to matrix multiplication and other sites that are less related.
Concerns:
It relies on Wikipedia links only for instruction. An instructor would need to create a worksheet with explanations and exercises in order for students to effectively learn from this tool.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The instructions are short and easy to follow. When a matrix is inputted incorrectly, there is a simple warning message that attempts to explain why the input was incorrect. When two matrices are of incompatible dimensions, there is an error message that states that the sizes are the matrices are not compatible. The import button that sends the result to the companion program is very simple to use and works perfectly. |
Course Goals and Philosophy
The purpose of this course is to revisit the content
of the elementary mathematics curriculum with the focus on
understanding the underlying concepts and justifying the solutions of
problems dealing with this material. The focus is not on being able to
perform the computations (the how to do it), although that is a
necessity as well, but on demonstrating an ability to explain
why you can solve the problem that way or why the
algorithm works that way. You will need to be able communicate your
explanations
both verbally and in writing with strict attention to the mathematical
accuracy and clarity of your explanation. You will have the chance
to work with mathematical concepts in an active, exploratory manner
as recommended by the National Council of Teachers of Mathematics
(NCTM):
Knowing mathematics means being able to use it in
purposeful ways.
To learn mathematics, students must be engaged in exploring,
conjecturing, and thinking rather than only rote learning of rules and
procedures. Mathematics learning is not a spectator sport. When
students construct knowledge derived from meaningful experiences, they
are much more likely to retain and use what they have learned. This
fact underlies the teacher's new role in providing experiences that
help students make sense of
mathematics, to view and use it as a tool for reasoning and problem
solving.
If you feel a need to review elementary school
mathematics, this is your responsibility. For this purpose, I
recommend reading our textbook and consulting with me outside of
class. For a reference on the content of elementary school
mathematics, here are the common core state standards
.
It is also the purpose of this
course to improve your ability to engage in mathematical thinking
and reasoning, to increase your ability to use mathematical knowledge
to solve problems, and to learn mathematics through problem
solving.
The emphasis in this course is on learning numerical mathematical
concepts through solving problems. You will often work with other
students for the following reasons: Group problem solving is
often
broader, more creative, and more insightful than individual
effort.
While working on problems with others, students practice putting their
mathematical ideas and reasoning into words. This ability to
explain
mathematics is clearly essential for future teachers. While
working
in groups, students learn to depend on themselves and each other
(rather
than the instructor) for problem solutions. In groups, students
can
motivate each other to excel and accept more challenging
problems. Motivation to persevere with a difficult problem may be
increased.
Socialization skills are developed and practiced. Students are
exposed to a variety of thinking and problem-solving styles different
from their
own. Interaction with others may stimulate additional insights
and
discoveries. Conceptual understanding is deeper and
longer-lasting when ideas are shared and discussed.
Participation
You are preparing to enter a profession where good
attendance is crucial and expected. It is important that you make
every attempt to attend class, since active involvement is an integral
part
of this course. Since much of the class is experiential, deriving
the
same benefits by merely examining someone's class notes or reading the
textbook would be impossible. Each class period you will be
working on activities with your group. If you are working in your
group you will receive
one participation point that day. If you also participate to the
class as a whole (answer a question, present a solution, ask an
insightful question or offer important relevant commentary) you will
receive two participation points for that day. If you are not
working in your group, you will receive no points for that day.
Working each day and never speaking in class will earn 80%.
Speaking every other day on which there is
an opportunity to speak will earn 95%. Scores between will be
scaled
linearly.
Weekly Questions
On Wednesdays, I will assign a question relating to
the topic for the previous week. They will be due approximately
once a month as indicated on the schedule. The goal of these
assignments is for you to write substantial explanations of the main
concepts presented in class. They will eventually be incorporated
into your final project. Before the final project, they will be
collected for completeness and marked with suggestions.
Assignments are due at the start of class and must be easy to read.
Late assignments will not be accepted.
These questions and papers will be graded on the
following scale
Question
(out of 2)
0 – missing question
1 – question attempted, but
incomplete work
2 – question addressed
seriously
and in depth
In order to provide you with extensive comments,
there may be delays in returning these papers.
Exams
Two in-class exams will be given. Their focus is
largely conceptual and problem solving based. You should be able to explain the concepts behind any
calculations, algorithms, etc. Material will come from lectures,
discussions in class, and the text. For example, you will need to be
able to explain clearly and with mathematical accuracy why we
can solve problems in certain ways or why various algorithms
or procedures work mathematically. You will also need to be able to use
and explain the use of the manipulatives relevant to the material.
In-class exams will take two days - the first day
devoted to a group exam, in which your group will complete an activity
much like those done in-class. You will submit one well-written
presentation of your findings from each group.
Individual exams will contain six questions: four of
the questions will be direct problems. Two of
the questions will be more open ended and ask you to explain key
concepts from class. The exams will be graded as follows:
you will receive 40 points for attempting the exam. You may earn
up to 10 points on each of the questions.
Make-ups for exams will be given only in extreme
cases with arrangements made with the instructor prior to
the exam or if there is a verifiable medical excuse or permission from
the Dean of Students. If you miss an exam and we have not made
arrangements prior to the missed exam, you must contact me before the
next class.
Final Project
This project will be a collection of
weekly question items that you will write up throughout the semester.
This collection
could one day be included in your professional portfolio to demonstrate
your level of mathematical understanding and preparation and your
ability to communicate mathematics in a clear and correct manner.
A complete, organised, well-presented compilation of all
materials is due on the last day of class. Your project will be
checked for inclusion of all assigned topics and will be evaluated
based on the clarity and accuracy of the explanations given as well as
the overall presentation (neat, easy to find sections and entries, easy
to read, well-written, & c). Somewhere in this portfolio you
must demonstrate appropriate uses of each of the manipulatives
used in class.
Feedback
Occasionally you will be given
anonymous feedback forms. Please use them to share any thoughts
or concerns for how the course is running. Remember, the sooner
you tell me your concerns, the more I can do about them. I have
also created a web-site
which accepts anonymous comments.
If we have not yet discussed this in class, please encourage me to
create a class code. This site may also be accessed via our course
page on a link entitled anonymous
feedback. Of
course, you are always welcome to approach me outside of class to
discuss these issues as well.
Math
Learning Center
This center is located in South Hall
332 and is open during the day and some evenings. Hours for the center
will be announced in class. The Math Learning Center provides free
tutoring on a walk-in basis.
Academic Dishonesty
While working on homework with one another is
encouraged, all individual write-ups of solutions must be your own. You are
expected to be able to explain any solution you give me if asked.
Exams will be done individually unless otherwise directed.
The
Student Academic Dishonesty Policy and Procedures
opportunity to make up missed work. You are responsible for
notifying
me no later than September 12 of plans to observe a holiday.
Postscript
This is a course in the mathematics
department. This is your mathematics content course. In
this course, you will develop a mathematical background necessary in
order to teach elementary school students. You will deepen your
understanding of gradeschool mathematics topics and connections.
You will not be learning how to teach mathematics to children, that is
the purpose of
your methods course in the school of education. As a
mathematician, I am trained to teach you mathematics, and I will do
that. I am not trained to teach you how to educate, and that is
not the goal of this course. Please keep this in mind.
We will be undertaking a great
amount of interactive group work in this course. You may
view these as games. If you come in eager to play, then you
will be more likely to be successful and perhaps occasionally enjoy
the games. If you come in saying "I don't want to play this
stupid
game," we will all be annoyed and frustrated, and the course as a whole
will be less successful. Please play nicely.
Out of necessity, I am more formal in class and more
personal out of class. If you ever want
additional help, please come to see me either during my office hours,
at an appointed time, or by just stopping by (I am frequently in my
office aside from the times that I will certainly be there). It
is important that you seek help when you start needing it, rather than
when you have reached desperation. Please be responsible.
Teaching is one profession where you have direct
impact on hundreds of lives. It is truly
an incredible responsibility. It is vitally important that
teachers set high expectations for themselves and their students.
Daily preparation of interesting, instructive lessons for twenty-five
or more active children of varying aptitudes is extremely
challenging.
I am dedicated to helping you prepare for this exciting career, and
will try to help you reach your full potential. Best wishes for a
challenging and fulfilling semester.
Schedule (This schedule is subject to change, but I
hope to hold mostly to this outline.) Two numbers separated by a
period refer to explorations that we will be studying that day in
class.
August 29 Introduction
31
8.8
September 2
8.8
7
8.1
9
8.4
12
8.5
14 8.7
16 8.9
19
8.10 WQ due
21
8.12
23
8.13
26
8.14
28
8.17
30
exam
October 3 exam
5
9.1
7
9.1
12
9.4 WQ due
14 9.4
17 9.6
19 9.7
21 9.9
24 10.5
26 10.7
28 10.11
31 10.12 WQ due
November 2 10.15
4 10.17
7 10.18
9 exam
11 exam
14 7.1
16 7.2
18 7.2
21 7.3 WQ due
28 7.12
30 7.13
December 2 overflow
5 7.15 WQ due
7 7.19
9
12 Review, Final Project Due
Friday, December 16 12N - 3p
Final Exam
Learning Outcomes
Upon successful completion of Math 141 - Math Concepts for Elementary Education II a student will be able to:
Probability and Statistics
• Design and implement a simulation to estimate experimental probability
• Calculate probabilities experimentally and theoretically.
• Recognize which events are equally likely and
which are not and calculate probabilities based on this knowledge.
• Recognize events that are mutually exclusive
and those that are not and calculate probabilities based on this
knowledge
• Use complementary events to solve probability problems
• Use probability to solve problems and make decisions.
• Model multistage experiments using tree diagrams
• Model and compare experiments with and without replacements
• Recognize and use dependent and independent events to solve probability problems.
• Use geometric probability to solve problems
• Create simulations to analyze problems in which experimentation is impossible or impractical.
• Develop interesting and relevant probability
experiments and games for children of varying abilities and backgrounds.
• Use odds and expected value to solve problems and made education decisions.
• Explain the connection between probability and odds.
• Differentiate between permutations and combinations and solve problems using this knowledge.
• Solve permutations and combination problems involving like objects.
• Distinguish between and interpret pictographs,
line plots, stem-and-leaf plots, histograms, bar graphs, circle graphs,
box-and-whisker plots, and scatter-plots
• Create stem-and-leaf plots, box-and-whisker plots and circle graphs
• Compute mean, median, and mode and evaluate their usefulness in given circumstances.
• Find outliers, range, and quartiles, variance, and standard deviation
• Interpret standard deviation tables
• Calculate how addition of data changes the mean
• Evaluate how outliers effect mean
• Evaluate abuses of statistics with regard to data collection and displays
Geometry and Measurement
• Name the undefined terms of points, lines, and
planes that are basic to geometry and state their properties.
• Model, illustrate, and symbolize geometric terms and concepts
• Differentiate between plane and solid geometry.
• Use paper folding and construction tools to
explore geometric properties of lines, angles, and polygons.
• Use geoboards and other manipulatives to explore geometric concepts
• Make conjectures based on observations and explorations and justify, prove, or defend the conjecture.
• Recognize the difference between a justification and a proof.
• Classify polygons according to their properties.
• Explain the difference between measuring tools and construction tools.
• Differentiate among acute, right, obtuse, and straight angles.
• Compare and contrast polygons to create a hierarchy.
• Use organized lists and sketches to ensure
that all possible cases have been accounted for using the given in a
problem.
• Demonstrate, model, and illustrate geometric concepts for beginning learners.
• Prove theorems and conjectures for more advanced learners.
• Explore definitions and properties of
perpendicular and parallel lines and use the knowledge to solve
problems.
• Verify that the sum of the measures of the
interior angles of a triangle applies to all triangles whether they are
acute, right or obtuse.
• Prove that the sum of the measures of the
interior angles of a triangle is 180 and that the sum of the interior
angles of a convex polygon having n sides is (n-2)*180.
• Prove that the sum of the measures of the
exterior angles (one at each vertex) of a convex polygon is 360.
• Using modeling rather than memorization to
determine the sum of the measures of the interior angles of a convex
polygon with n sides.
• Solve problems that require combinations of geometric concepts.
• Visualize three dimensions figures in order to
count the number of faces, vertices, edges, and diagonals associated
with these figures.
• Define and differentiate between regular polygons and solids and those that are not regular.
• Use knowledge of nets to determine
characteristics of the unseen sides of a cube given a net of the cube.
• Model nets for solids other than cubes.
• Sketch and use networks to solve problems.
• Recognize congruence and apply the knowledge to solve problems.
• Verify that triangles are congruent using s.a.s., a.s.a., s.s.s
• Verify that a.a.a is not sufficient to prove triangles congruent
• Use construction tools to perform elementary constructions.
• Use constructions to illustrate triangle congruences and similarities
• Use a Mira and paper folding for constructions
• Verify the Pythagorean theorem using construction and scissors
• Recognize the converse of a theorem
• Use the Pythagorean theorem and its converse
• Find surface areas of geometric solids
• Find volumes of geometric solids
• Verify the conversion factor between Centigrade and Fahrenheit
• Perform translations, reflections, and rotations by constructions, using dot paper and tracing paper
• Perform compositions of transformations
• Perform size transformations
• Analyze figures to determine symmetries
• Tessellate a page using a combination of transformations
• Discover properties of altitudes and medians of triangles.
• Prove or verify that constructions actually accomplish the required outcomes
• Discover and list properties of quadrilaterals
• Discover, list, and use properties of similar triangles
• Separate a line segment into n congruent parts by construction and by using lined paper
• Use the Cartesian coordinate system to determine slopes of lines
• Use the factor/label method for measurement conversions
• Use dot paper to find areas
• understand measurable attributes of objects
• identify the units, systems, and processes of measurement
• apply appropriate techniques, tools, and formulas to determine measurements
• Use indirect measurement to solve problems
• Justify area formulas for triangles, parallelograms, and trapezoids
• Find areas of regular polygons |
Curryed Away: Carrying Curry Education Away and Into the Classroom
Posts Tagged 'Algebra'
The lessons preceding this one focused on the concept of rates of change and slope. The students learned how to write equations of lines and how to switch between graphical (graphs) and algebraic (equations) representations of the same model. This lesson allows the students to apply that knowledge to a real-world situation, using data to create graphs, write equations, assess reasonableness, and make predictions. The differentiated lesson will include an array of different types of data depending on student interest and readiness level. Some students may choose to use Red Cross data for their Excel activities if the advanced organizer interests them, but they are allowed to choose the data that they use. The technology used in this lesson is a good way to help the students visualize the material. It will also introduce them to tools that may prove useful in other aspects of their lives in and out of school. (In a school where these technologies are not available, other visual aids can easily be supplemented.) The visual aids and technology will help engage student interest, as well as help the students to develop some practical skills that may prove necessary in the "digital age." |
Topic Study Groups 293 TSG 1: New development and trends in mathematics education at pre-school and primary level
298 TSG 2: New developments and trends in mathematics education at secondary level
303 TSG 3: New developments and trends in mathematics education at tertiary levels
307 TSG 4: Activities and programmes for gifted students
311 TSG 5: Activities and programmes for students with special needs
315 TSG 6: Adult and lifelong mathematics education
319 TSG 7: Mathematics education in and for work
323 TSG 8: Research and development in the teaching and learning of number and arithmetic
327 TSG 9: Research and development in the teaching and learning of algebra
331 TSG 10: Research and development in the teaching and learning of geometry
337 TSG 11: Research and development in the teaching and learning of probability and statistics
341 TSG 12: Research and development in the teaching and learning of calculus
346 TSG 13: Research and development in the teaching and learning of advanced mathematical topics
351 TSG 14: Innovative approaches to the teaching of mathematics
355 TSG 15: The role and the use of technology in the teaching and learning of mathematics
359 TSG 16: Visualisation in the teaching and learning of mathematics
363 TSG 17: The role of the history of mathematics in mathematics education
368 TSG 18: Problem solving in mathematics education
373 TSG 19: Reasoning, proof and proving in mathematics education
377 TSG 20: Mathematical applications and modelling in the teaching and learning of mathematics
382 TSG 21: Relations between mathematics and other subjects of science or art
388 TSG 22: Learning and cognition in mathematics: Students' formation of mathematical conceptions, notions, strategies, and beliefs
394 TSG 23: Education, professional life and development of mathematics teachers
399 TSG 24: Students' motivation and attitudes towards mathematics and its study
402 TSG 25: Language and communication in the mathematics classroom
407 TSG 26: Gender and mathematics education
412 TSG 27: Research and development in assessment and testing in mathematics education
417 TSG 28: New trends in mathematics education as a discipline
422 TSG 29: The history of the teaching and the learning of mathematics
Notes
All papers of the proceedings are available for downloading at
including the 64 papers based on the regular lectures.
According to the editor's foreword, it has not been possible to include reports on several other important Congress activities such as the five national presentations by Korea, Mexico, Romania, and Russia, and the Nordic host countries (Denmark, Finland, Iceland, Norway, and Sweden), the 46 Workshops, the 12 Sharing Experiences Groups, the more than 220 Posters, the five ICMI Affiliated Study Groups, and the several informal meetings.
The closing address was given, as usual, by the Secretary General of ICMI, Bernard Hodgson. Among the various innovations of this congress, he particularly mentions the creation of five so-called Survey Teams, each having as a mandate to survey the state-of-the-art with respect to a certain theme or issue, paying particular attention to the identification and characterisation of new knowledge, recent developments, new perspectives and emergent issues.
Participants numbered about 2.300, from nearly 100 different countries.
One volume, format about 24 cm x 17 cm; 560 pages and a CD. The CD has all the contents of the volume, and also includes the 64 papers based on the Regular Lectures (of which there were 74). |
math911 for High School Math Mastery our child.
.
Professor Martin Weissman has developed math911, a computer based product that covers all the typical topics for several high school level math courses. The program is NOT fancy nor does it have the feel of a video game like some programs for younger students. This is more about making sure the student can do the problems with success achieved when they've consistently answered correctly.
Unlike a traditional school approach, you don't get a bad grade for missed problems. Instead, you get more problems to do until you can do it well. Many educators are seeing the benefit for a mastery approach. And, from several years and different boys learning under my watchful eye, I can say that they fair better when they do not start considering themselves failures and therefore unable to ever do math well.
While there is no textbook supplied with math911, the topics covered would allow you could use it as a complete program. math911 provides step by step solutions with explanations for all problems. After clicking on see solution, that button changes its caption to see all steps. So, it is possible to have them learning as they work through the program or use it to check competency if using in conjunction with a textbook.
About Professor Martin Weissman:
Professor Martin Weissman has been teaching Mathematics for nearly 50 years. Passionate about the subject and fueled with the desire to help students overcome their fear of Mathematics and to master it, he developed the Math911 tutorial software.
Our Thoughts about math911:
P has only been doing review with the introductory algebra right now. His current learning plan had just geometry for math this year. However, we've made the decision to double up on math this school year so he's eligible for a summer program he wants to do next year and that means Algebra II has to be completed. So, he's going to be digging into the Intermediate Algebra Course soon.
We've also used it just on a single computer for the moment. Our family is setting up a network drive, though, and I plan to spend some time getting math911 installed on the network later this year so R can also be using the program.
I also took some time to test my abilities on that introductory algebra course and was pleased with the simplicity of the program as well as the breadth of topics covered. I'm also hopeful that the younger boys will enjoy this program when they are ready for it, even though they are more drawn to the colorful and action packed programs that look more like a video game. I also like that they offer free updates as they become available and make themselves available for technical support issues. There are plenty of options out there for educational programs, but not all provide great customer service and support.
Interested in using Math911 in your home? Here are your options:
1. The math911 Standard Version contains a complete Introductory Algebra Course (Algebra 1) and can be downloaded from No credit card nor Rebate required.
Professor Martin Weissman share a bit about the Activation Codes for Premier, Premier Password, Network Password. Upon purchase ($49.95) you should: 1. Click on Register button and email us the Registration Codes 2. Identify themselves as a home schooler. 3. They will receive a reply email with ALL Activation Codes for all versions listed below: a) Premier Version (one user no password) b) Premier Password (Multiusers with Passwords) c) Network Version (Multiusers with passwords) 4. Users can switch between versions by clicking the REGISTER button and entering the codes for the desired version. 5. Passwords are generated by the software.
Final opinion? This is a no frills program that will cover the typical topics for algebra in high school as well as some trigonometry and statistics. Considering that you can use it with multiple children for more than one year of math and not have to pay for updates later, the $49.95 for the download is quite appealing |
Operations on Functions
In this lecture you will learn Operations on Functions. After a quick introduction, our instructor will guide you through Arithmetic Operations before diving into Composition of Functions and how Composition is Not Commutative.
This content requires Javascript to be available and enabled in your browser.
Operations on Functions
The composition of
f and g exists only if the range of g is a subset of the domain of
f.
The composition of
f and g is almost never equal to the composition in the reverse
order.
Operations on Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth and twentieth century mathematicsArthur Cayley and the first paper on group theory / David J. Pengelley --
Putting the differential back into differential calculus / Robert Rogers --
Using Galois' ideas in the teaching of abstract algebra / Matt D. Lunsford --
Teaching elliptic curves using original sources / Lawrence D'Antonio --
Using the historical development of predator-prey models to teach mathematical modeling / Holly P. Hirst --
How to use history to clarify common confusions in geometry / Daina Taimina and David W. Henderson --
Euler on Cevians / Eisso J. Atzema and Homer White --
Modern geometry after the end of mathematics / Jeff Johannes --
Using 20th century history in a conbinatories and graph theory class / Linda E. McGuire --
Public key cryptography / Shai Simonson --
Introducing logic via Turing machines / Jerry M. Lodder --
From Hilbert's program to computer programming / William Calhoun --
From the tree method in modern logic to the beginning of automated theorem proofing / Francine F. Abeles --
Numerical methods history projects / Dick Jardine --
Foundations of statistics in American textbooks: probability and pedagogy in historical context / Patti Wilger Hunter --
Incorporating the mathematical achievements of women and minority mathematicians into classrooms / Sarah J. Greenwald --
Mathematical topics in an undergraduate history of science course / David Lindsay Roberts --
Building a history of mathematics course from a local perspective / Amy Shell-Gellasch --
Protractors in the classroom: an historical perspective / Amy Ackerberg-Hastings --
The metric system enters the American classroom: 1790-1890 / Peggy Aldrich Kidwell --
Some wrinkles for a history of mathematics course / Peter Ross --
Teaching history of mathematics through problems / John R. Prather.
Abstract:
Reviews
Editorial reviews
Publisher Synopsis
'Using the history of mathematics enhances the teaching and learning of mathematics. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediateadoption in the classroom and proven examplesto motivate innovation by the reader.' L'enseignement mathematiqueRead more... |
Product Synopsis
Oxford A Level Mathematics for Edexcel takes a completely fresh look at presenting the challenges of A Level. It specifically targets average students, with tactics designed to offer real chance of success to more students, as well as providing morestretch and challenge material. This Core book includes a background knowledge chapter to help bridge the gap between AS and A2 study, as well as a free CD containing a wealth of further practice material and worked solutions |
Welcome to the Math Circle
The Fall 2013 session will start on September 28th, 2013. There will be a very limited number of spots for new students. Please check back the web page in mid-late July for registration information.
Los Angeles Math Circle (LAMC) is a top-tier math circle open to elementary, middle and high school students interested in mathematics and eager to learn. LAMC is a program of the Department of Mathematics at UCLA and is supported by the National Science Foundation, the Boeing Employees Community Fund, Raytheon, a gift from the Glickman family, and math circle families donations.
Following the traditions of Russian and Eastern European math circles, the program focuses on showcasing the beauty of mathematics and its applications, improving problem solving skills, preparing students for a variety of contests and competitions, creating a social context for mathematically inclined students as well as attracting students to math-related careers.
The topics we cover are as varied as advanced plane geometry, elementary number theory, fractals, combinatorics, game theory for the older students, logic, counting techniques, basic combinatorics for the younger ones. The main goal is to learn wonderful mathematics not covered in a typical school curriculum but accessible to the mathematically inclined students. Another goal is to actively engage students in problem solving and to learn effective problem solving strategies. To get an idea of what we are doing, please look at the titles and descriptions of past meetings which are available on our "Circle calendar" for the current year and on our "Archive" page for previous years.
Math Circle Structure
In 2012-2013, Math Circle will have the following levels of participation:
High School Circle (grades 8-12; MS 6221), led by Mike Hall and Yingkun Li;
All Math Circle meetings take place on Sunday afternoons at UCLA.
Enrollment for Fall 2012
Please apply for Fall 2012 by going to "Apply to LAMC" on the left toolbar. Please submit your complete application before August 20th. We expect that the number of applicants will greatly exceed the number of spots we have in the math circle. Please be sure to answer all the questions in the application. While given some priority, previously enrolled students do not automatically get a spot in the math circle and need to go through the same application process.
Important Note: Math. Sci. Building Access
Starting in early April 2011, the Mathematical Science Building will be locked on Sundays. The glass doors on the 5th floor (entry from the breezeway with vending machines) should be unlocked during the times of the math circle. However, all other doors in the building will be locked. If you are accustomed to entering the building through other doors, please make sure that you know how to enter through the doors on the 5th floor. Please see our Directions Page for more information.
Please refer to FAQs if you have questions about the proper placement (choice of group) and other questions related to math circle.
Contact LAMC
If you have any questions or comments, please write to Dr. Olga Radko, director of the Los Angeles Math Circle, at [email protected] after consulting the FAQs.
If you would like to provide anonymous feedback on the circle please use "Contact us" form on the left toolbar. Keep in mind that if you want to receive an answer to your comments you need to provide a return address. |
This review of arithmetic and elementary algebra is designed to prepare the student to study MATH 100 (Mathematical Sampler) or MATH 101 (Finite Mathematics). The course is designed as a self-directed study experience. The student will have access to textbook explanations and online resources to gain mastery of the material. Appropriate testing is done with the tutors in the Mathematics Resource Center (MaRC). A nominal registration fee is charged. |
Discrete Mathematics With Application - 4th edition
Summary: Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such conce...show morepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. ...show less
2010 Hardcover172.80 +$3.99 s/h
LikeNew
BookCellar-NH Nashua, NH
0495391328 |
Financial Mathematics
This practical two-day program gives you a working knowledge of mathematics you need within financial markets trading. A hands-on combination of lectures and practical exercises guide you through the use of basic algebra, statistics, calculus and probability theory to price securities, forwards, futures, swaps and options. You will also learn how to hedge using swaps and options.
Related links
Program Summary
TITLE:
Financial Mathematics - 2-day Intensive
CE:
Up to 16hrs
FEE:
Member - $2,310 including GST
Non Member - $2,854.50 including GST
DATES:
Sydney TBA
About the Speaker
Steve Anthony, Consultant
Steve is the former Treasurer of Citibank. He joined Citibank as a Corporate Foreign Exchange dealer in 1982 and worked in foreign exchange and derivatives until 1996, including two years in Japan in 1991-92 running Citibank's Investment Management business. Steve was a member of the AFMA Executive Committee from 1993-1996 and Chairman of the AFMA Working Group on Compliance Reviews. He now runs a training company specialising in Financial Markets.
Who is it for?
This workshop is suited to financial market participants working in sales, trading or risk management wishing to gain a working knowledge of the maths used in financial markets. |
Mathwizard 2.0
Does so many operations in matrices, algebra, calculus, scientific calculations and plot multiple graphs. It does real and complex matrices and operations include inverse, determinats and solve system of equations and much more.
Advertisements
Description:
Does so many operations in matrices, algebra, calculus, scientific calculations and plot multiple graphs. It does real and complex matrices and operations include inverse , determinants , and solve system of equations and much more. In algebra operations include find roots, factorization, multiply, and divide and much more. It does integration and differentiation. It has a scientific calculator that understands hand written expressions. It can plot up to three graphs on one form.
EnCalcE calculates the cost of purchasing and running electrical appliances, allowing 2 items to be compared under the same or different running conditions. It also calculates CO2 generation. Requires a registration code.
Lite version converts several units of length. Plus version converts length, weight and capacity measures. By typing a number into box provided will instantly display the results without the user having to search through a confusing menu of choices...
PTC Mathcad Express is free-for-life engineering calculation software. You get unlimited use of the most popular capabilities in PTC Mathcad Prime allowing you to solve, document, share and reuse vital calculations.
Award-winning Windows calculator that includes nearly every feature imaginable, including a scrolling tape that automatically recalculates when you edit it. Ziff Davis named Judy's TenKey the Desktop Accessory of the Year! |
Elmhurst, IL CalculusDefinitions, Postulates, Theorems, and Proofs meets the world of polygons and circles. By now, you know you can figure out answers, but do you know *why* those answers are right? Can you break it down and provide evidence at each step? |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
MATH 52: MATLAB HOMEWORK 31. M-files So far your MatLab assignments have focused on built-in functionality. However, one of the strengths of MatLab is that you can write your own functions to solve whatever computational problem is interesting to you. Th
MATH 52: MATLAB HOMEWORK 21. Complex Numbers The prevalence of the complex numbers throughout the scientic world today belies their long and rocky history. Much like the negative numbers, complex numbers were originally viewed with mistrust and skepticis
MATH 52: MATLAB HOMEWORK 11. Approximating functions A typical method for understanding complicated mathematical objects is to attempt to approxmate them as limits of relatively simple objects. The prototypical example is to approximate an arbitrary func
While the Politicians Fiddle, America Goes BrokeAugust 12, 2004 By CHRISTOPHER CALDWELL When George W. Bush was governor of Texas, Peter G.Peterson tried to convince him that the rickety finances ofSocial Security and Medicare posed a pressing philos
Programming Logic and DesignFifth Edition, ComprehensiveChapter 8 Control BreaksObjectives Learn about control break logic Perform single-level control breaks Use control data within a heading Use control data within a footer Perform control breaks wi
Programming Logic and DesignFifth Edition, ComprehensiveChapter 4 Making DecisionsObjectives Evaluate Boolean expressions to make comparisons Use the relational comparison operators Learn about AND logic Learn about OR logic Make selections within ran
Programming Logic and DesignFifth Edition, ComprehensiveChapter 3 The Program Planning Process: Documentation and DesignObjectives Learn about documentation Learn about the advantages of modularization Learn how to modularize a program Declare local a
Programming Logic and DesignFifth Edition, ComprehensiveChapter 2 Understanding StructureObjectives Learn about the features of unstructured spaghetti code Understand the three basic structures: sequence, selection, and loop Use a priming read Appreci
April 21, 2004TRANSMITTALTO:Rebecca Scott Senate CouncilFROM: Cathy Owen Medical Center Academic CouncilAt its meeting on April 20, 2004, the Academic Council for the Medical Center approved, and recommends approval by the Senate Council, for the pro
Thomas L. Friedman: Outrage and silence The New York TimesTHURSDAY, MAY 19, 2005 http:/ WASHINGTON It is hard not to notice two contrasting stories that have run side by side during the past week.
Microarrays and Transcript Profiling Gene expression patterns are traditionally studied using Northern blots (DNA-RNA hybridization assays). This approach involves separation of total or polyA+ RNA on agarose gels and after transfer to a nitrocellulose me
Sniping and Squatting in Auction MarketsJeffrey C. Ely Tanjim HossainJuly 7, 2006Abstract We conducted a field experiment to test the benefit from late bidding (sniping) in online auction markets. We compared sniping to early bidding (squatting) in auc
Terminologies Reporter: the nucleotide sequence present in a particular location on the array (a.k.a. probe) Feature: the location of a reporter on the array Composite sequence: a set of reporters used collectively to measure an expression of a particular
COMP 110-001 (F '07), Stough, FinalDecember 10, 2007Your name: _ You may not use any course materials in completing this test, only "the pages of your mind." The test consists of four sections.There are 120 points possible, with 100 being the highest s
Module Delivery TestClient A Wants 100 seats Wants 2 modules (ones we put into WebCT) available to all 100 for free Start Aug. 1 Wants reports monthly on how many students have registered for and how many have passed each modulePersonal Information We
A3. Construct a table with the headings q, w, U, and H for each of the following processes, deduce whether each of the quantities listed is positive, negative, or zero (or that the answer is not clear without doing the math) a) Irreversible isothermal exp
1PHYSICS 6HOUR EXAM 2SPRING 2003NAME_ This is a closed book, closed notes exam, except for a copy of Copenhagen. You may use calculators. Make sure you show all your work! You will get partial credit for correct intermediate steps. Useful data and equ
GDP, Real GDP, and the Cost of LivingEC 105 O Le cture3.4 20 Octobe 2008 rGDP and Price Movements GDP is the sum of P x Q for all final goods and services. Example: Simple 3good economy If prices rise, Real GDP How can we measure changes in actual pr
What Bush Did Right on North KoreaSeptember 15, 2004 By Richard V. Allen Washington A fiery explosion in North Korea has set off an unhelpfuldebate in the American presidential campaign. Senator JohnKerry, the Democratic nominee, has pointed to the
Did You Bring Your Umbrella Today?G. Baker, Department of Statistics University of South Carolina; Slide 1StatisticsAssists us in making decisions based on partial data (samples).While controlling (or at least knowing) the probability that we may be w
Chap 2. Biology of Propagation1. General Terminologya. Genotype: the genetic make-up of an organism b. Phenotype: the external appearance of an organism (usually the outcome of interaction between a genotype and environment) c. Ploidy: Variation in the
Chapter 6.7 AnimationOverviewWhen to use animation Feedback to player about interaction with UI and ingame action Communicating environmental conditions Conveying emotion and expression in player characters and NPC For visual appeal and dynamic intere
Practice Final Exam PY 205 Monday 2004 May 3Name_ There are THREE formula pages. Read all problems carefully before attempting to solve them. Your work must be legible, and the organization must be clear. Correct answers without adequate explanation wil
Information for the Quiz on Ch. 6 and for Exam 2Fundamental Concepts Things you must know: (1) Definition of and approximation for average velocity (and the position update formula) 1 (2) Definition of momentum = 2 1 - ( v c) (3) The Momentum Principle (
PY 205-004/005 Practice Test 1, 2004 Feb. 10Print name_Lab section_ I have neither given nor received unauthorized aid on this test. Sign ature:_When you turn in the test (including formula page) you must show an NCSU photo ID to identify yourself. Do n
Lab Report Checklist Peer ReviewStudents Names: Lab report title: Reviewers Names: This is a checklist intended to help guide you through the preparation of your final lab report as efficiently as possible, focusing on many points often overlooked by stu
Assuming the Role of the Systems Analyst1Systems Analysis and Design, 7e Kendall & Kendall2008 Pearson Prentice HallLearning Objectives Recall the basic types of computerbased systems that a systems analyst needs to address Understand how users work
Fundamentals of Human Resource ManagementNinth EditionDeCenzo and RobbinsChapter 5Human Resource Planning and Job AnalysisFundamentals of Human Resource Management 9e, DeCenzo and RobbinsIntroductionHuman resource planning is a process by which an |
Welcome to the CHS Math Department!
Faculty
Department Chair: Jessica Dunford
Brenda Elswick
Chad Freeman
Matthew Rose
Available Courses
Algebra I (9th grade) 2 semesters
Algebra I includes the introduction of variables, constants, expressions, equations, and functions. The language of numbers is examined. Topics include solving equations, simplifying expressions, understanding order of operations, performing operations with positive and negative numbers, exploring polynomials, factoring, graphing (linear and quadratic equations), working with radicals, and expanding arithmetic knowledge.
Geometry (1 semester)
This course is for students who have successfully completed the standards for Algebra I. The course includes the deductive axiomatic method of proof to justify theorems and to tell whether conclusions are valid. Methods of justification will include paragraph proofs, flow charts, two-column proofs, and verbal arguments. There is an emphasis on two-and three dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving techniques are used to implement these standards, including algebraic skills.
Algebra II (1 semester)
This course is for students who have successfully completed the standards for Algebra I. Functions, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Emphasis is placed on practical applications and modeling. Graphing utilities will be used to enhance the understanding of realistic applications through mathematical modeling and aid in the investigation and study of functions and their inverses. They will also provide an effective tool for solving and verifying equations and inequalities.
Math Analysis
This course is for students who have successfully completed the standards for Geometry and Algebra II. The content of this course will serve as appropriate preparation for a calculus course. Math analysis is intended to extend students' knowledge of function characteristics and to introduce them to another mode of mathematical reasoning.
Computer Mathematics
This course is intended to provide students with experiences in using the computer and graphing calculator to solve problems which can be set up as mathematical models. Students who successfully complete the standards for this course may earn high school mathematics credit. Programming, ranging from simple programs involving only a few lines to complex programs involving subprograms, will permeate the entire course. Fundamental concepts and principles in the field of computer science will be covered. Students will develop and refine skills in logic, organization, and precise expression that will enhance learning in other disciplines.
Math 163/164 is for students who have successfully completed math analysis. Math 163 presents college algebra, matrices, and algebraic, exponential, and logarithmic functions. Math 164 presents trigonometry, analytic geometry, and sequences and series. These courses are available through dual enrollment through Mountain Empire Community College or Southwest Virginia Community College. The classes are taught on-site at Clintwood High School via the internet or fiber optic classroom setting. |
\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2011c.00317}
\itemau{Gould, Doug; Schmidt, Denise A.}
\itemti{Trigonometry comes alive through digital storytelling.}
\itemso{Math. Teacher 104, No. 4, 296-301 (2010).}
\itemab
Summary: Story problems are a part of most mathematics curricula and are sometimes used as writing exercises in mathematics classrooms. Such writing exercises may include requiring students to rewrite story problems in their own words, using language that is familiar to them, or rewriting story problems using simpler number facts. The current emphasis on rigor and relevance in classrooms places even more significance on connecting such problems to real-life situations and solutions in relationship to mathematical thinking. In this article, the authors describe a digital storytelling project that allows high school students to create digital story problems about real-life situations and then apply trigonometric functions to solve these problems. This digital storytelling project provides students with a learning opportunity that connects mathematical concepts to their real-world experiences. The real-life settings and the stories told have captured students' attention and held it. (Contains 2 figures.) (ERIC)
\itemrv{~}
\itemcc{D40 G60}
\itemut{writing exercises; trigonometry; story telling; high school students; secondary school mathematics; video technology; photography; educational technology; teaching methods; mathematical applications}
\itemli{
\end |
Mathematics for Physicists 1 B
School of Physics and Astronomy
College of Engineering and Physical Sciences
Details
Code 19753
Level of study First Year
Credit value 30
Semester Full Term
Module description
The laws of physics are written in mathematical form, and it is clear that we will need to understand a certain amount of mathematics if we are to solve any physical problems. To see what is required, let us consider Newton¿s second law of mechanics: force equals mass times acceleration. Force and acceleration are vector quantities, having magnitude and direction, whereas mass is a scalar quantity, having only magnitude. It follows that we will have to recognise and manipulate both scalar and vector quantities. Acceleration is the rate of change, or time derivative, of velocity; it follows that we will need to understand differentiation, and its inverse process of integration. If we next consider electromagnetism, we see that electric and magnetic fields exist at every point of three dimensional space, and every instant of time; we must therefore understand functions of more than one variable, and in fact extend the ideas of differentiation and integration to such functions. Finally we may notice that all the major laws of physics involve derivatives, and thus are differential equations; we will need to understand such equations, and how to solve them in various circumstances. This two semester course develops these mathematical techniques needed by physics modules in the first and subsequent years. The sequence of topics is carefully chosen to support the physics modules in the first and second semesters. Where possible, mathematical ideas are linked to physics topics, and there is a strong emphasis on problem solving. The topics covered are: Semester 1: Scalars and vectors; differentiation; complex numbers |
Book Description: Year 9 Practice Book 1 is for students working at levels 4-5, helping them to progress with confidence from level 4 to level 5 and succeed in the National Tests. With hundreds of levelled practice questions corresponding to topics covered in Year 9 Pupil Book 1, it is an ideal resource for extra class work, homework and catch-up classes. This Practice Book offers: * Clear levelling for all questions so that students can gain essential extra practice at the right level and easily track their progress * Hundreds of levelled extra practice questions to consolidate and revisit topics covered in New Maths Frameworking Year 9 Pupil Book 1 and prepare for the National Tests * Full colour artwork to engage pupils
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it |
Language, notation and formulas
Communication is as vital in mathematics as in any language. This unit...
Communication is as vital in mathematics as in any language. This unit will help you to express yourself clearly when writing and speaking about mathematics. You will also learn how to answer questions in the manner that is expected by the examiner.
By the end of this unit you should be able to:
lay out and, where appropriate, label simple mathematical arguments;
understand the precise mathematical meaning of certain common English words;
Language, notation and formulas
Introduction
An integral part of learning mathematics involves communication.
Writing mathematics is a specific skill which needs to be developed and practised: there is a lot of difference between putting down a few symbols for your own use and writing a mathematical solution intended for someone else to read. In attempting mathematical questions, you may previously have written down very little, just enough, perhaps, to convince yourself that you could answer the questions. This may suffice now, but you may want to use your notes and solutions for revision so you will want them to be self-contained, able to stand on their own and easy to read. This will also be the case if you are writing mathematics for somebody else to read.
This unit is from our archive and is an adapted extract from Mathematics: a foundation course (MU120 |
I am a college graduate considering returning to school for a systems graduate degree. One of the key courses (besides Calc III and Linear Algebra) that I am missing is discrete mathematics. I was wondering if you could provide me with any information on discrete mathematics and/or any primers or other resources to this branch of math that are available on the web. |
NIC Math Competition
The NIC math competition is held on the first Tuesday of November. It is an all-day event that offers students a chance to show off their mathematical problem solving skills. An understanding of Algebra through basic Calculus is helpful but many students are in Algebra II or Precalculus. We take the top 20 math students with priority given to students in Calculus working down to Algebra II. Many students are also on the Academic Team and use study lab to practice/prepare for the event.
There are winners selected in the 'senior' division and the 'non-senior' division. These students win things like ipods or graphing calculators and scholarships to NIC. The scores are compiled and the top school's earn trophies and bragging rights. |
McGraw-Hill Education Announces Interactive E-books with ALEKS 360
McGraw-Hill Education has introduced ALEKS 360, a mathematics solution that combines an artificial intelligence and personalized learning program with a fully integrated, interactive e-book package. ALEKS 360 delivers assessments of students' math knowledge, guiding them in the selection of appropriate new study material, and recording their progress toward mastery of course goals. Through adaptive questioning, ALEKS accurately assesses a student's knowledge state and delivers targeted instruction on the exact topics a student is most ready to learn.
The e-books featured within ALEKS 360 are interactive versions of their physical counterparts, which offer virtual features such as highlighting and note-taking capabilities, as well as access to multimedia assets such as images, video, and homework exercises. E-books are accessible from ALEKS Student Accounts and the ALEKS Instructor Module for convenient, direct access.
The initial e-books to be offered in ALEKS 360 include: Introductory Algebra, Second Edition, by Julie Miller and Molly O'Neill; Intermediate Algebra, Second Edition, by Miller and O'Neill; College Precalculus, Second Edition, by John W. Coburn; and College Algebra, Second Edition, by Coburn. |
Algebra II: A Fresh Approach worktext is a 713-page complete Algebra II program. It is the second book in the Algebra: A Fresh Approach series and follows the same teaching formula as the first book in the series (Algebra I). In 21 chapters (see the table of contents at students are instructed in traditional Algebra II material and are introduced to Probability and Trigonometry.
Algebra II is a softcover worktext. In other words, students write in this book. Because it is consumable, it is not going to be passed down in the family. However, this is a small price to pay for an easy-to-understand and user-friendly Algebra II curriculum. Answers to odd-numbered questions are included in the back of the book and Ms. Walters is working on a complete solutions manual for the even-numbered problems.
Worktext pages are printed on 60-pound paper (standard copy paper is 20 pound) and the cover is 100 pound cover stock. These two features make Algebra II durable and able to hold up to daily use without falling apart.
A typical day's lesson would be one section of a chapter (chapters have between 4 and 6 sections). Each parent/student should feel free to move faster or slower if desired. The author recommends spending less time on the first few chapters and more time on the later chapters. Plan to spend 30-60 minutes each day on math. Problems get harder as students progress through each section. Even if your student finishes the book in less than a year, award one credit for Algebra II because they have learned a full year's worth of math. Since the last 5-6 problems in each section are more difficult, parents can call the class an "honors class" if students do all these problems.
In Chapter 6, "Solving Quadratic Equations," section 3 contains a lesson on completing the square. I remember learning this many years ago and teaching it to my high school age daughters, and I found Ms. Walters's instructions much easier to understand and follow than the way I learned it previously. Her directions to all of the exercises I have done are clear, and this particular lesson impressed me with its logical and systematic instructions.
As with Algebra I, Algebra II is a well thought out algebra course. It is logical, easy to use, and easy to teach. I look forward to the publication of the solutions manual because sometimes I need step-by-step solutions to figure out where my student is making mistakes, and most days I can't do the work myself.
Ms. Walters is available via email for worktext support. Simple questions that require minimal time are free of charge, while more extensive questions will incur a $45 per hour fee. She plans to write a Pre-Algebra worktext once the solutions guide to Algebra II is completed. |
Mathematics For Elementary Educators II –
mth214
(3 credits)
This is the second course in a two-part series designed for K-8 pre-service teachers to address the conceptual framework for mathematics taught in elementary school. The focus of part two will be on measurement, geometry, probability and data analysis.
Applications of Geometry
Introduction to Geometry
Use visualization, spatial reasoning, and geometric modeling to solve problems.
Identify geometric figures and shapes based on mathematical arguments.
Apply characteristics and properties of two- and three-dimensional geometric shapes in problem solving.
Data Analysis and Probability
Develop inferences and predictions based on data.
Apply basic concepts of probability.
Use appropriate statistical methods to analyze data |
The ImagiMath suite provides an integrated set of software applications that turns a Palm OS handheld computer into a compelling mathematics learning environment. The suite provides three applications for exploring mathematics: ImagiGraph, a mathematics visualizer; ImagiCalc, a full-featured calculator; and ImagiSolve, a mathematical worksheet and equation solver. Offering unprecedented ease of use, flexibility, and power, ImagiMath meets the calculation and graphing requirements of science and math education |
*Denotes classes that are available for "College in High School" credit
LEVEL DESCRIPTION FOR MATH PROGRESSION
Since 97% of Serra graduates go on to some form of higher education,
we offer a college preparatory curriculum that is designed to prepare
all of our students for success.
Level 1: This level is
intended for students not adequately prepared for a full year of
Algebra 1 as freshmen. Therefore, Algebra 1 is spread out over two
years to lay a solid foundation for further study. Students then go on
to Geometry in the junior year and finish with a year of Basic
Trigonometry/Algebra 2.
Level 3: This is the
normal sequence of classes for a college prep student. Our level 3
students take Algebra 1 as freshmen, Geometry as sophomore, Algebra 2 as
juniors and Trigonometry/Advanced Algebra as seniors. These students
are prepared for either Calculus or College Algebra/Trig when entering
college.
Level 5: The level 5
student at Serra is an exceptional math student. Our objective in level
5 is to prepare this student to take Calculus during his/her senior
year. Our level 5 students take a sequence of Algebra 1, Algebra 2,
Geometry, Pre-Calculus Mathematics, Pre-Calculus Trigonometry and
Computer Programming – finishing the normal sequence of high school math
by the end of their junior year. The senior year is reserved for
either Engineering Calculus or Business Calculus and computer
programming in Visual Basic and/or Java. Senior level 5 classes are
offered for college credit through the University of Pittsburgh. These
students are prepared to move on to Calculus 2 in college.
Electives Offered
Course
Level/Grades Offered
Description
Basic 1 & Basic 2
Level 3
Grades 10 - 12
An introductory course
in programming in Visual
Basic.
Computer Programming 1 and 2
Level 5
Grades 11 - 12
A second course in Visual
Basic. May be taken for
college credit.
College in High School Credits Offered through the University of Pittsburgh
Course Number
Course Title
Credits
Math 0220
Analytical Geometry & Calculus 1
4
Math 0120
Calculus (for Business & Social Sciences)
4
CS 0004
Intro. to Computer Programming in Basic
3
CS 0007
Intro. to Computer Programming in Java
3
*Students may elect to take the AP test in Calculus or Computer Science.
Technology
All students are required to have and use a TI-83 or TI-84 graphing calculator.
Interactive white boards in most classrooms.
Academic Competitions Pennsylvania Math League: Monthly state-wide contest sponsored by the Pennsylvania Mathematics League American High School Math Competition: Annual
Nationwide competition sponsored by the Mathematical Association of
America; a series of contests to identify mathematically talented high
school students MCWP Algebra 1 Contest: This contest recognizes talented Algebra 1 students, sponsored by the Mathematics Council of Western Pennsylvania. |
Careers
Links
Math majors can choose from a wide range of careers.
These include teaching, research, software engineering, statistics,
operations research, finance, and many others. In addition, law schools,
medical schools, and other professional schools look favorably on math majors.
A recent study
ranked mathematics as the best career.
Here
is a long term study showing math tied with computer science for the
third highest paying major.
If you envision a career involving computers, the web site or ACM
(Association for Computing Machinery) has lots of useful information
at
The Department Career Planning Guide
This guide contains information helpful towards discovering career
possibilities in business, industry, and government where mathematics
is an essential part of ones competence. You can get a free printed
copy of the guide from the Mathematics Department (Hylan 917).
It is divided into several
sections:
Section 1
Mathematicians.
This is an article from the U.S. government Dept. of Labor statistics.
It gives an overall, general view.
Section 2
Career profiles.
This information comes from the American
Mathematical Society. It gives brief profiles of careers followed by
people and is grouped according to last degree obtained.
Section 3
Mathematics That Counts. This is a reprint of titles from
SIAM articles. This section lists a number of mathematical methods of
present day use in industry. All of them are treated in our
undergraduate course offerings. The
mathematical applications index
is a guide to further information.
Section 4
General remark. All of the above information is of use in planning
your elective course work.
Section 5
Constructing your resume. The information here can be of
help in getting started.
First of all:
The goal of the resume is to obtain a job interview, not to receive
an offer.
The burden is on you to persuade a potential employer that you have
something of value to offer.
Computing skills of all levels are essential.
The guide below gives information about organizing your resume to make
it more attractive to its readers. In view of point (2) above, it is
especially important that your resume contain concise and forceful
language, highlighting your skills. Two possible activities to
highlight are summer work in the area where you are seeking a job or a
computer simulation, including graphics, or a problem, which you know
is of interest to the potential employer.
Section (3) above can be consulted for topics.
If further information is desired on careers in math, please contact the
Mathematics Department at 275-4411 or e-mail to:
office (at) math (dot) rochester (dot) edu |
ÀEvery student has the ability to be successful. It is the attitude and expectation of each individual that will set the stage for one's own success.
ÀWorking problems is a key component to understanding concepts but it is only one component. Students must understand and connect new concepts with concepts already stored in long term memory. Achieving this mastery level learning may require pre-reading concepts, reviewing or rewriting notes, practicing examples, and concluding via group practice and assessment.
Places to go:
ÀTeacher tutorial and homework assistance after school.
ØAfter school from 2:30 p.m. until 3:30 p.m.
ØAfter 3:30 until 4:30 by appointment
ÀAdditional lessons and practice can be accomplished in the computer labs during study periods before school or after school.
Requirements to follow:
ÀPlease write your name, date, and period in the upper right-hand corner of each sheet for all assignments, tests, and quizzes.
ÀPlease write your assignment at the top center of each assignment.
ÀProvide all work on tests, quizzes, and assignments.No credit will be given unless all work is shown.
ÀAll work must be written in pencil or typed.
Materials to bring:
ÀA binder with dividers ( at least 1½")
ÀPencil with eraser
Calculator use:Calculators are not required by the students. They will be used but only in the second semester. Calculators will be provided when necessary.
Computer Labs:Computer labs are located on the top floor in rooms 222 and 224.There will be two programs available for student use. They are the SAS in school and Larson's PREALGEBRA programs. Both programs provide excellent tutorials for students to independently attain skill and concept mastery. |
Precalculus Modeling Our World
In the COMAP tradition, contemporary applications and mathematical modeling are presented in novel ways to help teach and motivate students. Throughout the text, students explore a number of essential concepts and develop important modeling, data analysis, and problem-solving skills necessary to prepare them for the future.
College and high-school versions have different covers but the same content."Precalculus: Modeling Our World uses contemporary applications and mathematical modeling to teach and motivate students. Students learn to build, test, and present models that describe a variety of real-world situations, while activities throughout the text engage them in everyday problems that help illuminate mathematical principles. For example, the error correction capability of compact disk players demonstrates the importance of polynomials. Optional graphing calculator technology is integrated throughout the text and provides students with more opportunities to explore data graphically."
show more show less
List price:
$70.99
Edition:
N/A
Publisher:
W. H. Freeman & Company
Binding:
Trade Cloth
Pages:
464
Size:
8.00" wide x 10.00" long x 1.25 |
Comment: ***SIMPLY BRIT*** We have dispatched from our UK warehouse books of good condition to over 1 million satisfied customers worldwide. we are committed to providing you with a reliable and efficient service at all times
Comment: A few small marks to the page edgesThis Workbook (including answers and a free Online Edition) contains a huge range of practice questions for Higher Level GCSE Maths - it's ideal for building up the vital skills throughout the course. Complete answers are at the back of the book, so it's easy to check your progress. A free digital Online Edition is also included, accessed using the unique code printed in the book. Study notes for every topic are available in the matching CGP Revision Guide (9781841465364 |
Form your own Mathematical Equations in Google Chrome
More or less we all are dependent on internet. Even if we do not get a solution for a problem we put our questions on Google and scroll down to search the desired result. This proves that now days your Web Browser is no longer just a program on your computer.
Mathematical problems are a great threat to the students. At some point of time I too disliked Math as there were lots of formulae to remember. Now with introduction of an extension in Chrome store you will be able to create and edit equations to get your problems solved (but we would still like you to try solving yourselves ) :
1. Create formulas with the click of a button.
2. Create formulas with TeX input editor. (latex)
3. Changing the size and layout of the formula.
4. Images created with a formula to save to your PC.
5. Text files created with a formula to save to your PC.
6. Support common text input.
7. Support copy and paste.
8. Support task history.
Many formulas are pre written in this extension and you can add many more equations for your problems. It will be proved as a blessing for science as well as commerce students. All the students will really like this extension. So grab the extension and get your problems solved. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
18INORGANIC CHEMISTRYShriver & Atkins Inorganic ChemistryPeter Atkins, University of Oxford, Tina Overton, University of Hull, Jonathan Rourke, University of Warwick, Mark Weller, University of Southampton and Fraser Armstrong, University of OxfordShrProcess ModelsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Process Models1/8Introduction to Process ModelsWhat is a Process Model?A process model is a set of equations, including the necessary input data to solve the equations,
General Form of Dynamic ModelsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)General Form of Dynamic Models1 / 20General Form of Dynamic Process ModelsMathematical RepresentationA general representation of the dynamic process mod
Solution of Linear Dierential EquationsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Solution of Linear Dierential Equations1 / 15Exponential of a MatrixExponential of a MatrixThe quantity e at where a and t are scalar is an inn
Analysis of Linear System DynamicsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Analysis of Linear System Dynamics1 / 16Dynamics of a Linear SystemRecapA linear dynamical system in deviation form is represented as dX = AX + BU d
Forced Dynamics of a Linear SystemSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Forced Dynamics of a Linear System1 / 12Dynamics of a Linear SystemA linear dynamical system in deviation form is represented as dX = AX + BU dt X (0
Process OutputsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Process Outputs1/7Process OutputsDenitionVery often, we are not interested in calculating the response for the entire state vector, x (t ); we may care about only a fe
Interconnected SystemsSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Interconnected Systems1 / 12Interconnected SystemsLarger Systems by Connecting Sub-SystemsSo far in this course, we have done the following: Developed dynamic m
Dynamics of Commercial ControllersSrinivas PalankiUniversity of South AlabamaSrinivas Palanki (USA)Dynamics of Commercial Controllers1 / 18Commercial ControllersControllerA controller is an electronic device that helps to:1regulate a process at
ECH 452: Chemical Process Control SIMULATION PROJECT Propylene glycol is produced by the hydrolysis of propylene oxide in a CSTR. The reaction is normally conducted using excess water.H2SO4CH2-CH-CH3 + H2O OCH2-CH-CH3 OH OHA+BCThe objective of thiHome AssignmentNote: All the problems below have MULTIPLE steady-state solutions. Make sure you get all of them. For example, Problem 1 has steady states (+0.781, +1.603) and (-0.781, +1.603). It is a good idea to plug in your solutions into the original
Home AssignmentProblem 1: Consider the following dynamic system in deviation form: dX = AX + BU dt If the input U = 0, compute the unforced response for the following A matrices assuming that all elements of X (0) are equal to 1. 1. A= 2. A= 3. 1 2 3 A =
Principles of Economics EC 1 UCLA Dr. Bresnock Fall, 2010 Quiz 6 Answers Choose the best answer to each question and mark it on your answer form. 1. The term "marginal social benefit" means (a) Benefits that are just above the margin of being zero (b) The
Principles of Economics EC 1 UCLA Dr. Bresnock Quiz 7 Answers Choose the best answer to each question and mark it on your answer form. 1. When total utility is at a maximum, marginal utility is: A) rising. B) at its average value. C) at a maximum. D) zero
Principles of Economics EC 1 UCLA Dr. Bresnock Quiz 10 Answers Choose the best answer to each question and mark it on your answer form. A) is incorrect because, for a monopoly, the MR does not equal the demand curve. 1. The demand curve for a monopoly is:
T hink about the last time you attended a lecture or were in a classroom. Applying the i nformation processing model, why did some things make it into your short-term memory and some things into your long-term memory? How can knowing this process increase
Membrane Processes A membrane is a selective barrier that permits the separation of certain species in a fluid by combination of sieving and diffusion mechanisms Membranes can separate particles and molecules and over a wide particle size range and molecu
DIALYSIS and ELECTRODIALYSISMaretva Baricot Ronnie Juraske Course: Membrane Separations December, 20031DialysisWhat is dialysis?Dialysis is a membrane process where solutes (MW~<100 Da) diffuse from one side of the membrane (feed side) to the other (
CE 370Membrane Processes Part 21Reverse osmosis - DefenitionIt is the process of forcing a solvent (like water) from a region of high solute (such as salts of Soudium, Potasium, etc) concentration through a membrane to a region of low solute concentra |
With a scope that spans the mathematics curriculum from middle school to college, The Geometer's Sketchpad brings a powerful dimension to the study of mathematics. Sketchpad is a dynamic construction and exploration tool that enables students to explore and understand mathematics in ways that are simply not possible with traditional tools or with other mathematics software programs.
Tree Diagram Generator is a mathematical tool, aimed at students, teachers, and examiners who wish to avoid the hassle of drawing complex probability tree diagrams by hand. With a real-time point-and-click interface, you can create any number of stems and directly input probabilities and labels onto the canvas. |
Mt/CS 410 Mathematical Modeling - Fall 2002
Study Guide for Test #2
Test Date: Tuesday, November 5
In this course, the projects give you many opportunities to apply the
principles of mathematical modeling creatively to various problem
scenarios. In the test you will be asked to demonstrate mastery of the
various mathematical strategies and calculational techniques
that are introduced in this course. You may use your text book (but not
your notes) during the test. This test will cover material in Chapters 1 -
6 of our text. The relevant sections will be announced about a week prior
to the test.
I assume that you will bring a scientific calculator with you
to use during the test.
You should be able to sketch a graph of a function given by any of the
one-term models in the Ladder of Powers or Ladder of Transformations
(pages 169 - 170).
You should be able to
identify or give examples of situations (i.e., problem scenarios)
which might be described by these models.
Given a scatterplot of a set of data, you should be able to choose one
of the above models as appropriate for the situation, and explain your
choice.
You should be able to distinguish between a power curve (y f(x) = x^n)
and an exponential curve (y = f(x) = e^x).
Given a problem scenario involving change such as those discussed
in Section 3.2, you should be able to formulate a dynamical system of
equations to model the situation.
Given a dynamical system, a(n+1) = f(a(n)) with
a(0) = value, you
should be able to calculate the first several values of a(n).
You should be able to discuss the long-term (or "limiting")
behavior of a dynamical system,
a(n+1) = f(a(n)) with a(0) = value. That is, does the
system have an equilibrium value? Does the system reach a stable or
unstable equilibrium? Does the behavior approach a limit? Is the long-term
behavior of the system periodic? ... or chaotic?
You should be able to use the idea of proportionality to develop a
model.
Given data and several graphs representing various transformations
of the data, you should be able to select the transformation in which
proportionality is a reasonable assumption, and fit a model to the data.
Given data and several graphs representing various transformations
of the data, you should be able to use "eyeball analysis" to select the
"best" model. You should be able to explain why the one you choose is
best, and estimate parameters for the model from the graph.
You should be able to estimate parameters (slope, intercept) for a
linear model from a graph, and give an equation for the model.
Once you have used graphical analysis to estimate parameters from the
transformed data, you should be able to transform the equation so that the
model is expressed in terms of the original data.
If two objects are geometrically similar and their linear measurements
are related by a constant k, then you should be able to show algebraically
that their area measurements are related by k^2, and their volume
measurements are related by k^3.
You should be able to use the least-squares criterion and methods of
calculus to derive the equations and solve for the parameters in a model of
a given form.
You should be able to set up the Lagrangian form of a polynomial to
fit a given set of data. You should be able to identify the (maximum)
degree of the polynomial for a given set of data, and show that the graph
of this polynomial really does go through each point in the given data set.
(The question on the test will ask you to fit a
polynomial to no more than six data points. You would not be asked to
simplify this polynomial; you may leave it in the form given on page 183.)
You should be able to set up a divided difference table for a given
set of data. Then using this divided difference table, you should be able
to determine what lower-degree polynomial (if any) would be an appropriate
interpolating polynomial for a given data set.
You should be able to estimate probabilities for specified events
given a set of frequency data for a particular scenario.
You should be able to describe a simulation experiment which
would generate data to model the situation in a given problem.
Return to Sr. Barbara E. Reynolds
Home Page.
Return to
course list
for 2002 -- 2003.
Go to Mt/CS 410:
Mathematical Modeling Syllabus.
Return to Mt/CS 410:
Mathematical Modeling Assignments.
The easiest way to contact me is to send an
email message to Sr. Barbara E.
Reynolds.
This page was updated on October 28, 2002. |
Your grade in this class will be based upon your performance on
homework, quizzes, tests, learning logs, participation, graded review, and projects (if/when they are given). Your grade will be the percentage
of points earned out of the maximum points possible (different every quarter).
Grades:
To keep track of the grades received in this class, I encourage
both the student and the parent(s) to use the Infinite Campus Student/Parent
Portal.
Notes will be given almost daily. When you are given a
note sheet, it must be filled in with pencil!
Each note sheet will be recorded on the Math 7H Notes ~ Table
of Contents and they should be kept, in order, in the Notes section
of your 3-ring binder.
Homework:
Homework will be assignedalmost every time you have class.
Homework must be completed in PENCIL!
Homework will be collected/checked daily or may be collected and
graded (for example...a review worksheet).
Each student must turn in his/her own independent work.
Copying will not be tolerated and all students involved will get a
zero for that homework assignment.
A list of answers results in 0 credit for the homework
assignment; work must be shown when required.
If you are unable to complete a problem on a homework
assignment, make note of the problem and come in early, ask for help during my
office hours, or stay after school. DO NOT wait until class time to
ask for help.
1st and 2nd Quarter HOMEWORK POLICY:
Students will receive a print-out of missing assignments prior to interims &
report cards. At interims, students can complete missing assignments for 4
out of 5 points. At report cards, students can complete missing
assignments from before interims for 3 out of 5 points and assignments from
after interims for 4 out of 5 points.
3rd Quarter HOMEWORK POLICY:
Students will receive a print-out of missing assignments prior to
the report card only. Students can complete missing assignments for 3
out of 5 points.
4th Quarter HOMEWORK POLICY:
Students will not receive any print-outs of missing assignments.
If students inquire about assignments on their own, and make up these
assignments prior to the interim and/or report card, they will receive 2.5
out of 5 points for that assignment.
If you are absent the day an assignment is due, it is then
due the day you come back. The total number of days you are absent
will equal the number of days you have to make up MISSED WORK ONLY.
After your make up days, the late homework policy begins for any assignment not
handed in on time.
Should you miss class (for any reason) it is YOUR
responsibility to pick up any necessary worksheets and note-sheets. You
will also be responsible for handing in your current homework assignment,
getting any notes taken in class, checking the homework calendar, and making up
any quizzes or tests. Any homework, quiz, or test not made up within 5
days will result in a 0 grade.
You will receive a homework grade at the end of the quarter.
Total number of points depends on the number of homework assignments for the
quarter.
Learning Log (composition notebook):
Students will complete learning log entries in class almost
daily on either the lesson taught in the previous class or any material already
covered in the school year.
Learning Logs will be checked at the end of the quarter
and will count towards the participation grade.
Students do not need to make up Learning Log entries for
classes they are absent from and the missing entries will not count
towards the student's grade.
Learning Logs will be left in the classroom.
Projects:
Students will be assigned unit specific projects throughout the school year.
More details on the project will be given as they are
assigned.
Projects will count as 30 - 100 points.
Quizzes/Tests:
Quizzes may be announced or unannounced.
Tests will be given at the end of each unit. Tests will
always be announced so students can prepare in advance.
Anything and everything discussed in class, on note sheets, and
in learning logs can appear on the quiz/test.
Individuals will complete quizzes/tests. Any observable
suspicious behavior will result in serious consequences for all students
involved.
If you use pen on a quiz/test you will automatically lose 10
points on your quiz/test!
This page is maintained in accordance with Shenendehowa's web
publishing guidelines by
Brittany D. Miller. |
Calculus for Scientists and Engineers, CourseSmart eTextbook
Description
Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' years of teaching experience resulted in a text that reflects how students generally use a textbook: they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.
Table of Contents
1. Functions
1.1 Review of functions
1.2 Representing functions
1.3 Trigonometric functions and their inverses
Review
2. Limits
2.1 The idea of limits
2.2 Definitions of limits
2.3 Techniques for computing limits
2.4 Infinite limits
2.5 Limits at infinity
2.6 Continuity
2.7 Precise definitions of limits
Review
3. Derivatives
3.1 Introducing the derivative
3.2 Rules of differentiation
3.3 The product and quotient rules
3.4 Derivatives of trigonometric functions
3.5 Derivatives as rates of change
3.6 The Chain Rule
3.7 Implicit differentiation
3.8 Derivatives of inverse trigonometric functions
3.9 Related rates
Review
4. Applications of the Derivative
4.1 Maxima and minima
4.2 What derivatives tell us
4.3 Graphing functions
4.4 Optimization problems
4.5 Linear approximation and differentials
4.6 Mean Value Theorem
4.7 L'Hôpital's Rule
4.8 Newton's method
4.9 Antiderivatives
Review
5. Integration
5.1 Approximating areas under curves
5.2 Definite integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with integrals
5.5 Substitution rule
Review
6. Applications of Integration
6.1 Velocity and net change
6.2 Regions between curves
6.3 Volume by slicing
6.4 Volume by shells
6.5 Length of curves
6.6 Surface area
6.7 Physical applications
6.8 Hyperbolic functions
Review
7. Logarithmic and Exponential Functions
7.1 Inverse functions
7.2 The natural logarithm and exponential functions
7.3 Logarithmic and exponential functions with general bases
7.4 Exponential models
7.5 Inverse trigonometric functions
7.6 L'Hôpital's rule and growth rates of functions
Review
8. Integration Techniques
8.1 Basic approaches
8.2 Integration by parts
8.3 Trigonometric integrals
8.4 Trigonometric substitutions
8.5 Partial fractions
8.6 Other integration strategies
8.7 Numerical integration
8.8 Improper integrals
Review
9. Differential Equations
9.1 Basic ideas
9.2 Direction fields and Euler's method
9.3 Separable differential equations
9.4 Special first-order differential equations
9.5 Modeling with differential equations
Review
10. Sequences and Infinite Series
10.1 An overview
10.2 Sequences
10.3 Infinite series
10.4 The Divergence and Integral Tests
10.5 The Ratio, Root, and Comparison Tests
10.6 Alternating series
Review
11. Power Series
11.1 Approximating functions with polynomials
11.2 Properties of power series
11.3 Taylor series
11.4 Working with Taylor series
Review
12. Parametric and Polar Curves
12.1 Parametric equations
12.2 Polar coordinates
12.3 Calculus in polar coordinates
12.4 Conic sections
Review
13. Vectors and Vector-Valued Functions
13.1 Vectors in the plane
13.2 Vectors in three dimensions
13.3 Dot products
13.4 Cross products
13.5 Lines and curves in space
13.6 Calculus of vector-valued functions
13.7 Motion in space
13.8 Length of curves
13.9 Curvature and normal vectors
Review
14. Functions of Several Variables
14.1 Planes and surfaces
14.2 Graphs and level curves
14.3 Limits and continuity
14.4 Partial derivatives
14.5 The Chain Rule
14.6 Directional derivatives and the gradient
14.7 Tangent planes and linear approximation
14.8 Maximum/minimum problems
14.9 Lagrange multipliers
Review
15. Multiple Integration
15.1 Double integrals over rectangular regions
15.2 Double integrals over general regions
15.3 Double integrals in polar coordinates
15.4 Triple integrals
15.5 Triple integrals in cylindrical and spherical coordinates
15.6 Integrals for mass calculations
15.7 Change of variables in multiple integrals
Review
16. Vector Calculus
16.1 Vector fields
16.2 Line integrals
16.3 Conservative vector fields
16.4 Green's theorem
16.5. Divergence and curl
16.6 Surface integrals
16.6 Stokes' theorem
16.8 Divergence theorem
Review |
Posted On: September 27, 2011 05:30 pm
Samacheer kalvi curriculum..
Video Lessons:.
Online Tests:
Home work Help: This section contains crisp reference notes that can help you break down complex theories and difficult numerical problems. It has an exhaustive database of intelligently prepared solved questions and textbook solutions (NCERT and R D Sharma) to help you complete home task fast.
Exam Resources: This particular section contains sample papers, solved board papers and exam tips and tricks. By going through all these materials and attempting both solved and unsolved questions, you prepare yourself well for examinations.
Textbook Solutions: Get complete solutions to the questions given in NCERT and R D Sharma textbooks. This will not only help you enhance your understanding of the concepts but also help you finish home work fast.
.
.
Are you reading in a school affiliated with Samacheer Kalvi? If yes, then the Topper's Samacheer Kalvi pack is definitely a thing for you. Visit Samacheer Kalvi. To avail all the benefits, subscribe it now. Become the master of the course assigned to you and lead the world!!!
For any future problem please feel free to write in to us at [email protected] |
Mathematics With Infotrac A Good Beginning
9780534529055
ISBN:
0534529054
Publisher: Thomson Learning
Summary: More than just a textbook, this is a complete instructional program that serves a multitude of curriculum needs. This edition is solidly grounded in the latest research on how children learn mathematics and how teachers develop attitudes, beliefs, and knowledge that promote successful teaching0534529054 BRAND NEW. We are a tested and proven company with over 700, 000 satisfied customers since 1997. Choose expedited shipping (if available) for much faster delivery. [more]
0534529054 |
General Question
Can anyone advise me on these math courses?
This is a very general question as the semester just started. I am taking linear algebra and calc-based probability and statistics. Simply put, of those who have taken either of the courses, can you provide me with any words of wisdom to help me not fail?
7 Answers
1. Study the material before your professor lectures on it. While you won't understand everything you're reading, you will ultimately understand much more if you read before the lecture.
2. Do your homework well in advance. This gives you the time needed to process difficult questions and then to visit your professor if you are still unable to understand them.
3. Do all of your homework. In math, homework is the best way to study. If you notice that you still don't really get it after completing the assigned homework, do some more. Keep working problems until you truly know the concepts.
4. Review your homework, tests, and quizzes. If you get questions wrong, make sure you understand both why they are wrong, and what you should have done.
5. Visit your professor with good questions. That means you don't just walk in and say, "I don't understand this," while pointing at a problem or an entire section of your book. Figure out exactly what it is that you do not understand and ask specific questions.
6. Pay attention to notation. If you're not sure about notation, pay attention to how your professor writes things in class. You can't go wrong if you follow that notation.
7. Be careful to justify the steps in your proofs. A proof is an argument, not just a calculation. Make sure you write out the details.
8. Be familiar with the theorems. Know them well, and know how to apply them.
9. Study groups are only helpful if you are with a group of students that are dedicated to learning. If they are just trying to finish the problems and get out, they will likely miss important details and hurt your understanding.
10. Above all else, know your definitions like you know your own name. Math is meaningless without a proper understanding of the definitions. Make sure you learn them as they are taught so you do not have to look them up. You will be much more prepared for the test if you learn them as you go.
You're quite welcome. These are the steps to make it through any upper level math course. Everything worth doing is worth working hard at. Good luck this semester! This question shows that you're off to a good start.
Sometimes having access to tutor to go over concepts as you move through the course can help ward off having problems. It's good to have one-on-one access to someone that confirm you understand the concepts fully and answer your questions. |
Search Course Communities:
Course Communities
Lesson 44: Nonlinear Systems
Course Topic(s):
Developmental Math | Systems of Equations
Using a cost/revenue application problem, the lesson begins with systems involving quadratic equations. Systems with conics are introduced next along with the elimination method for solving these systems. |
Mathematics
< Sci and Tech
< Thought
< escouve
Overview Microsoft Mathematics provides a set of mathematical tools that help students get school work done quickly and easily. With Microsoft Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus.
The writing of textbooks and making them freely available on the web is an idea whose time has arrived. Most college mathematics textbooks attempt to be all things to all people and, as a result, are much too big and expensive. This perhaps made some sense when these books were rather expensive to produce and distribute--but this time has passed. Professor Jim Herod and I have written Multivariable Calculus ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... |
This activity demonstrates one of the many ways Sketchpad can be used in a calculus or math analysis class. Students manipulate a tangent line to a curve to investigate what it means for a curve to ha... More: lessons, discussions, ratings, reviews,...
The main objective of this activity is to find an approximation for the value of the mathematical constant e and to apply it to exponential growth and decay problems. To accomplish this, student |
Synopsis
Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard University course on the subject.
Found In
eBook Information
ISBN: 9780511345685 |
If anyone is looking for a handy study booklet that contains most of the GMAT math concepts and formulas, I strongly recommend the GMAT Math Study Sheet at It's a 4-page condensed study note that has GMAT math relevant concepts as well as examples elaborating on those concepts. I am not saying that you will be able excel in the math portion just by staring at that study sheet. You will definitely need go through numerous practice problems. But the study sheet will give you a much clearer overview of math needed and the overall structure of the test. I think they have a preview version of the study sheet in which only the first page is displayed. Here is the preview link.
Good point. So how much are you willing to pay for that?
I've plowed through the free stuffs online before. None are as comprehensive as that study sheet. Also, the material online are not filtered for the GMAT math exam. Nonetheless, you would have to actually spend time searching for them and decide if they are relevant or not. After all, time is money.
Let's have a quick survey here. How much would you pay for such a study sheetThe point of having a formula sheet is not tailoring one but rather having one with ALL formulas that might be needed to solve the math section. Not eveybody knows which math concepts will be key to pass the test.
Math concepts required for the test are not subjective, so if you are willing to pay for a cheat sheet why not pay less (than the $20 one mentioned above). |
iJournals
Informative Journals
iJournals is a website that gathers informative journals, articles and other publications regarding the education and research aspects of the computational software program Mathematica.
Mathematica is a computational software program used in the scientific, engineering, economic and mathematical fields as well as other areas of technical computing. It was created by Stephen Wolfram and is developed by Wolfram Research.
Mathematica is an invaluable tool for modeling and simulation on a large number of issues and mathematical problems. Doing much more than simply grinding out numbers, doing statistical estimations and rendering graphical plots and visuals, Mathematica enables these users to do all of that and more in a unified environment.
Please visit the Mathematica official site to learn more.
This iJournals site
On this site you will find many resources pertaining to Mathematica and other useful computational software.
The "Journals" page you will find a wealth of Journals and other publications regarding mathematical. Including: The Mathematica Journal, which publishes articles and packages on all aspects of Mathematica and on related subjects. As well as the Journal of Statistical Software, which publishes articles, book reviews, code snippets, and software reviews on the subject of statistical software and algorithms.
Our "News" page has all the update information that users of computational software should know. Please see the recent article about the new research that seems to suggested a link between the use of professional interpreter services during emergency department (ED) visits and higher levels of patient and provider satisfaction.
Books and software related to Mathematica and other computational software can be found on the "Products" page. The list includes a wide range of software available at the Wolfram website, as well as many books on the uses of Mathematica for various fields of mathematic study.
If you might have any questions or comments about this site, please submit them on our "Contact" page. |
Summary: The fundamental goal in Tussy and Gustafson's BASIC MATHEMATICS FOR COLLEGE STUDENTS, Third Edition is to teach students to read, write, and think about mathematics through building a conceptual foundation in the language of mathematics. The book blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills. Also students planning to take an introductor...show morey algebra course in the future can use this text to build the mathematical foundation they will need.
Tussy and Gustafson understand the challenges of teaching developmental students and this book reflects a holistic approach to teaching mathematics that includes developing study skills, problem solving, and critical thinking alongside mathematical concepts. New features in this edition include a pretest for students to gauge their understanding of prerequisite concepts, problems that make correlations between student life and the mathematical concepts, and study skills information designed to give students the best chance to succeed in the course. Additionally, the text's widely acclaimed Study Sets at the end of every section are tailored to improve students' ability to read, write, and communicate mathematical ideas.
New to the Edition
Check Your Knowledge: Pretests, situated at the beginning of every chapter, have been added to this edition as a way to gauge a student's knowledge base for the upcoming chapter. An instructor may assign the pretest to see how well prepared their students are to understanding the chapter; thereby, allowing the instructor to teach accordingly to their students' abilities from the results of the pretest. Students may also take the pretest by themselves and check their answers at the back of the book, which gives them the opportunity to identify what they already know and on what concepts they need to concentrate.
Study Skills Workshop: At the beginning of each chapter is a one-page study skills guide. This complete mini-course in math study skills provides extra help for developmental students who may have weak study skills, as well as additional assistance and direction for any student. These workshops provide a guide for students to successfully pass the course. For example, students learn how to use a calendar to schedule study times, how to take organized notes, best practices for study groups, and how to effectively study for tests. This helpful reference can be used in the classroom or assigned as homework and is sequenced to match the needs of students as they move through the semester.
Think It Through: Each chapter contains either one or two problems that make the connection between mathematics and student life. These problems are student-relevant and require mathematics skills from the chapter to be applied to a real-life situation. Topics include tuition costs, statistics about college life and many more topics directly connected to the student experience.
New Chapter Openers with TLE Labs: TLE (The Learning Equation) is interactive courseware that uses a guided inquiry approach to teaching developmental math concepts. Each chapter opens with a lab that has students construct their own understanding of the concept to build their problem-solving skills. Each lab addresses a real-world application, with the instruction progressing the student through the concepts and skills necessary for solving the problem. TLE enhances the learning process and is perfect for any instructor wanting to teach via a hybrid course.
ThomsonNOW with HOMEWORK FUNCTIONALITY. Assigned from the instructor, the enhanced iLrn functionality provides direct tutorial assistance to students solving specified questions pulled from the textbook's Problem Sets. This effective and beneficial assistance gives students opportunity to try similar, algorithmically-generated problems, detailed tutorial help, the ability to solve the problem in steps and helpful hints in solving the problem.
iLrn/MathNOW a personalized online learning companion that helps students gauge their unique study needs and makes the most of their study time by building focused personalized learning plans that reinforce key concepts. Completely tailored to the Tussy/Gustafson text, this new resource will help your students diagnose their concept weaknesses and focus their studies to make their efforts efficient and effective. Pre-Tests give students an initial assessment of their knowledge. Personalized Learning Plans, based upon the students' performance on the pre-test quiz, outline key learning needs and organize materials specific to those needs. Post-Tests assess student mastery of core chapter concepts; results can be emailed to the instructor!
Features
STUDY SETS are found at the end of every section and feature a unique organization, tailored to improve students' ability to read, write, and communicate mathematical ideas; thereby, approaching topics from a variety of perspectives. Each comprehensive STUDY SET is divided into six parts: VOCABULARY, CONCEPTS, NOTATION, PRACTICE, APPLICATIONS, and REVIEW.
VOCABULARY, NOTATION, and WRITING problems help students improve their ability to read, write, and communicate mathematical ideas.
The CONCEPT problems section in the STUDY SETS reinforces major ideas through exploration and foster independent thinking and the ability to interpret graphs and data.
PRACTICE problems in the STUDY SETS provide the necessary drill for mastery while the APPLICATIONS provide opportunities for students to deal with real-life situations. Each STUDY SET concludes with a REVIEW section that consists of problems randomly selected from previous sections.
SELF CHECK problems, adjacent to most worked examples, reinforce concepts and build confidence. The answer to each Self Check is printed adjacent to the problem to give students instant feedback.
The KEY CONCEPT section is a one-page review found at the end of each chapter that reinforces important concepts.
REAL-LIFE APPLICATIONS are presented from a number of disciplines, including science, business, economics, manufacturing, entertainment, history, art, music, and mathematics.
ACCENT ON TECHNOLOGY sections introduce keystrokes and show how scientific calculators can be used to solve application problems, for instructors who wish to integrate calculators into their course.
CUMULATIVE REVIEW EXERCISES at the end of Chapters 2, 4, 6, 8 and 10 help students retain what they have learned in prior chapters 0495188956New
One Planet Books Columbia, MO
Ships out same day or next |
... read more
Calculus: Problems and Solutions by A. Ginzburg Ideal for self-instruction as well as for classroom use, this text improves understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. Over 1,200 problems, with hints and complete solutions. 1963Product Description:
ideas may be applied. Rather than an exhaustive treatment, it represents an introduction that will appeal to a broad spectrum of students. Accordingly, the mathematics is kept as simple as possible. The first of the two-part treatment deals principally with the general properties of differintegral operators. The second half is mainly oriented toward the applications of these properties to mathematical and other problems. Topics include integer order, simple and complex functions, semiderivatives and semi-integrals, and transcendental functions. The text concludes with overviews of applications in the classical calculus and diffusion problems |
Contact us
QUANTITATIVE BIOLOGY AND BIOINFORMATICS
email:
Academic Coordinator Carole Hom
clhom at ucdavis dot edu
FAQ
Why do these modules use Mathcad?
The most important consideration in our choice of software is how well a particular software package can facilitate the goal of teaching students to think quantitatively. We have found that the "look" of Mathcad documents reassures students. Equations written in Mathcad look (more or less) like equations on paper. Even fairly complex operations like solving ordinary differential equations can be accomplished fairly visually, without anything that looks like a program. And problems often can be framed in ways that make the most intuitive sense, rather than in the way that is most efficiently processed. Further, students can purchase a Mathcad license to use indefinitely at a price that is only a fraction of most college textbooks.
What's with the blue and beige boxes in the module?
We use colors to indicate different types of regions. Beige boxes contain explanatory material. Blue indicates instructions for a specific problem. These are followed by white regions where students type text or do calculations in response to the problem.
We use pale red as a warning to avoid common errors.
Why is the first row of an array numbered "0" instead of "1"?
Mathcad's default convention is to begin numbering arrays at 0. You can change this by resetting the ORIGIN. However, this can lead to errors in other parts of these worksheets because we assume ORIGIN=0.
My syllabus orders topics differently than the course modules. Is it OK to assign them in a different order?
Yes, with one exception: all modules depend on completion of Module 1, Introduction to Mathcad. Otherwise, all modules are independent. We do use the convention that higher-numbered modules are conceptually more challenging than lower-numbered modules.
What are "Mini-modules"?
Because all modules are independent, we provide instruction in methods common to multiple modules (e.g., graphing) within short units that we call mini-modules. This allows us to avoid repeating basic instruction within the module and also provides students with a quick reference on these techniques.
I'm having trouble with a particular method. Got suggestions?
If you're running into difficulty with graphing, 3-D graphing, making histograms, writing find-solve blocks, or solving differential equations, consult one of the Mini-modules on these topics. You may be making a common error addressed in the mini-module. For other errors, consult Mathcad's help files.
My students have really benefitted from these modules. Are there others I can download? |
Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Seventh Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Seventh Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts. |
Summary: Math 3B/3C Syllabus
SIMS Program, Grace Kennedy
SIMS Website: programs/sims.html
Course Website:
Email: [email protected]
Expectations :
· After attending lecture, reviewing concepts, applying them to homework
problems and applications with your peers, you will be able to
1. solve integrals using "reverse 3A logic" and a variety of integration
techniques
2. relate these integration techniques to derivation techniques
3. understand what a differential equation is and what it means to be
a solution to a given differential equation
4. determine solutions to differential equations
5. identify and apply integration techniques helpful in solving differen-
tial equations
· Please be on time or a few minutes early. We will spend the first few
minutes working on a problem I'll have on the board.
· Please turn off cell phones. If a cell goes off, you will be expected to
lead us in a round of the quadratic formula song. (Don't worry, we'll sing |
reading advisory level provides the
student with the requisite skills to meet this expectation.
Advisory Writing - 2 Levels Prior
to Transfer
writing advisory level provides the
student with the requisite skills to meet this expectation.
Prerequisite MATH C050
Students entering PHSC C111 are required to solve
problems involving mathematical operations such as ratios, square roots,
surface areas related to radius, and solving for a single variable
(pre-algebra).
Math C050 provides students with the requisite
skills to solve these problems |
The first pre-algebra topic to focus on is knowing and understanding types of numbers, such as integers, fractions, decimals and negative numbers. Once that is clear you will be able to use various operational properties like the commutative, associative, and distributive properties. Generally,... |
Part II(g): Mathematics
DAISY 3 Structure Guidelines
Last Revised: June 4, 2008
This section of the guidelines explains how to use elements
to mark up mathematical expressions in DAISY books.
The elements described here come
from the W3C
MathML Standard.
MathML forms the basis of DAISY's
Modular Extension for Mathematics, which is the normative reference
upon which these guidelines are based.
Information Object: Math
Definition
A mathematical expression is a collection of symbols representing
a mathematical idea.
A mathematical expression may be as simple as a single variable or it may be a complex expression that spans many lines.
It may occur either inline or in a block context.
Markup
All content that represents mathematical expressions should
be marked up using MathML; images (pictures) alone should not be used because
these can not be rendered with synthetic speech or converted to braille.
Mathematical content must be enclosed in the <math> element. The children
of the <math> element must be valid MathML presentation elements. While MathML does not require the
altimg and alttext attributes to be present on the <math>
element, the MathML in DAISY Specification does require these attributes to be specified. These attributes provide a fallback
mechanism for basic DAISY players that are not capable of rendering MathML. The resolution of the
image referenced by the altimg attribute should be such that it is readable when scaled for large print.
The alttext value should
unambiguously describe the mathematical expression.
Syntax
<math>...</math>
Examples
Example 1
This example shows markup for math that involves units.
Units require special markup so that they are displayed properly and so that
they can be spoken properly. For example, "km" should be spoken as
"kilometer" or "kilometers".
A unit is indicated by adding to the mi tag the
class attribute value "MathML-Unit".
See Units in MathML for more details.
In addition to using the class attribute value "MathML-Unit", two additional points should be noted:
units are typically preceded or followed by an expression and should typically be separated from the expression by an operator representing multiplication;
monetary signs such as "$" should be treated as units.
In the example below, ⁢ is the Unicode character representing invisible times. It separates the expression from the unit ("ft").
Example 2
This example shows markup for math that has textual
annotations next to it.
Math such as this should be marked up using table with the math being in
one column of the table and text in the other column. It should
not be marked up with mtable and mtext in the second column.
This does not apply to text used for equation numbering.
For that, an mtable is appropriate;
the equation number should be part of an mlabeledtr element.
Example 3
This example shows markup for simple inline math and
illustrates two points:
Single letter variables should be marked up using MathML.
There should be navigation points surrounding the math.
Even though this example just consists of a single letter variable, it is
important to mark this up as math so that both braille and speech translations
handle it appropriately. Some braille math codes will mark variables and symbols differently than
the corresponding character codes. For speech, some variables need to have a specific
pronunciation. For example, the letter "a" in English should always have the long "a" sound
when used as a math variable.
In order to allow navigation to before or after the math (e.g., to skip reading the math after hearing the first part of it),
there should be elements immediately before and after the math element that have their
id attribute set.
For inline math, this requires introducing span elements as shown below if there are
no other elements with ids adjacent to the math element.
<span>, where </span>
<m:math display="inline" xmlns:dtbook="
alttext="s" altimg="images/p281-028.png">
<m:mi>s</m:mi>
</m:math>
<span> is the length of a side, to find the volume of each cube.</span>Illustrated Example 3
Only part of the sample page is given in the XML below. What is
shown below encodes the first two lines of text on the page.
The highlighted section corresponds to the use of the variable "s" and the spans that
surround it.<p>
<sent>
<strong>Geometry</strong>
Use the formula
<imggroup>
<img src="images/p281-001.png" alt="V equals s cubed"/>
</imggroup>
, where
<imggroup>
<img src="images/p281-028.png" alt="s"/>
</imggroup>
is the length of a side, to find the volume of each cube.
</sent>
</p> |
Job Title
Math Teacher
Summary
Teach courses
pertaining to mathematical concepts, statistics, and actuarial science and to
the application of original and standardized mathematical techniques in
solving specific problems and situations. |
Integration theory
For all studies of analysis in higher mathematics it is fundamental to understand the concept of integration. Our intuitive idea of the integral of a function is as the area under its graph, and this can be turned into a formal definition through approximating Riemann sums. This leads to the Riemann integral which works fine in many circumstances, but has its limitations.
One problem with the Riemann integral is that it does not manage functions with too many discontinuities, for example the function f(x) which is 1 if x is rational and 0 if x is irrational cannot be integrated. Morally the integral should have the value zero since the rationals form a countable set which should not contribute to the integral. A more serious problem is that the Riemann integral does not behave nicely when one studies sequences of functions, such as the partial sums of a Fourier series approximating a periodic function. When can one move the limit inside the integral?
In this course we will study the Lebesgue integral, and more general concepts of integrals and measure. Among other things we will see how the above problems are resolved and we will study the important L^p spaces of functions.
The material in this course is fundamental also for the study of probability theory.
Foundations of analysis
Chaotic dynamical systems
For a number of years now, chaotic dynamical systems have received a lot of scientific attention. One aspect is chaos, fractals, etc., often illustrated with the fantastic pictures -- the Mandelbrot set, Julia sets, etc. -- that computer simulations of iterations of complex polynomials give rise to.
Another aspect is formed by the so-called "strange attractors", that occur in conjunction with computer simulations of ordinary differential and difference equations. Some of the best known mathematical experiments were carried out by the meteorologist E. Lorenz and the astronomer M. Hénon, and here at the department precisely these models have been studied rigorously and chaotic behaviour was proved for them. D. Ruelle and F. Takens have proposed that turbulent phenomena might at least partially be explained via strange attractors.
The physicist M. Feigenbaum made the fundamental discovery that many systems first go through a characteristic period doubling and then behave in a random (chaotic) way, even though they are deterministic. Later, one has shown that such period doublings occur in liquid helium flow.
From a mathematical viewpoint, the course is quite special. On a relatively elementary level, one obtains insight in phenomena that lie quite close to current research. One or two computer experiments will probably be part of the course. However, the course's main emphasis will be on the mathematical theory, which in itself has a long history with names such as Poincaré, Fatou, Birkhoff, and Smale, and which lately has developed quickly, partly in symbiosis with computer experiments.
Elementary differential geometry
In this course we study curves and surfaces. This subject has the beauty that one can start from knowing only basic calculus, and reach many deep and interesting facts.
An important concept is that of curvature, which appears in many different forms, with the common property that it measures how much an object differs from being flat (for example an ordinary sphere has constant positive curvature, and the curvature becomes smaller as the radius is increased).
One of the important results covered in the course is the Gauss-Bonnet theorem, which relates the curvature of a surface to a topological quantity (the Euler characteristic).
Two books that will be used in the course are:
"Differential Geometry of Curves and Surfaces" by Manfredo P.do Carmo
"Differential Geometry:curves-surfaces-manifolds" by Wolfgang Kuehnel
Topology
SU, SF2721, Rikard Bögvad
Topology is the study of spaces from an abstract viewpoint. One is interested both in the fine structure of a space and in global features such as the number of holes. A fundamental concept is that of a continuous function, or continuous map, and the goal is to understand what properties such a map can have without using ideas like distance or derivative.
For instance, it might seem obvious that a simple closed curve in the plane divides the plane into an "inside" and an "outside" region. This observation is correct, but to really prove it assuming only that the curve is continuous is not an easy task. In fact, this was a hard problem for a long time, studied by many mathematicians in the 19th century. In the course we will see a proof of this "Jordan curve theorem", and other results such as the "Ham sandwich theorem" (one can always divide a three layer sandwich into two equal pieces with just one cut) and the "Hairy ball theorem" (one cannot comb a hedgehog).
A classical example in topology is that, in a world of perfect rubber, a coffee cup cannot be distinguished from a doughnut, but is fundamentally different from a ball. What does this observation mean? And how can one turn it into computable mathematics? The answer, perhaps surprisingly, involves group theory and abstract algebra. In the course we will see how to find and classify all two-dimensional surfaces. The doughnut and the ball are two of them.
Discrete mathematics
Commutative Algebra and Algebraic Geometry
Geometry and algebra might appear to be two totally unrelated subjects. The truth is, however, that affine algebraic geometry and commutative algebra are perfectly dual to each other. Grasping this duality is very satisfactory and rewarding. The main purpose of the course is to initiate the fermenting process needed to achieve this understanding.
Commutative algebra is about the structure of commutative rings. A commutative ring is a set with two operations, sum and multiplication, satisfying some natural conditions. The ring of integers and the polynomial rings are typical examples to have in mind. The notion of ideals arises when one tries to form quotients of a ring. Prime ideals are a particular class of ideals that, as the name suggests, generalize the notion of prime number.
The set of prime ideals in a ring naturally form a topological space; the spectrum of a commutative ring. The spectrum of prime ideals is a geometric object where the ideals correspond to closed subsets.
In the course we will give an introduction to these two subjects, and we will stress how to use the dictionary between algebraic geometry and commutative algebra. In particular we will focus on how algebraic notions and results are to be understood and implemented in the geometric context.
Topics in mathematics III: The mathematical theory of option pricing
An option is a security/contract giving the right to buy or sell an asset subject to certain conditions, within specified period of time.
Trading option in a more organized and controlled way dates back to the founding of Chicago Board Option Exchange (CBOE) in 1973. The same year also saw a breakthrough in the theory of option pricing, with publication of the famous result of Fischer Black and Myron Scholes in the Journal of Political Economy. The mathematical model of Black-Scholes is still the most widely used tool for pricing financial derivatives.
Although uncertainty underpins the valuation of any financial instrument, the derivation of the Black-Scholes model is heavily relied on partial differential equations rather than stochastic calculus.
This model is also used for valuation of almost all financial derivatives: pricing options, pricing commodities (mines), warrants, index, ...
Since its birth, this theory has evolved to embrace very complicated phenomena beyond financial markets: Political decisions, Operating strategies, Decision under uncertainty.
In this course we shall discuss the most basic facts of this theory, using tools from PDE.
Functional analysis
The main goal is to give an introduction to the basics of functional analysis and operator theory, and to some of their (very numerous) applications.
First lecture will be on Tuesday January 18 between 14:15-16:00 in the seminar room 3721, institutionen för matematik. We continue our lectures every second Tuesday, please for more details see the course homepage.
Applied combinatorics
The course will cover several topics of modern combinatorics. One important question is how many are there of a certain object? We will learn techniques, such as recursions, power series and tools from algebra, to answer this question. Important objects will be permutations and partitions. We will also study some applications of graph theory, in particular flows in networks. An other interesting area is error correcting codes, where we will learn som of the basic theory. Finally we will also discuss the mathematics of voting procedures.
Prerequisite: A basic course in Discrete Mathematics. A basic course in linear algebra.
The history of mathematics
Groups and rings
As James Newman once said, algebra is "a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing".
Abstract algebra is the area of mathematics that investigates algebraic structures. By defining certain operations on sets one can construct more sophisticated objects: groups, rings, fields. These operations unify and distinguish objects at the same time. Adding matrices work similarly to adding integers while matrix multiplication is quite different from multiplication modulo n. Because structures like groups or rings are richer than sets we cannot compare them using just their elements, we have to relate their operations as well. For this reason group and ring homomophisms are defined. These are functions between groups or rings that "respect" their operation. This type of function are used not only to relate these objects but also to build new ones, quotients for example.
Although at this point it may seem like the study of these new and strange objects is little more than an exercise in a mathematical fantasy world, the basic results and ideas of abstract algebra have permeated and are at the foundation of nearly every branch of mathematics.
Galois theory
Galois theory is a beautiful and fundamental part of algebra dealing with field extensions and field automorphisms. The main theorem gives a 1-1 correspondence between the subextensions of a given field extension satisfying certain properties and the subgroups of a group of automorphisms associated to the extension.
Galois theory has many applications. Some of the best known applications are the proof of the impossibility of the trisection of a general angle with ruler and compass only and the proof that the solutions of a general algebraic equation of degree five or higher cannot be given only in terms of n-th roots and the basic algebraic operations.
Topics in mathematics IV: Applied topology
How can a topological space and its properties be described? One could try to use geometric and descriptive language. For example one might write: a 2 dimensional bounded subspace of the 3 dimensional Euclidean space without a boundary with 2 holes. Such a descriptive language however is often imprecise and may lead to wrong conclusions. For example same description could be visualize in different ways by different people. To remedy this problem, Algebraic Topology uses the precise language of algebra to describe geometry. Homology and cohomology are one of the most important tools in this translation process. It has been a great achievement in mathematics to realize that some important geometric properties of spaces can be described by these invariants. In this course we will study two specific cohomology theories: K-theory and De Rham cohomology. They both have the advantage of being elementary, and can be studied with no particular previous knowledge. K-theory deals with vector bundles over a space. An example of a vector bundle is the Möbius band which consists of a family of lines twisting around the circle. De Rham cohomology uses ideas well known from vector analysis. We will see how these theories are used to compute invariants of spaces, and we will try to give several applications.
Game Theory
Game theory provides mathematical tools for the analysis of strategic interactions, with applications to many fields, ranging from political science and economics to biology and computer science. One half of this course is devoted to classical game theory and deals with "games" in a very broad sense of the word. The other half is devoted to combinatorial game theory, where we restrict our attention to a class of two-player games with perfect information, including many well-known board games like chess and go. |
Linear Algebra Done Right
Sheldon Axler
Preface to the Student
You are probably about to begin your second exposure to linear
algebra. Unlike your first brush with the subject, which probably emphasized
Euclidean spaces and matrices, we will focus on abstract vector
spaces and linear maps. These terms will be defined later, so don't
worry if you don't know what they mean. This book starts from the
beginning of the subject, assuming no knowledge of linear algebra.
The key point is that you are about to immerse yourself in serious
mathematics, with an emphasis on your attaining a deep understanding
of the definitions, theorems, and proofs.
You cannot expect to read mathematics the way you read a novel. If you zip
through a page in less than an hour, you are probably going too fast.
When you encounter the phrase "as you should verify", you should
indeed do the verification, which will usually require some writing on
your part. When steps are left out, you need to supply the missing
pieces. You should ponder and internalize each definition. For each
theorem, you should seek examples to show why each hypothesis is
necessary. |
This is the homepage for MATH 1150 (Mathematics of Games). This page will be updated throughout the term with important information for our course, including homework assignments, review materials, and more.
Most of us have played games such as Tic-Tac-Toe, chess, Go, checkers, and poker. Many games can be studied mathematically using a branch of mathematics called game theory.
We will discuss various facets of elementary game theory, including (but not limited to!) how to formulate strategies, what makes some strategies "better" than others, what
makes some games difficult or impossible to analyze, and applications to real-world concepts. Specific topics we may cover include the Nash equilibrium, the prisoner's dilemma,
and bluffing in poker.
The class will not be purely theoretical; we will spend lots of time applying the course concepts by playing various games. A homework assignment might involve analyzing a
simple game, devising a winning strategy, and then trying it out during class.
The course will be roughly broken up into two halves. The first half will be devoted to games where both players move simultaneously, without knowledge of the other
player's move. (These are also called matrix games.) In the second half, we will focus on games where the players move sequentially, taking turns, until the game ends.
(These are also called sequential games.)
Grading scheme
Your term grade will consist of homework assignments (which may include problems from the text, problems I make up, or slightly longer open-ended projects), one midterm exam, and one final exam, broken down in the following way:
Assignment 6 and solutions. (NOTE: the bottom line on page 2 was cut off during scanning. It only
says that every remaining position can reach the "big L" shape, which is a L(oss), so all remaining positions are W(ins).)
Students in this course are expected to abide by the University of Denver's Honor Code and the procedures put
forth by the Office of Citizenship and Community Standards. Academic dishonesty - including, but not limited to,
plagiarism and cheating - is in violation of the code and will result
in a failing grade for the assignment or for the course. As student members of a community
committed to academic integrity and honesty, it is your responsibility to become familiar with the DU
Honor Code and its procedures: see |
Definitions, including the properties of linearity, interval addition, estimation, and integrating backwards. Also includes several examples, the absolute values property, and the change of variables formula. |
Too many students are starting science and engineering degrees without studying maths at A-level, according to a report.
Around seven in 10 biology undergraduates, almost two-fifths of those taking chemistry at university and a fifth of those on engineering courses have not studied maths past GCSE level, it found.
Lord Willis of of Knaresborough, chairman of the House of Lords sub-committee which published the report, said he was "absolutely gobsmacked" by the figures.
The report suggests that the level of maths required by universities to study science-based courses is not demanding enough, and is deterring people from taking the subject at A-level.
It calls for all teenagers to continue studying maths past the age of 16, and for all students who want to study STEM (science, technology, engineering and maths) at university to study the subject to A-level standard.
"We were absolutely gobsmacked that 20% of engineering undergraduates do not have A2 (A-level) mathematics, 38% of chemistry and economics undergraduates do not have A2 maths and 70% of biology undergraduates do not have A-level maths," Lord Willis said.
"If we are talking about a world-class STEM base, where mathematics is the cornerstone of virtually every science programme, then it is really quite amazing that we have so few students who have studied maths, literally, beyond GCSE and often, not even with a grade A."
The report, which investigated STEM subjects in higher education, says that universities must toughen up their maths entry requirements for science and maths based degrees.
Professor Sir William Wakeham, international secretary and senior vice-president of the Royal Academy of Engineering, who was the specialist adviser for the committee said they had spoken to pharmaceutical industries who have "enormous demand" for statistical analysis on the effects of their drugs.
Many of their graduates have studied biological science and "not studied maths from the age of 16 with a minimal level of statistics", he said.
"Employers are rather keen that all of their students should have these kinds of skills," he said.
Sir William added that because of the modularisation of exams, it is possible "to avoid whole subjects in maths, like calculus and still find yourself in an engineering discipline where maths is essential."
There are some engineering students that have "virtually no understanding" of mechanics, Lord Willis said.
A number of university vice-chancellors told the sub-committee that their institution was being forced to offer remedial maths classes not only for those that had not studied the subject at A-level, but for those who had taken it and done well, the report said.
Professor Sir Christopher Snowden, vice-chancellor of Surrey University, told the group: "I think that in pretty much every university the issues over maths skills apply.
"Indeed, this has been an issue now for many years within universities, partly due to the increase in the breadth of maths that is studied at schools but with a lack of depth.
"In some cases, for example, there is a complete absence of calculus, which is an issue in many subjects."
The sub-committee recommends that the Government should make maths compulsory for all students after GCSE.
"We share the view that all students should study some form of maths post-16, the particular area of maths depending on the needs of the student.
"For example, prospective engineering students would require mechanics as part of their post-16 maths, whereas prospective biology students would benefit from studying statistics."
It adds: "We recommend also that maths to A2 level should be a requirement for students intending to study STEM subjects in higher education."
A Department for Education spokeswoman said: "We want the majority of young people to continue studying maths up to 18 to meet the growing demand for employees with maths skills.
"We are reviewing how maths is taught in schools and overhauling GCSEs and A-levels to make sure they are robust and in line with the best education systems in the world."
I was the only student at my 6th form college to study physics without maths in conjunction, and at the beginning I had a lot of gaps to fill. However I did manage to learn the necessary skills in my own time and secured a high grade thankfully. From that experience I'd say if a student wants to achieve then they will learn the required skills whether they've got an A level or not.
Loading comments…
I did a Chemistry degree without Maths A level although I did have Additional Maths O level ie basic calculus etc and I found a number of courses very difficult and one or two impossible. So I would have thought maths essential for Physics and Engineering although not for Biology.
Loading comments…
Loading comments…
Why do people not see the obvious. A Levels do not equip students for higher education anymore. We should abandon them in favour of Highers or equivalent. I went to University in Canada and they require Higher Levels: Math, English, Science for almost every subject. Six Highers makes much more sense that two, three, or even four A Levels. Oh by the way I taught at Unviersity for 17 years and can confirm math and english skills are, with a few exceptions, appalling in the UK.
Loading comments…
As a hobby. I am reading a little A level physics and maths which to some regret I chose not to do at school.. In my casual study maths does seem essential, such as using trigonometry when studying mechanics. Maths does seem to be an important part of most sciences, so I support the view that science students should get a good understanding by doing A level maths as soon as possible.
Loading comments…
You can't really cope with scientific analysis without a skill in mathematics. Interestingly, I am informed, we have only one science based graduate MP in the House of Commons. It can be appreciated that an MP without a science background is not suited to lead a science based Ministry. Likewise mathematics for the Exchequer, or the bankers will blind the fumbling MP
with s c i e n c e !
Belthazor_A: You can't really cope with scientific analysis without a skill
Loading comments…
Quite a question. During my Maths degree, by far the best mathematicians in the electromag calculus classes were the Physics degree students who were there because they needed that particular technique. They were birilliant because they used it, rather than merely learned it for a degree - so perhaps we should ask them.
Loading comments…
Pass it,probably not but they must be made aware of the importance of it ahead. I believe they only have to be familiar with the concepts so they can know where to reference what they need when demanded. But they do not have to be Mathematicians |
...Using a student-centered approach, I help the student navigate unfamiliar waters in this subject. Topics covered include functions, "families of functions," equations, inequalities, systems of equations and inequalities, polynomials, rational and radical equations, complex numbers, and sequences... |
Description
This new textbook in Signals and Systems provides a pedagogically-rich approach to what can oftentimes be a mathematically 'dry' subject. Chaparro introduces both continuous and discrete time systems, then covers each separately in depth. Careful explanations of each concept are paired with a large number of step by step worked examples. With features like historical notes, highlighted 'common mistakes,' and applications in controls, communications, and signal processing, Chaparro helps students appreciate the usefulness of the techniques described in the book. Each chapter contains a section with Matlab applications.
pedagogically rich introduction to signals and systems using historical notes, pointing out 'common mistakes,' and relating concepts to realistic examples throughout to motivate learning the material introduces both continuous and discrete systems early, then studies each (separately) in more depth later
extensive set of worked examples and homework assignments, with applications to controls, communications, and signal processing throughout provides review of all the background math necessary to study the subject
Matlab applications in every chapter
Recommendations:
Save
3.63%
Save
7.13%
Save
4.79%
Save
4.29%
Save
5.58%
Save
25.8896 |
Here are my online notes for my Linear Algebra course that I teach here at Lamar University. Despite the fact that these are my "class notes" they should be accessible to anyone wanting to learn Linear Algebra or needing a refresher.
These notes do assume that the reader has a good working knowledge of basic Algebra. This set of notes is fairly self contained but there is enough Algebra type problems (arithmetic and occasionally solving equations) that can show up that not having a good background in Algebra can cause the occasional problem.
Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn Linear Algebra I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn't covered in class.
2. In general I try to work problems in class that are different from my notes. However, with a Linear Algebra course while I can make up the problems off the top of my head there is no guarantee that they will work out nicely or the way I want them to. So, because of that my class work will tend to follow these notes fairly close as far as worked problems go. With that being said I will, on occasion, work problems off the top of my head when I can to provide more examples than just those in my notes. Also, I often don't have time in class to work all of the problems in the notes and so you will find that some sections contain problems that weren't worked in class due to time restrictions.
3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible in writing these notes up, but the reality is that I can't anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that I've not included here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are.
4. This is somewhat related to the previous three items, but is important enough to merit its own item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!! Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class.
Here is a listing and brief description of the material in this set of notes.
Systems of Equations and Matrices Systems of Equations – In this section we'll introduce most of the basic topics that we'll need in order to solve systems of equations including augmented matrices and row operations. Solving Systems of Equations – Here we will look at the Gaussian Elimination and Gauss-Jordan Method of solving systems of equations. Matrices – We will introduce many of the basic ideas and properties involved in the study of matrices. Matrix Arithmetic & Operations – In this section we'll take a look at matrix addition, subtraction and multiplication. We'll also take a quick look at the transpose and trace of a matrix. Properties of Matrix Arithmetic – We will take a more in depth look at many of the properties of matrix arithmetic and the transpose. Inverse Matrices and Elementary Matrices – Here we'll define the inverse and take a look at some of its properties. We'll also introduce the idea of Elementary Matrices. Finding Inverse Matrices – In this section we'll develop a method for finding inverse matrices. Special Matrices – We will introduce Diagonal, Triangular and Symmetric matrices in this section. LU-Decompositions – In this section we'll introduce the LU-Decomposition a way of "factoring" certain kinds of matrices. SystemsDeterminants The Determinant Function – We will give the formal definition of the determinant in this section. We'll also give formulas for computing determinants of 2 × 2 and 3× 3 matrices. Properties of Determinants – Here we will take a look at quite a few properties of the determinant function. Included are formulas for determinants of triangular matrices. The Method of Cofactors – In this section we'll take a look at the first of two methods form computing determinants of general matrices. Using Row Reduction to Find Determinants – Here we will take a look at the second method for computing determinants in general. Cramer's Rule – We will take a look at yet another method for solving systems. This method will involve the use of determinants.
Linear Algebra Dot Product & Cross Product – Here we'll look at the dot product and the cross product, two important products for vectors. We'll also take a look at an application of the dot product. Euclidean n-Space – We'll introduce the idea of Euclidean n-space in this section and extend many of the ideas of the previous two sections. Linear Transformations – In this section we'll introduce the topic of linear transformations and look at many of their properties. Examples of Linear Transformations – We'll take a look at quite a few examples of linear transformations in this section.
Vector Spaces Vector Spaces – In this section we'll formally define vectors and vector spaces. Subspaces – Here we will be looking at vector spaces that live inside of other vector spaces. Span – The concept of the span of a set of vectors will be investigated in this section. Linear Independence – Here we will take a look at what it means for a set of vectors to be linearly independent or linearly dependent. Basis and Dimension – We'll be looking at the idea of a set of basis vectors and the dimension of a vector space. Change of Basis – In this section we will see how to change the set of basis vectors for a vector space. Fundamental Subspaces – Here we will take a look at some of the fundamental subspaces of a matrix, including the row space, column space and null space. Inner Product Spaces – We will be looking at a special kind of vector spaces in this section as well as define the inner product. Orthonormal Basis – In this section we will develop and use the Gram-Schmidt process for constructing an orthogonal/orthonormal basis for an inner product space. Least Squares – In this section we'll take a look at an application of some of the ideas that we will be discussing in this chapter. QR-Decomposition – Here we will take a look at the QR-Decomposition for a matrix and how it can be used in the least squares process. Orthogonal Matrices – We will take a look at a special kind of matrix, the orthogonal matrix, in this section.
Eigenvalues and Eigenvectors Review of Determinants – In this section we'll do a quick review of determinants. Eigenvalues and Eigenvectors – Here we will take a look at the main section in this chapter. We'll be looking at the concept of Eigenvalues and Eigenvectors. Diagonalization – We'll be looking at diagonalizable matrices in this section.
Introduction We will start this chapter off by looking at the application of matrices that almost every book on Linear Algebra starts off with, solving systems of linear equations. Looking at systems of equations will allow us to start getting used to the notation and some of the basic manipulations of matrices that we'll be using often throughout these notes.
Once we've looked at solving systems of linear equations we'll move into the basic arithmetic of matrices and basic matrix properties. We'll also take a look at a couple of other ideas about matrices that have some nice applications to the solution to systems of equations.
One word of warning about this chapter, and in fact about this complete set of notes for that matter, we'll start out in the first section or to doing a lot of the details in the problems, but towards the end of this chapter and into the remaining chapters we will leave many of the details to you to check. We start off by doing lots of details to make sure you are comfortable working with matrices and the various operations involving them. However, we will eventually assume that you've become comfortable with the details and can check them on your own. At that point we will quit showing many of the details.
Here is a listing of the topics in this chapter.
Systems of Equations – In this section we'll introduce most of the basic topics that we'll need in order to solve systems of equations including augmented matrices and row operations.
Solving Systems of Equations – Here we will look at the Gaussian Elimination and Gauss- Jordan Method of solving systems of equations.
Matrices – We will introduce many of the basic ideas and properties involved in the study of matrices.
Matrix Arithmetic & Operations – In this section we'll take a look at matrix addition, subtraction and multiplication. We'll also take a quick look at the transpose and trace of a matrix.
Properties of Matrix Arithmetic – We will take a more in depth look at many of the properties of matrix arithmetic and the transpose.
Inverse Matrices and Elementary Matrices – Here we'll define the inverse and take a look at some of its properties. We'll also introduce the idea of Elementary Matrices.
LU-Decompositions – In this section we'll introduce the LU-Decomposition a way of "factoring" certain kinds of matrices.
SystemsLinear Algebra Systems of Equations Let's start off this section with the definition of a linear equation. Here are a couple of examples of linear equations. 5
6x − 8 y +10z = 3 7x − x = 1 − 1 2 9 In the second equation note the use of the subscripts on the variables. This is a common notational device that will be used fairly extensively here. It is especially useful when we get into the general case(s) and we won't know how many variables (often called unknowns) there are in the equation.
So, just what makes these two equations linear? There are several main points to notice. First, the unknowns only appear to the first power and there aren't any unknowns in the denominator of a fraction. Also notice that there are no products and/or quotients of unknowns. All of these ideas are required in order for an equation to be a linear equation. Unknowns only occur in numerators, they are only to the first power and there are no products or quotients of unknowns.
Next we need to take a look at the solution set of a single linear equation. A solution set (or often just solution) for (1) is a set of numbers t , t ,…, t so that if we set x = t , x = t , … , 1 2 n 1 1 2 2 x = t then (1) will be satisfied. By satisfied we mean that if we plug these numbers into the left n n side of (1) and do the arithmetic we will get b as an answer.
The first thing to notice about the solution set to a single linear equation that contains at least two variables with non-zero coefficents is that we will have an infinite number of solutions. We will also see that while there are infinitely many possible solutions they are all related to each other in some way.
Note that if there is one or less variables with non-zero coefficients then there will be a single solution or no solutions depending upon the value of b.
Let's find the solution sets for the two linear equations given at the start of this section.
Now, what this tells us is that if we have a value for x then we can determine a corresponding 2 value for x . Since we have a single linear equation there is nothing to restrict our choice of x 1 2 and so we we'll let x be any number. We will usually write this as x = t , where t is any 2 2 number. Note that there is nothing special about the t, this is just the letter that I usually use in these cases. Others often use s for this letter and, of course, you could choose it to be just about anything as long as it's not a letter representing one of the unknowns in the equation (x in this case).
Once we've "chosen" x we'll write the general solution set as follows, 2 5 1
x = t − x = t 1 2 63 7
So, just what does this tell us as far as actual number solutions go? We'll choose any value of t and plug in to get a pair of numbers x and x that will satisfy the equation. For instance picking 1 2 a couple of values of t completely at random gives,
1 t = 0 : x = − , x = 0 1 2 7
5 1 t = 27 : x = 27 − = 2, x = 27 1 ( ) 2 63 7
We can easily check that these are in fact solutions to the equation by plugging them back into the equation. ⎛ 1 ⎞ 5 t = 0 : 7 − − (0) = 1 − ⎜ ⎟ ⎝ 7 ⎠ 9
t = ( ) 5 27 : 7 2 − (27) = 1 − 9
So, for each case when we plugged in the values we got for x and x we got -1 out of the 1 2 equation as we were supposed to.
(b) 6x − 8 y +10z = 3 We'll do this one with a little less detail since it works in essentially the same manner. The fact that we now have three unknowns will change things slightly but not overly much. We will first solve the equation for one of the variables and again it won't matter which one we chose to solve for. 10z = 3 − 6x + 8 y
3 3 4 z = − x +
y 10 5 5
In this case we will need to know values for both x and y in order to get a value for z. As with the first case, there is nothing in this problem to restrict out choices of x and y. We can therefore let them be any number(s). In this case we'll choose x = t and y = s . Note that we chose different letters here since there is no reason to think that both x and y will have exactly the same value (although it is possible for them to have the same value).
As with the first part if we take either set of three numbers we can plug them into the equation to verify that the equation will be satisfied. We'll do one of them and leave the other to you to check. ⎛ 3 − ⎞ ⎛ 26 ⎞
6 −8 ⎜ ⎟ (5) +10 = 9 − − 40 + 52 = 3 ⎜ ⎟
⎝ 2 ⎠ ⎝ 5 ⎠ [Return to Problems]
The variables that we got to choose for values for ( x in the first example and x and y in the 2 second) are sometimes called free variables.
We now need to start talking about the actual topic of this section, systems of linear equations. A system of linear equations is nothing more than a collection of two or more linear equations. Here are some examples of systems of linear equations. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.