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Cleveland, TX Calculus the integration of material from other programs such as Microsoft Word into PowerPoint. Pre-algebra begins the student's entry into higher math. In many ways it is more important than the upper level math courses.
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This research is an attempt to use animation to display complex math problems on computer-based testing. To translate math problem into mathematical expression is one of the key factors in math. However, examinees who cannot understand the literal meaning of the sentence will not be able to express it mathematically, even if they have the necessary mathematical skills. To solve this problem, this research explores the possibility of using animation for delivering math problems to examinees. This paper describes an experiment carried out with 19 college students using 4 different complex math problems, delivered either in all-text mode or in all-animation mode, to examine whether the modes affects in understanding the math problems. The result indicates that although the students felt it easier to understand the math problem from the all- animation mode, there were no significant differences in the test scores, between 2 modes.
Published in 2009.
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by other sources not affiliated with Microsoft Academic Search.
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Calcoolate: Calcoolate provides users with a simple calculator with advanced expression support, mathematic functions, and history for viewing past calculations.
Calcr: Similar to Calcoolate, Calcr is a web-based calculator with mathematic expression and function support as well as history logging in a very minimalist design.
Create a Graph: Create a Graph is a free tool by Students' Classroom that aims to make it easy for students to create bar graphs, line graphs, area graphs, pie charts, and point graphs. Navigate through its easy to understand visual interface to add data and customize graphs.
e-Tutor Graphing Calculator: Advanced web-based graphing calculator allowing students to enter one or more equations and view them with position/intersection indicators and zooming functionality.
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Let's Review: Geometry
Anticipating the New York State Board of Regents? new examination in geometry, this brand-new classroom text presents a detailed review of all topics prescribed as part of the high school curriculum. Separate chapters analyze and explain: the language of geometry; parallel lines and polygons; congruent triangles and inequalities; special quadrilaterals and coordinates; similarity (including ratio and proportion, and proving products equal); right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and working in space (an introduction to solid geometry). Each chapter includes practice exercises with answers provided at the back of the book.
TABLE-OF-CONTENTS: Preface The Language of Geometry Parallel Lines and Polygons Congruent Triangles and Inequalities Special Quadrilaterals and Coordinates Ratio, Proportion, and Similarity Right Triangles and Trigonometry Circles and Angle Measurement Transformation Geometry Locus and Coordinates Area and Volume of Solids Answers and Solution Hints to Practice Exercises Glossary of Geometry Terms Some Geometric Relationships Worth Remembering
Let's Pretend This Never Happened
Subject: Pride and Self-Esteem, Friends and Friendship, Feelings and Emotions, Middle School
Read (who Jamie thinks is a goon!) and the impending visit of her troll-like little cousin.
Will Jamie survive? Will she go mad? Will she send her mom's nasty casserole to starving children in Wheretheheckistan? You'll just have to read the first installment of Dear Dumb Diary to find out!
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Facing a tough numeracy test to get the job of your dreams? Need to develop your advanced numeracy skills? Want plenty of practise so you'll pass with flying colours? With record levels of unemployment psychometric and numeracy testing have become t…
Chambers Adult Learners' Guide to Numeracy is a completely new book aimed at adults who lack confidence in their numeracy skills. The book provides users with an understanding of the key concepts and methods, then applies them in real-world situatio…
Is this the right book for me? An ideal trigonometry handbook Whether you're new to trigonometry or just need to refresh your knowledge, Understand Trigonometry is the ideal handbook. Offering a complete introduction, with fully worked examples and…
This new edition of Chambers Adult Learners' Guide to Numeracy is aimed at adults who lack confidence in their numeracy skills, now in a new, more accessible format. The book provides users with an understanding of the key concepts and methods, then…
For most of us, math is a struggle--even when adding up the price of shopping, or calculating how much should be in our bank accounts. George Lane has devised a series of simple steps, and in this wonderful and fun book teaches us how to perform a r…
Master math at your own pace! Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school? Quick Arithmetic, Third Edition i…
Guides you through the basics of primary school maths and covers the dilemmas and problems you are likely to be confronted with, including: number bonds, place value and decimals; long multiplication and division; fractions, percentages and decimals…
Aptitude tests assess a person's abilities or intelligence, often as part of an IQ test, whilst personality questionnaires help to reveal an individual's characteristics or personality traits. Both are of equal value to employers as they can indicat…
Includes the activities that use real-life adult contexts - work, home, health and leisure - to ensure that numeracy is relevant to adult learners. This title offers resources that are matched to the Adult Numeracy Core Curriculum. It features activ…
Maths can often leave children - and parents - perplexed. This book explains the various ways of teaching maths. It shows you how to: master 'number bonds' and 'number lines'; divide by 'chunking'; multiply using 'the grid method'; work with fractio…
Every day we are faced with financial decisions. Should I buy that DVD player or 100 lottery tickets? What percentage of my salary should I allocate to my 401(k)? How much should I be saving for my daughter's college education? Will I be better off…
"Test Your Numerical Aptitude" will allow those who are uncertain of their numerical ability to build their confidence, slowly and surely, until they are ready to tackle any kind of numerical test. For those who already have some numerical skills, t…
Maths is one of those tricky subjects that continues to throw us problems, even after our school days. From splitting the bill in a restaurant, to counting out change at a till or working out exchange rates, maths can still send us into a sweat in o…
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Find a Griffith MathReal world applications are presented within the course content and a function's approach is emphasized. This course builds on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials, imaginary and complex numbers, quadratics, and includes the study of trigonometric functions.
...I would work with a student to isolate and determine the area in which there is a need for clarity and instruction and develop lessons that coincide with school-related texts and reflecting real-life scenarios. I have programmed in various Cobol versions from AcuCobol, RM-Cobol and M-F Cobol sin...
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Book Description: Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader's practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers. Volume 1: Operations on Rational Numbers Linear Equations of Single Variable Multiplication Formulae Absolute Value and Its Applications Congruence of Triangles Similarity of Triangles Divisions of Polynomials Solutions to Testing Questions Volume 2: Congruence of Integers Decimal Representation of Integers Pigeonhole Principle Linear Inequality and System of Linear Inequalities Inequalities with Absolute Values Geometric Inequalities Solutions to Testing Questions
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201308150 / ISBN-13: 9780201308150
Mathematics All Around
"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking ...Show synopsis"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.Hide synopsis
Sound copy, mild reading wear. May have scuffs or missing...Good. Sound copy, mild reading wear. May have scuffs or missing DJ. May have some note, highlighting or underlining. Purchasing this item helps us provide vocational opportunities to people with barriers to employment.
Reviews of Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff
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So What Are Logarithms Good For, Anyway?
Summary: A teacher's guide to the applications of logarithmic functions.
As always, things get harder when we get into word problems. There are a few things I want them to take away here.
First—logs are used in a wide variety of real world situations.
Second—logs are used because they compress scales. In other words, because they grow so slowly, we use logarithmic scales whenever we want to work with a function that, by itself, grows too quickly. Or, to put it another way, we use logarithms whenever something varies so much that you don't care exactly what is, just what the power of 10 is. Don't say all this before they start working, but hopefully they will come up with something like this on #6.
Homework:
"Homework: What Are Logarithms Good For, Anyway?"
In addition to following up on the in-class work, the homework here also introduces the common and natural logs. It's a bit of a weak connection, but I had to stick them somewhere.
Time for Another Test!
The sample test is actually pretty important here. It pulls together a lot of ideas that have been covered pretty quickly.
The extra credit is just a pun. The answer is log cabin or, better yet, natural log cabin. Who says math can't be fun?
According to my reckoning, you are now approximately halfway through the curriculum. Mid-terms are approaching. If there are a couple of weeks before mid-terms, I would not recommend going on to radicals—spend a couple of weeks reviewing. Each topic (each test, really) can stand a whole day of review. It may be the most important time in the whole class
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Product Description
Microsoft Excel is the perfect partner for any mathematics curriculum. Applicable to several versions of Microsoft Excel, these books contain prepared templates and lessons that can be utilized to stimulate group discussions, put on-line as a supplemental tutorial, completed as a group visiting the computer lab, or set up as stations in a classroom. Aligned with NCTM & TEKS Standards. Grades 6
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Advanced Calculus Textbooks
Advanced calculus textbooks examine complicated principles and applications of calculus. As a result, advanced calculus textbooks are used mostly at college level. Students often continue to find use in advanced calculus textbooks as their careers progress from pre-calculus textbooks. With this in mind, Textbooks.com has the most comprehensive and up-to-date advanced and applied calculus textbooks available
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The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts — ...
Titles in Barron's extensive Painless Series cover a wide range of subjects as they are taught on middle school and high school levels. These books are written for students who find the subjects unusually difficult and confusing--or in many cases, just plain boring. Barron's Painless Series authors' main goal is to clear up students' confusion and perk up their interest by emphasizing the intriguing and often exciting ways in which they ...
Now students have nothing to fear … Math textbooks can be as baffling as the subject they're teaching. Not anymore. The best-selling author of The Complete Idiot's Guide to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared ...
It used to take years or even decades for disruptive innovations to dethrone dominant products and services. But now any business can be devastated virtually overnight by something better and cheaper. How can executives protect themselves and harness the power of Big Bang Disruption? Just a few years ago, drivers happily spent more than $200 for a GPS unit. But as smartphones exploded in popularity, free navigation apps exceeded ...
From astrophysics to condensed matter theory, nearly all of modern physics employs the path integral technique. In this presentation, the developer of path integrals and one of the best-known scientists of all time, Nobel Prize–winning physicist Richard P. Feynman, presents unique insights into this method and its applications. Avoiding dense, complicated descriptions, Feynman articulates his celebrated theory in a clear, concise manner, ... But how does one exactly do data science? Do you have to hire one of these priests of the dark arts, the "data scientist," to ...
Your step-by-step solution to mastering precalculus Understanding precalculus often opens the door to learning more advanced and practical math subjects, and can also help satisfy college requisites. Precalculus Demystified , Second Edition, is your key to mastering this sometimes tricky subject. This self-teaching guide presents general precalculus concepts first, so you'll ease into the basics. You'll gradually master functions, graphs of ...
Prov ...
This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity ...
This edition includes the most recent Integrated Algebra The book reviews all pertinent math topics, including sets, algebraic language, linear ...
When the numbers just don't add up… Following ... Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra ...
Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately, there's Schaum's ...
This edition includes the most recent Algebra 2/Trigonometry Regents tests through June 2013. These ever popular guides contain study tips, test-taking strategies, score analysis charts, and other valuable features. They are an ideal source of practice and test preparation. The detailed answer explanations make each exam a practical learning experience. In addition to practice exams that reflect the standard Regents format, this book reviews ... ...
Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to ...
Over the last thirty years, many influential church leaders and church planters in America have adopted various models for reaching unchurched people. An "attractional" model will seek to attract people to a local church. Younger leaders may advocate a more "missional" approach, in which believers live and work among unchurched people and intentionally seek to serve like Christ. While each of these approaches have merit, something is ...
People are hungry to make a difference in their community, yet most don't know where to start. In fact, "serving the least" is often one of the most neglected biblical mandates in the church. Barefoot Church shows readers how today's church can be a catalyst for individual, collective, and social renewal in any context. Whether pastors or laypeople, readers will discover practical ideas that end up being as much about the Gospel and ...
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plex Numbers, Vectors and Matrices
Summary: This module sets out to instruct about complex numbers: what they are, what they mean, how to manipulate them, and the different ways to describe them (i.e. polar form). The second half of this module proposes to introduce the characteristics of complex vectors and matrices and how they compare to the laws governing standard vectors and matrices.
Complex Numbers
A complex number is simply a pair of real numbers. In order to
stress however that the two arithmetics differ we separate the
two real pieces by the symbol
i.
More precisely, each complex number,
zz, may be uniquely expressed by
the combination
x+iyxy,
where xx and
yy are real and
i denotes
-1-1.
We call xx the real part and
yy the imaginary part of
zz. We now summarize the main
rules of complex arithmetic.
Complex Vectors and Matrices
A complex vector (matrix) is simply a vector (matrix) of
complex numbers. Vector and matrix addition proceed, as in the
real case, from elementwise addition. The dot or inner product
of two complex vectors requires, however, a little
modification. This is evident when we try to use the old
notion to define the length of a complex vector. To wit, note
that if:
z=(1+i1−i)z11
then
zTz=1+i2+1−i2=1+2i−1+1−2i−1=0zz12121211210
Now length should measure the distance
from a point to the origin and should only be zero for the
zero vector. The fix, as you have probably guessed, is to sum
the squares of the magnitudes of the
components of zz. This is
accomplished by simply conjugating one
of the vectors. Namely, we define the length of a complex
vector via:
z=z¯Tzzzz
(4)
In the example above this produces
|1+i|2+|1−i|2=4=2121242
As each real number is the conjugate of itself, this new
definition subsumes its real counterpart.
The notion of magnitude also gives us a way to define limits
and hence will permit us to introduce complex calculus. We say
that the sequence of complex numbers,
znn=12…n12…zn,
converges to the complex number
z0z0
and write
zn→z0znz0
or
z0=limit n→∞znz0nzn
when, presented with any
ε>0ε0
one can produce an integer NN for which
|zn−z0|<εznz0ε
when
n≥NnN.
As an example, we note that
i2n→02n0.
Examples
Example 1
As an example both of a complex matrix and some of the rules
of complex
arithmetic, let us examine the following matrix:
F=(11111i-1−i1-11-11−i-1i)F11111-11-11-11-1
(5)
Let us attempt to find
FF¯FF.
One option is simply to multiply the two matrices by brute
force, but this particular matrix has some remarkable
qualities that make the job significantly
easier. Specifically, we can note that every element not on
the diagonal of the resultant matrix is equal to
0. Furthermore, each element on the
diagonal is 4. Hence, we quickly arrive at the matrix
FF¯=(4000040000400004)=4iFF40000400004000044
(6)
This final observation, that this matrix multiplied by its
transpose yields a constant times the identity matrix, is
indeed remarkable. This particular matrix is an example of a
Fourier matrix, and enjoys a number of interesting
properties. The property outlined above can be generalized
for any
FnFn,
where FF refers to a Fourier
matrix with nn rows and
columns
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Prepare for algebra with simple equations, powers, polynomials and much more. More than 120 hours of instruction and 139 lessons on 10 interactive CDs with lectures, problems, step-by-step solutions, tests and automated grading. Includes a 750-page student workbook, answer key and 17 chapter tests. Version 2.0. Windows and Mac compatible.
The new and improved edition includes:
Interactive lectures
Automated grading
Over a dozen more lessons and hundreds of new problems and solutions
Hints and second chance options for many problems
Animated buddies to cheer the student on
Non-Consumable Textbook w/ full lecture
Reference numbers for each problem so students and parents can see where a problem was first introduced
A digital gradebook that can manage multiple student accounts and be easily edited by a parent
Built in back up and gradebook transfer feature
Compatible with PC (Windows XP or later) and Mac (OS 10.4 or later)
Students watch video lectures on CD-ROM, do problems from the 600-page workbook. When they need help or review, you've got a printed Answer Key plus audiovisual step-by-step solutions to every homework and quiz problem.
Sample Pages
Sample Lectures
TheLecture & Practice CD'scontain 10-15 minute lectures for every lesson in the print textbook. They also feature multimedia step-by-step explanations to the 5 practice problems that accompany each lesson. This set of CDs is ideal for students who prefer listening and watching to reading.
Sample Solutions
TheSolution CD's contain a multimedia step-by-step explanation to every single one of the almost 3,000 homework problems in the textbook. If you're tired of having to help your child do half his homework, or if you simply want to give him access to a library of quality explanations which will undoubtedly supplement and reinforce his understanding, this is the tool you need.
by Deborah G on 2013-05-28 We used Singapore for my oldest dd until 7th grade. Then, per Sonlight's recommendation, we switched to TT. We've done Pre-Algebra and 1/2 a year of Algebra. And my daughter who does complex math games in her spare time for fun has started complaining about math. I finally sat down and talked to her about it. She feels TT is too easy. I then really looked at it and I totally agree. The exercises are basic "chew it up and spit it out" type questions, and much of the time any "meat" is already half digested. No critical thinking required. I cannot believe Sonlight recommends this product.
I am giving it two stars because dd#2 ended up with about three years of patchy math instruction as we dealt with life. However, in 6th grade, she is excelling in the Pre-Algebra course -- in spite of all the holes in her math learning. She's a smart cookie, but not that smart. But it is doing an excellent job at helping her patch up the holes. We'll be switching back to Singapore next year.
by Lisa L on 2013-02-13 I have enjoyed using Teaching Textbooks with my son. I find that, even though it is easy, my son is learning the concepts well. I love that each question tells them what lesson they first learned the concept on, so they can go back and review if need be.
by Rina F on 2011-06-22 TT is great. DO take the placement test to find the correct level for your child. My daughter went from hating math to enjoying math. I was worried about how much she was retaining since it was so much fun. However, we are required to take standardized tests each year and she did excellent! VERY satisfied!
by Shannon S on 2011-06-09 Very easy to implement. My daughter did this program mostly independently. When she would run into something she didn't understand (once every 10-20 lessons or so), I could figure out how to help her simply by briefly reading the text with her and going over the examples they presented.
by JESSICA P on 2010-09-09 TT has saved our homeschool. Yes, it is a bit easy, so DO the PLACEMENT TESTS and place your child in the right level. It may be easy but it is also thorough. It DOES teach everything it ought to if you stick with it through the years. Who says learning math has to be difficult? I want my dd to learn math, not be frustrated. My dd is finally loving math. I honestly could not homeschool without TT, now that I've had a taste of how wonderful it is. Thank you, Sonlight for being the first to tell me about this awesome program!
by CINDY S on 2010-04-26 I have not used this series, but the problem I see is that the exercises do not list the lesson where the problem concept can be found. I know the problems are worked out on the CDs, but I think it is important for the student to look up the information so he can figure it out for himself. JMHO!
by JENNIFER S on 2009-10-25 I was excited to try Teaching Textbooks because of the high reviews; however, we found the grade 7 program to be far below what our son was doing in 6th grade math in public school. I exchanged the 7th grade package for the pre-algebra package and was even more disappointed. The content was so elementary he could do the entire book without ever using the teaching program. I am going to return this and try Singapore Math. Otherwise, I fear he will be far behind in his math skills by the time he enters high school.
by KARIN B on 2008-08-20 Inspite of the high ratings this math program has received, I and my son found it disappointing. After having done 6th grade "Horizons" math, combined with another textbook, my son skipped the 1st ten chapters of this book because it was too easy. I also spoke with other homeschooling mothers who used it for Algebra 1 and believe it left their kids ill prepaired to go into higher math. Perhaps it is good for kids who have not mastered basic math skills, but it does not challenge students or help them further their logical thinking skills.
by JENNIFER B on 2008-04-23 I highly recommend for all students. Even my 10 year old was able to understand the concepts easily.
by Kelby H. on 2008-04-01 Teaching Textbooks has made quite a difference in this household. No longer am I a frustrated math teacher! No longer do I take it personally when my child misses a problem, nor do I have to rant and rave about the "simple" mistake he made. The videos completely, patiently, and thoroughly explain all problems without judgement on the user. The result is a less frustrated math mom and jubilant, confident kids. I have to say that all of our math-i-tudes have improved. The material is challenging and relevant. The word problems are a hoot. And the best and worst thing is, everbody was good at math before, but hated it. Now we are still good (if not better, because we aren't killing each other), and LOVE it. My youngest child will also be switching in the fall to Teaching Textbooks 6.
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Matlab is a mathematics software package that is programmed in 'C' and 'C++'. Matlab
offers all of the standard math operations that come in other mathematics software
packages (such as Maple and Mathematica), in the form of functions (much like a 'C'
program). In addition, Matlab has its own high-level interpreted programming language,
which makes it a favorite among engineering professors and professional engineers.
Matlab is widely used in junior and senior level electrical and computer engineering
classes. It is also available at the Tiger-Lan locations in the engineering building.
The following links are a series of Matlab tutorials that may be helpful.
Matthew Bledsoe is a busy man. He is pursuing a dual major in Electrical and Computer Engineering and expects to graduate in the Spring of 2012. In addition, he is a non-comissioned officer (NCO) in the US Army where he is currently engaged in a major competition for NCO of the Year. More ...
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books.google.com - If... mathematical & physical formulas
If how to solve every kind of math and physics problem you're likely to encounter in school and business, and it explains simply and easily how to find answers fast, learn key formulas and definitions, study quickly and learn more effectively--from fundamental mathematical rules to physical definitions and constants. Presents all formulas, rules, and definitions precisely, simply, and clearly. Covers metric units of measurement, U.S. units of measurement (USCS), tables of equivalents metrics and USCS units. Reviews the fundamentals of algebra, geometry, trigonometry, and analytical geometry. Presents the application of differential equations and integral calculus. Solves problems concerning simple interest, compound interest, effective rate, annuity, amortization of loans, and sinking fund payment. Shows the comparative advantages of binomial distribution, standard distribution, Poisson distribution, and normal distribution. Includes most used definitions and formulas of kinematics, dynamics, statics, mechanics of fluids, thermal variable of state, thermodynamics, electricity and magnetism, light, and basic definition of atomic and nuclear physics. Offers most used fundamentals of physical constants.
From inside the book
22 pages matching resistance in this book
Page xviii
Review: Applied Mathematical and Physical Formulas Pocket Reference
User Review - Em Chitty - Goodreads
I copy-edited this book, actually--it's by a Bosnian refugee whom I helped resettle in Knoxville. It is a fantastic little book of mathematical formulas for every purpose under the sun. Everything you ever didn't want to know about math but needed to. Even has some mortgage calculations, etc.Read full review
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What's the sure road to success in calculus? The answer is simple: Precalculus.
Traditionally studied after Algebra II, this mathematical field covers advanced algebra, trigonometry, exponents, logarithms, and much more. These interrelated topics are essential for solving calculus problems, and by themselves are powerful methods for describing the real world, permeating all areas of science and every branch of mathematics. Little wonder, then, that precalculus is a core course in high schools throughout the country and an important review subject in college.
Unfortunately, many students struggle in precalculus because they fail to see the links between different topics?between one approach to finding an answer and a startlingly different, often miraculously simpler, technique. As a result, they lose out on the enjoyment and fascination of mastering an amazingly useful tool box of problem-solving strategies.
And even if you're not planning to take calculus, understanding the fundamentals of precalculus can give you a versatile set of skills that can be applied to a wide range of fields?from computer science and engineering to business and health care.
Mathematics Describing the Real World: Precalculus and Trigonometry is your unrivaled introduction to this crucial subject, taught by award-winning Professor Bruce Edwards of the University of Florida. Professor Edwards is coauthor of one of the most widely used textbooks on precalculus and an expert in getting students over the trouble spots of this challenging phase of their mathematics education.
"Calculus is difficult because of the precalculus skills needed for success," Professor Edwards points out, adding, "In my many years of teaching, I have found that success in calculus is assured if students have a strong background in precalculus."
A Math Milestone Made Clear
In 36 intensively illustrated half-hour lectures, supplemented by a workbook with additional explanations and problems, Mathematics Describing the Real World takes you through all the major topics of a typical precalculus course taught in high school or college. Those who will especially benefit from Professor Edwards's lucid and engaging approach include
* high school and college students currently enrolled in precalculus who feel overwhelmed and want coaching from an inspiring teacher who knows where students stumble;
* parents of students, who may feel out of their depth with the advanced concepts taught in precalculus;
* those who have finished Algebra II and are eager to get a head start on the next milestone on the road to calculus;
* beginning calculus students who want to review and hone their skills in crucial precalculus topics;
* anyone motivated to learn precalculus on his or her own, whether as a home-schooled pupil or as an adult preparing for a new career.
35. Elementary Probability
What are your chances of winning the lottery? Of rolling a seven with two dice? Of guessing your ATM PIN number when you?ve forgotten it? Delve into the rudiments of probability, learning basic vocabulary and formulas so that you know the odds.
36. GPS Devices and Looking Forward to Calculus
In a final application, locate a position on the surface of the earth with a two-dimensional version of GPS technology. Then close by finding the tangent line to a parabola, thereby solving a problem in differential calculus and witnessing how precalculus paves the way for the next big mathematical adventure.
HOme:
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From a review of the first edition:
This book is suitable for those who lack confidence … It is particularly useful as a revision guide... Tasks and practical exercises are included throughout the book. Worth buying a copy' - Primary Mathematics
This task-driven text emphasizes strategies and processes and is very different from the usual style of mathematics textbooks. For example, algebra is treated as a way of thinking mathematically, rather than merely manipulating symbols. Each of the sections is designed to stand alone so that they can be studied in any order or dipped into as needed.
The Second Edition has been updated to meet the needs of anyone wanting to refresh their knowledge and understanding of mathematics to GCSE level. There is an emphasis on learning and doing mathematics, with an expanded section on measures and proportion, and statistics.
Trainees and students have reported that the book has not only helped them to raise their knowledge and understanding to the required standard but also greatly improved their mathematical confidence.
This is a set book for the Open University Course, 'Ways of Knowing: language, mathematics and science in the early years'.
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Complex Analysis for Mathematics, Science, and Engineering
This book provides a comprehensive introduction to complex variable theory and its applications. The Second Edition features a revised and updated ...Show synopsisThis book provides a comprehensive introduction to complex variable theory and its applications. The Second Edition features a revised and updated presentation that reflects the latest theories and their applications to current engineering problems
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These suggestions are intended to make your life easier. Some of them
may seem like extra work, but really they cause you less work in the
long run.
This is a preliminary document, i.e. a work in progress.
1.
Be tidy and systematic. Whenever you have data in tables,
especially when place-value is important, be sure to keep things
lined up in neat columns and neat rows. See section 4 for
an example of how this works in practice.
2.
If your columns are wobbly, get a pad of graph
paper and see if that helps. If you don't have a supply of
store-bought graph paper, you can make graph paper on your computer
printer. There are freeware programs that do a very nice job of
this.
If that's too much bother, start with a plain piece of paper and
sketch in faint guidelines when necessary.
3.
Paper is cheap. If you find that you are
running out of room on this sheet of paper, get another sheet of
paper, rather than squeezing the calculation into a smaller space.
See section 4 for an example of using extra paper to
achieve a better result.
4.
The whole calculation should be structured as a succession
of true statements. The first statement is true, the next statement
is true, and the statement after that, et cetera. Each statement is
a consequence of the previous statements (in conjunction with known
theorems, and the "givens" of the problem). Finally, we get to the
bottom line, and we know it is true. An example of this can be seen
in reference 1.
5.
Sometimes, especially for long and/or complex calculations, it
helps to organize your calculation in two columns. An example of
this can be seen in reference 1. In the left column, you
write an equation. In the right column, make a note as to how you
derived that equation. (Numbering all your equations makes this
easier.) If there isn't enough width to do this easily, turn the
paper 90 degrees, so it becomes wider and less tall. (Writing paper
isn't suitable for this, so use graph paper ... or lacking that,
plain white paper.)
6.
Avoid writing down an un-named number like 17, or an un-named
expression like a+17 ... because you might forget the meaning
thereof. Instead, whenever possible, write down an equation
such as b=a+17. That way you can point to every item on the page
and say that's true, that's true, that's true... in accordance with
the strategy described in item 4.
If the meaning of variables such as a and b is not obvious, write
down a legend somewhere (like the legend of a map), explaining in a
sentence or two the meaning of each variable. That is, a name is not
the same as an explanation. Do not expect the structure of a name or
symbol to tell you everything you need to know. Most of what you
need to know belongs in the legend. The name or symbol should allow
you to look up the explanation in the legend.
7.
It is important to be able to go back and check the
correctness of the calculation you have done. See
section 4 and/or reference 1 for examples of
what this means in practice.
8.
As a corollary of item 7: Don't perform
surgery on your equations. That is, once you write down a correct
equation, don't start crossing out terms (or, worse, erasing terms)
and replacing them with other expressions. Such a substitution may
be "mathematically" correct, if the replacement is equal to the
thing being replaced ... but it is a bad strategy, because it makes
it hard for you to check your work. Instead, write a new equation.
Leave the old equation as it is. Paper is cheap. An example of this
can be seen in reference 1.
9.
Keep track of the units for each expression. For example,
the statement "x=2.5 inches" means something rather different
from "x=2.5 meters" ... and if you shorthand it as "x=2.5"
you're just asking for trouble.
Sometimes the penalty for getting this wrong is 328 million dollars,
as in the case of the Mars Climate Orbiter
(reference 2).
Most computer languages do not automatically keep track of the units,
so you will have to do it by hand, in the comments. If the
calculation is nicely structured, it may suffice to have a
legend somewhere, spelling out the units for each of the
variables. If variables are re-used and/or converted from one set of
units to another, you need more than just a legend; you will need
comments (possibly quite a lot of comments) to indicate what units
are being used at each point in the code.
One policy that is sometimes helpful (but sometimes risky) is to
convert everything to SI units as soon as it is read in, even in
fields where SI units are not customary. Then you can do the
calculation in SI units and convert back to conventional units (if
necessary) immediately before writing out the results. (This is
problematic when writing an "intermediate" file. Should it be SI
or customary? How do you know the difference between an
"intermediate" result and a final result?)
It is certainly possible for computer programs to keep track of the
units automatically. A nice example is reference 3. It is
a shame that such features are not more widely available
10.
The factor-label method is a convenient and
powerful way of converting units when necessary. The correctness of
this method is a direct consequence of the axioms of algebra, since
it starts by multiplying by unity, which is allowed by the axioms.
11.
Haste makes waste, especially with multi-step processes. If
you work methodically, you'll get the right answer the first time,
and that's all there is to the story. If you try to do it twice as
fast, you'll get the wrong answer, and then you'll have to do it over
again ... and again ... and again.
Here's a classic example: The task is to add 198 plus 215. The
easiest way to solve this problem in your head is to rearrange it as
(215 + (200 − 2)) which is 415 − 2 which is 413. The small point
is that by rearranging it, a lot of carrying can be avoided.
One of the larger points is that it is important to have multiple
methods of solution. This and about ten other important points are
discussed in reference 4.
The classic "textbook" diagram of an inequality uses shading to
distinguish one half-plane from the other. This is nice and
attractive, and is particularly powerful when diagramming the
relationship between two or more inequalities, as shown in
figure 2.
Obviously the hatched depiction is not as beautiful as the shaded depiction,
but it is good enough. It is vastly preferable on cost/benefit
grounds, for most purposes.
Some refinements:
I recommend hatching the excluded half-plane, so that the
solution-set remains unhatched rather than hatched. This is
particularly helpful when constructing the conjunction (logical
AND) of multiple inequalities.
I recommend using solid lines versus dashed lines to distinguish
"≥" inequalities from ">" inequalities. If you're going to
hatch the excluded half-plane, use solid lines for the ">"
inequalities, to show that the boundary itself is excluded.
As suggested in figure 4, for linear
inequalities you can do the hatching faster and more accurately with
the help of a ruler or straightedge, which makes it easy to ensure
that none of the hatches stray into the wrong region.
Short multiplication refers to any multiplication problem where you
just memorize the answer. You must memorize the multiplication
table for everything from 0×0 through 9×9. You get the
next step (up to 10×10) practically for free, and it is often
worthwhile to keep going up to 12×12.
Long multiplication refers to multiplying larger numbers. This works
by breaking the numbers down into their individual digits, then
multiplying on a digit-by-digit basis (using the short multiplication
facts for zero through nine) and then combining all the results with
due regard for place value.
We now discuss a nice way to do long multiplication.
The first steps are shown in figure 5.
There are two parts to the figure, representing two successive
stages of the work. Anything shown in black is something you actually
write down, whereas anything shown in color is just commentary, put
there to help us get through the explanation the first time.
We start with the leftmost part of the figure. This is just the
statement of the problem, namely 4567×321. The important point
here is to line up the numbers as shown, so that the ones' place of
the top number lines up with the ones' place of the bottom number, et
cetera. Keeping things aligned in columns is crucial, since the
colums represent place value. If you have trouble keeping things
properly lined up, use grid-ruled paper. You can see such a grid in
figure 5. If you don't have grid-ruled paper, you
can always sketch in some guide lines. As mentioned in item 1,
tidiness pays off.
You may omit the multiplication sign (×) if it is obvious from
context that this is a multiplication problem (as opposed to an
addition problem).
Tangential remark: Some people attempt to
call one of these numbers the multiplier and the other the
multiplicand, but since multiplication is commutative the
distinction is meaningless. People often use the terms in ways
inconsistent with the supposed definition. I call both of
them multiplicands, which is more-or-less Latin for "thing being
multiplied". In figure 6 we have two things being
multiplied. Note that since multiplication is associative, you
could easily have many things being multiplied, as in
12×32×65×99, in which case it again makes sense to
call each of them multiplicands, and it is obviously hopeless to
attempt to distinguish "the" multiplier from "the"
multiplicand. As a related issue, there are also holy wars as to
whether 4567×321 means 4567 "times" 321, or 4567
"multiplied by" 321. Again the distinction is meaningless.
Don't worry about it.
If one of the multiplicands is longer than the other, it will usually
be more convenient to place the longer one on top. That's not
mandatory, but it makes the calculation slightly more compact.
We now proceed digit by digit, starting with the rightmost digit in
the bottom multiplicand, which in this case is a 1. We multiply this
digit into each digit of the upper multiplicand, working in order
right-to-left, which makes sense because it is the direction of
increasing place value (even though it is opposite to the direction of
reading normal text).
We place these results in order in row c, with due regard for place
value. The 1×7 result goes in the ones' place, the 1×6
result goes in the tens' place, and the 1×5 result goes in the
hundreds' place, and so forth. Actually, multiplication by 1 is so
easy that you could just copy the whole number 4567 into row c
without thinking about it very hard.
You may wish to leave a little bit of space above the
numbers in row c, for reasons that will become apparent later.
That is all we need to do with the low-order digit of the bottom
multiplicand. We now move on to the next digit, working
right-to-left. In this case it is a 2.
Again we multiply this digit into each digit of the upper
multiplicand. The result of the first such multiplication is
2×7=14, which we place in row d. This is most clearly seen in
the middle column of the figure 6. Alignment is crucial
here. The 14 must be aligned under the 2 as shown. That's because it
"inherits" the place value of the 2.
Next we multiply 2×6=12. You might be tempted to write this in
row d, but there is no room for it there, so it must go on row e,
as shown in the middle column of the figure. Again alignment is
critical. The 12 is shifted one place to the left of the 14, because
it inherits additional place value. It inherits some from the 2 and
some from the 6. Since we are working systematically right-to-left,
you don't need to think about this too hard; just remember that each
of these short-division products must be shifted one place to the left
of the previous one.
We have now more than half-way finished. We have reached the stage
shown in figure 5.
The next step is the 2×5=10 multiplication. There is room for
this on row d, which is a good place to put it. Next we do the
2×4=8 multiplication. There is room for this on row e, which
is a good place to put it. Note the pattern of placing successive
short-division results on alternating rows. This is guaranteed to
work, because the product of two one-digit numbers can never have more
than two digits.
At this point (or perhaps earlier), if you are not using grid-ruled
paper, you should lightly sketch in some vertical guide lines, as
shown by the dashed lines in figure 7. The tableau has
become large enough that there is some risk of messing up the
alignment, i.e. putting things into the wrong columns, if you don't
put in guide lines.
That's all for the "2" digit in the bottom multiplicand. We now
progress to the "3" digit. The work proceeds in the same fashion.
All the short-multiplication results are put in rows f and g.
In the tableau, you can see where everything comes from. The
color-coded background indicates which digit of the upper multiplicand
was involved, and the row indicates which digit of the bottom
multiplicand was involved.
At this point you can draw a line under row g as shown in the
figure. All that remains is a big addition problem, adding up rows
c through g inclusive. You can use the space above row c to
keep track of carries if you wish, but this is not mandatory. (There
are never very many carries, so keeping track of them is easy, no
matter how you do it. Some people just count them on their fingers.)
The result of the addition is the result of the overall multiplication
problem, as shown on row h.
Let's do another example, as shown in figure 7, which
illustrates one more wrinkle.
This example calls attention to the situation where some of the
short-multiplication products have one digit, while others have two.
You can see this on row c of the figure, where we have 3×3=9
and 3×8=24. In most cases it is safer to pretend they all have
two digits, which is what we have done in the figure, writing 9 as 09.
Similarly on line d we write 6 as 06. This makes the work fall into
a nice reliable pattern. It helps you keep things lined up, and
makes the work easier to check.
In some cases, such as 345×1 or 432×2, all the
short-multiplication products have one digit, so you can write them
all on a single line, if you wish. This saves a little
bit of paper. On the other hand, remember the advice in
item 3: paper is cheap. You may find
it helpful to write the short-multiplication products
as two digits even if you don't have to.
Mathematically speaking, writing one-digit products as two digits is
unconventional, but it is entirely correct. It has the advantage of
making the algorithm more systematic, and therefore easier to check.
In any case, the result of the addition is the result of the overall
multiplication problem, as shown on row g of figure 7.
That's all there is to it.
This algorithm uses two rows of intermediate results for each digit in
the bottom multiplicand (except when the digit is zero or one). This
has two advantages: First of all, you don't need to do any adding or
carrying as you go along; you just write down the short-multiplication
results "as is". Secondly, it makes it easy to check your work.
Each of the short-multiplication results is sitting there in an
obvious place, almost begging to be checked.
This differs from the old-fashioned "textbook" approach, which uses
only one row per digit, as shown below. The old-fashioned approach
supposedly uses less paper – but the advantage is slight at best, and
if you allow room keeping track of "carries" throughout the tableau,
the advantage becomes even more dubious.
What's worse is that the old-fashioned approach is significantly more
laborious. It may look more compact, but it involves more work. You
have to do the same number of short multiplications, and a
greater number of additions. It requires you to do additions
(including carries) as you go along.
Last but not least, it makes it much harder to check your work.
4
5
6
7
×
3
2
1
4
5
6
7
9
1
3
4
1
3
7
0
1
1
4
6
6
0
0
7
The old-fashioned approach.
Not recommended.
Remember, paper is cheap (item 3) and it is important
to be able to check your work (item 7).
The usual "textbook" instructions for how to do long division are
both unnecessarily laborious and unnecessarily hard to understand.
There's another way to organize the calculation that is much less
mysterious and much less laborious (especially when long multi-digit
numbers are involved).
Note that as discussed above, keeping things lined up in columns
is critical. It may help to use grid-ruled paper, or at least to
sketch in some guidelines.
After writing down the statement of the problem, and before doing any
actual dividing, it helps to make a crib, as shown in the lower
left of the figure. This is just a multiplication table, showing all
multiples of 13 (or, more generally, all multiples of the assigned
divisor). It is super-easy to construct such a table, since no
multiplication is required. Successive addition will do the job. We
need all the multiples from ×1 to ×9, but you might as
well calculate the ×10 row, by adding 117+13, as a check on
all the additions that have gone before.
The first step is to consider the leading digit of the dividend (which
in this case is a 7). Since this is less than the divisor (13), there
is no hope of progress here, so we proceed to the next step.
Now consider the first two digits together, namely the 7 and the 5. Look at
the crib to find the largest entry less than or equal to 75. It is
65, as in 5×13=65. Write copy this entry to the division
problem, on row b, directly under the 75. Since this came from row
5 of the crib, write a 5 on the answer line, aligned with the 75 and
the 65, as shown. Check the work, to see that 5 (on the answer line)
times 13 (the divisor, on line a), equals 65 (on line b).
Now do the subtraction, namely 75−65=10, and write the result
on line c as shown.
We now shift attention from the first column to the middle column of
figure 8. Bring down the 2 from the dividend, as shown by
the red arrow in the middle column of the figure. So now the number
we are working on is 102, on line c.
The steps from now on are a repeat of earlier steps.
Look at the crib to find the largest entry less than or equal to 102.
It is 91, as in 7×13=91. Write copy this entry to the division
problem, on row d, directly under the 102. Since this came from row
7 of the crib, write a 7 on the answer line, aligned with the 102 and
the 91, as shown. Check the work, to see that 7 (on the answer line)
times 13 (the divisor, on line a), equals 91 (on line d). Do the
subtraction.
As a check on the work, when doing this subtraction,
the result should never be less than zero, and should never be
greater than or equal to the divisor. Otherwise you've used the
wrong line from the crib, or made an arithmetic error.
We now shift attention to the rightmost column of figure 8.
Bring down the 7, look in the crib to find the largest entry less
than or equal to 117, which is in fact 117, as in 9×13=117.
Since this came from line 9 of the crib, write a 9 on the answer line,
properly aligned.
The final subtraction yields the remainder on line g. The remainder is
zero in this example, because 13 divides 7527 evenly.
Perhaps the crib's most important advantage, especially when people
are first learning long division, is that the crib removes the mystery
and the guesswork from the long division process. This is in contrast
to the "trial" method, where you have to guess a quotient digit, and
you might guess wrong. Using the crib means we never need to do a
short division or trial division; all we need to do is skim the table
to find the desired row.
We have replaced trial division by multiplication and table-lookup.
Actually we didn't even need to do any multiplication, so it would be
better to say we have replaced trial division by addition.
Another advantage is efficiency, especially when the dividend has many
digits. That's because you only need to construct the crib once (for
any given divisor), but then you get to use it again and again, once
for each digit if the dividend. For long dividends, this saves a
tremendous amount of work. (This is not a good selling point
when kids are just learning long division, because they are afraid
of big multi-digit dividends.) Setting up the crib is so fast that
you've got almost nothing to lose, even for small dividends.
Another advantage is that it is easy to check the correctness of the
crib. It's just sitting there begging to be checked.
When bringing down a digit, you
may optionally bring down all the digits. For instance, in
the middle column of figure 8, if you bring down all the
digits you get 1027 on row c. One advantage is that 1027 is a
meaningful number, formed by the expression
7527−13×5×102. This shows how the steps of the
algorithm (and the intermediate results) actually have mathematical
meaning; we are not not blindly following some mystical mumbo-jumbo
incantation. I recommend that if you are trying to
understand the algorithm, you should bring down all the digits a few
times, at least until you see how everything works.
A small disadvantage is that bringing down all the digits requires
more copying. The countervailing small advantage is that it may
help keep the digits lined up in their proper columns. Whether the
advantages outweigh the cost is open to question, and probably
boils down to a question of personal preference.
Another remark: Division is the "inverse function" of
multiplication. In a profound sense, for any function that can be
tabulated, you can construct the inverse function – if it exists –
by switching columns in the table. That is, we interchange abscissa
and ordinate: (x,y)↔(y,x). That's why we are able to
perform division using what looks like a multiplication table; we just
use the table backwards.
The modern numeral system is based on place value. As we understand
it today, each numeral can be considered a polynomial in powers of
b, where b is the base of the numeral system. For decimal
numerals, b=10. As an example:
Given two expressions such as (a+b+c) and (x+y), each of which has
one or more terms, the systematic way to multiply the expressions is
to make a table, where the rows correspond to terms in the first
expression, and the rows correspond to terms in the second expression:
In the special case of multiplying a two-term expression by another
two-term expression, the mnemonic FOIL applies. That stands for
First, Outer, Inner, Last. As shown in figure 9, we start with
the First contribution, i.e. we multiply the first term from in each
of the factors. Then we add in the Outer contribution, i.e. the first
term from the first factor times the last term from the last factor.
Then we add in the Inner contribution, i.e. the last term from the
first factor times the first term from the last factor. Finally we
add in the Last contribution, i.e. we multiply the last terms from
each of the factors.
Most square roots are irrational, so they cannot be represented
exactly in the decimal system. (Decimal numerals are, after all,
rational numbers.) So the name of the game is to find a decimal
representation that is a sufficiently-accurate approximation.
We start with the following idea: For any nonzero x we know that
x÷√x is equal to √x. Furthermore, if s1 is
greater than √x it means x/s1 is less than √x. If
we take the average of these two things, s1 and x/s1, the
average is very much closer to √x. So we set
and then iterate. The method is very powerful; the number of digits
of precision doubles each time. It suffices to use a rough estimate
for the starting point, s1. In particular, if you are seeking the
square root of an 8-digit number, choose some 4-digit number as the
s1-value.
This is a special case of a more general technique called
Newton's method, but if that doesn't mean anything to you, don't
worry about it.
Note that the square of 1.01 is very nearly 1.02. Similarly, the
square of 1.02 is very nearly 1.04. Turning this around, we find the
general rule that if x gets bigger by two percent, then √x
gets bigger by one percent ... to a good approximation.
We can illustrate this idea by finding the square root of 50. Since
50 is 2% bigger than 49, the square root of 50 is 1% bigger than 7
... namely 7.07. This is a reasonably good result, accurate to better
than 0.02%.
If we double this result, we get 14.14, which is the square root of
200. That is hardly surprising, since we remember that the square
root of 2 is 1.414, accurate to within roundoff error.
Sine and cosine are transcendental functions. Evaluating them will
never be super-easy, but it can be done, with reasonably decent
accuracy, with relatively little effort, without a calculator.
In particular:
You can always start with a zeroth-order approximation: For
angles near zero, the sine will be near zero. For angles near
90∘, the sine will be near 1. For angles near 30∘, the sine
will be near 0.5, et cetera.
You can draw a graph, using the anchor points in equation 4 as a guide. You can then use graphical interpolation to
obtain values for any angle.
A simple Taylor series gives a result accurate to 2.1% or
better using only a couple of multiplications. Remember to express
the angle in radians before using these formulas.
The following facts serve to "anchor" our knowledge of the sine
and cosine:
Actually, that hardly counts as "remembering" because if you ever
forget any part of equation 4 you should be able to
regenerate it from scratch. The 0∘ and 90∘ values are
trivial. The 30∘ is a simple geometric construction. Then the
60∘ and 45∘ values are obtained via the Pythagorean theorem.
The value for 45∘ should be particularly easy to remember,
since √2 = 1.414 and √½ = ½√2.
The rest of this section is devoted to the Taylor series. A low-order
expansion works well if the point of interest is not too far from the
nearest anchor.
For angles between −10∘ and +10∘, the approximation
sin(x)≈x is accurate to better than 0.51%. This is a
one-term Taylor series. Let's call it the Taylor[1] approximation.
It is super-easy to evaluate, since it involves no additions and no
multiplications, or at most one multiplication if we need to convert
to radians from degrees or some other unit of measure. See
equation 5c and the blue line near x=0 in figure 10.
For angles from 25∘ to 65∘, all the points are with a
few degrees of one of the anchor points in equation 4.
This means the first-order Taylor series is accurate to better than 1
percent in this region. We can call this the Taylor[0,1]
approximation. It requires knowing the sine and the cosine at the
nearest anchor point ... which we do in fact know from equation 4. See equation 9 and the blue line in
figure 10.
For a rather broad range of angles near the top of the sine,
from 65∘ to 115∘, the approximation sin(x)≈1−x2/2
is accurate to better than half a percent. This is a second-order
Taylor series with only two terms, because the linear term is zero.
Let's call this the Taylor[0,2] approximation. See equation 5e and the green line near x=90∘ in figure 10.
This leaves us with a region from 10∘ to 25∘ that
requires some special attention. Options include the following:
For most purposes, the best option is to use the Taylor[1,3]
approximation anchored at zero. This requires a couple more
multiplications, but the result is accurate to better than 0.07%.
If you really want to minimize the number of multiplications, we can
start by noting that the Taylor[1] extrapolation coming up from zero
is better than the Taylor[0,1] extrapolation coming down from
30∘, so rather than using the closest anchor we use the 0∘
anchor all the way up to 20∘ and use the 30∘ anchor above
that. This has the advantage of minimizing the number of
multiplications. Disadvantages include having to remember an obscure
fact, namely the need to put the crossover at 20∘ rather than
halfway between the two anchors. The accuracy is better than 2.1%,
which is not great, but good enough for some applications. The error
is shown in figure 11.
If you can maintain even a vague memory of the form of equation 7, you can easily reconstruct the exact details. Use the
fact that it has to be symmetric under exchange of a and b (since
addition is commutative on the LHS). Also it has to behave correctly
when b=0 and when b=π/2.
If we assume b is small and use the small-angle approximations from
equation 5, then equation 7 reduces to the
second-order Taylor series approximation to sin(a+b).
You can use the Taylor series to interpolate between the values given
in equation 4. Since every angle in the first quadrant
is at least somewhat near one of these values, you can find the sine
of any angle, to a good approximation, as shown in figure 10.
| 677.169 | 1 |
explanation
This is a very complete book: ita has good explanations for people who cannot understand the topics that are being covered, but there are also challeging exercises for the poeple who is good at calculus.
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Description of Lifepac Math: Grade 8: Unit 7: Integers by Alpha Omega
Repetition, drills and application ensure mastery of computational skills with Lifepac Math. Students will progress to higher-level cognitive reasoning and analysis as their problem solving ability increases.
Perfect for students who flourish in a self-paced, individualized learning format, each consumable LIFEPAC combines lessons, exercises, projects, reviews and tests.
Product:
Lifepac Math: Grade 8: Unit 7: Integers
Vendor:
Alpha Omega
Binding Type:
Paperback
Media Type:
Book
Minimum Grade:
8th Grade
Maximum Grade:
8th Grade
Weight:
0.5 pounds
Length:
11 inches
Width:
8.5 inches
Vendor Part Number:
MAT 0807
Subject:
Math Math: Grade 8: Unit 7: Integers.
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Nice that it is broken up into seperate LifePacs, allowing the feeling of progress for the student.
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more details
Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pã³lya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics. This volume contains the contributions of the participants of the Conference on Inequalities and Applicationsnbsp;held in Noszvajnbsp;(Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice
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Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a v... read more
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Product Description:
Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles. A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections, and spin structures
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Mathematics for 3D Game Programming and Computer Graphics, Third Edition
BOOK DESCRIPTION
This updated third edition illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and
game engines at the professional level. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more
advanced topics in 3D programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that
the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review
the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.
ABOUT THE AUTHOR
Eric Lengyel is a veteran of the computer games industry with over 16 years of experience writing game engines. He has a PhD in Computer Science from the
University of California at Davis and an MS in Mathematics from Virginia Tech. Eric is the founder of Terathon Software, where he currently leads ongoing development
of the C4 Engine.
TABLE OF CONTENTS
Preface
What's New in the Third Edition
Contents Overview
Notational Conventions
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Starting at $12 College Algebra, 5th Edition is designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates readers to grasp abstract ideas by solving real-world problems. The problems lie on a continuum from basic algebraic drills to open-ended, non-routine questions. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in the social, physical, and life sciences. The goal of Explorations in College Algebra, 5th Edition is to prepare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us.
Table of Contents
An Introduction to Data and Functions
Describing Single-Variable Data
Visualizing Single-Variable Data
Numerical Descriptors: What is "Average" Anyway?
An Introduction to Algebra Aerobics
An Introduction to Explore and Extend
Describing Relationships between Two Variables
Visualizing Two-Variable Data
Constructing a "60-Second Summary"
Using Equations to Describe Change
An Introduction to Functions
What is a Function?
Representing Functions: Words, Tables, Graphs and Equations
Input and Output: Independent and Dependent Variables
When is a Relationship Not a Function?
The Language of Functions
Function Notation
Domain and Range
Visualizing Functions
Is There a Maximum or Minimum Value?
When is the Output of the Function Positive, Negative or Zero?
Is the Function Increasing or Decreasing?
Is the Graph Concave Up or Concave Down?
Getting the Big Idea
Chapter Summary
Check Your Understanding
Chapter 1 Review: Putting it all Together
Exploration 1.1 Collecting, Representing, and Analyzing Data
Rates of Change and Linear Function
Average Rates of Change
Describing Change in the U.S. Population over Time
Defining the Average Rate of Change
Limitations of the Average Rate of Change
Change in the Average Rate of Change
The Average Rate of Change is a Slope
Calculating Slopes
Putting a Slant on Data
Slanting the Slope: Choosing Different End Points
Slanting the Data with Words and Graphs
Linear Functions: When Rates of Change are Constant
What if the U.S. Population Had Grown at a Constant Rate?
Real Examples of a Constant Rate of Change
The General Equation for a Linear Function
Visualizing Linear Functions
The Effect of b
The Effect of m
Finding Graphs and Equations of Linear Functions
Finding the Graph
Finding the Equation
Special Cases
Direct Proportionality
Horizontal and Vertical Lines
Parallel and Perpendicular Lines
Breaking the Line: Piecewise Linear Functions
Piecewise Linear Functions
The absolute value function
Step functions
Constructing Linear Models for Data
Fitting a Line to Data: The Kalama Study
Reinitializing the Independent Variable
Interpolation and Extrapolation: Making Predictions
Looking for Links between Education and Earnings: Using Regression Lines
| 677.169 | 1 |
Course
This is an introductory course on converting survey field observations/data into a form suitable to the end user. Students apply principles and precepts learned in courses of mathematics and surveying to surveying problems, develop analysis techniques and perform those computations required for plane surveying problems encountered by the surveyor, land developer and civil engineer. Traverse computations, subdivision computations, route surveying computations, etc., are addressed.
| 677.169 | 1 |
Trigonometry With Infotrac
9780534403928
ISBN:
0534403921
Edition: 5 Pub Date: 2003 Publisher: Thomson Learning
Summary: This text provides students with a solid understanding of the definitions and principles of trigonometry and their application to problem solving. Identities are introduced early in Chapter 1. They are reviewed often and are then covered in more detail in Chapter 5. Also, exact values of the trigonometric functions are emphasized throughout the textbook. There are numerous calculator notes placed throughout the text....
McKeague, Charles P. is the author of Trigonometry With Infotrac, published 2003 under ISBN 9780534403928 and 0534403921. One hundred seventy nine Trigonometry With Infotrac textbooks are available for sale on ValoreBooks.com, fifty eight used from the cheapest price of $0.92, or buy new starting at $4 pages bent. CD included. infotrac not included. worn
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0321028473
9780321028471
A Graphical Approach to College Algebra:This major revision reflects the authors combined years of experience as classroom teachers, and underscores their enthusiasm for the use of the graphing calculator as a teaching tool. Their approach is to present the various classes of functions, examine the nature of its graph, and discuss the analytic solution of equations based on that function. Then, graphical support for the solution is provided with a graphing calculator. Using graphing technology to study math has opened up a new area of error analysis, so the authors have included a What Went Wrong feature to discuss typical errors. Throughout, the accent is on using both analytical and graphical methods to solve interesting applications for various functions. The new edition also includes a reference chapter on basic algebraic concepts for those needing a refresher course.
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Rent A Graphical Approach to College Algebra 2nd edition today, or search our site for John textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Addison-Wesley.
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Student Solutions Manual contains worked-out solutions to odd-numbered problems in the text. It displays the detailed process that students should use to work through the problems. The manual also provides interpretation of the answers and serves as a valuable learning tool for the student.
| 677.169 | 1 |
The Algebra Word Problem Tutor DVD series teaches students how to set up algebra word problems and solve them. This episode, Number Problems, teaches students how to solve word problems that involve number relations, including how to set up the appropriate algebraic equation and solve for the unknown. Grades 5-9. 35 minutes on DVD.
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Higher Education Solutions
The U.S. Department of Education reported Basic Algebra to have the highest failure and withdrawal rates among post-secondary math courses. Intermediate Algebra and Developmental Math followed closely behind. More than half of the mathematics courses offered at two-year colleges and 10-20 percent of the mathematics courses offered at four-year colleges are developmental math courses. Seventy-five percent of new students enrolling in two-year colleges must take one or more developmental mathematics courses, and on average, half of those student do not pass.
All of your students can achieve proficiency in mathematics with the Carnegie Learning Developmental Math Software Solution. Our solution provides students of all ages and skill levels with highly differentiated and self-paced instruction that meets their exact needs to improve their developmental math skills. That means your developmental math courses will be able to retain more students and quickly promote them into their degree programs.
Be sure to read about the effect that Carnegie Learning Developmental Math Solution has on retention rates in the Success Stories tab on the left. For detailed information about the program components, visit the Higher Education Curricula page.
Read more about our Developmental Math offerings by visiting the following pages:
Many students want to prepare for an upcoming test or refresh their knowledge of prior course content before advancing onto their next math course. These students will greatly benefit from the Cognitive Tutor software in their Learning Support Center.
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Bob Blitzer,s unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus ...Show synopsisBob Blitzer,s-See It, Hear It, Try It-makes examples easy to follow, while frequent annotations offer the support and guidance of an instructor,s voice. Every page is interesting and relevant, ensuring that students will actually use their textbook to achieve success Fair condition. Text only has white used book stickers...Fair. Fair condition. Text only has white used book stickers all over the cover. Blitzer Algebra and Trigonometry 5th Edition By Robert Blitzer Product Details Hardcover ISBN-10: 0133101169 ISBN-13:
Reviews of Algebra and Trigonometry
I got this book to finish my algebra requirement and it has really helped me...plus I have a talented instructor. Although I find the book a great asset, I think the author has tried too hard to explain things with too many details. All the labels and arrows are hard to follow and do more to confuse
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Loci Browse Articles
This article explores the symmetry method in elementary differential equations, which uses the invariance of the equation under certain transformations to create a coordinate system in which the equation greatly simplifies.
Geometry Playground (v1.3) is a free Java application for doing "ruler and compass" constructions in both Euclidean, Spherical, Projective, Hyperbolic, Toroidal, Manhattan and Conical geometries. Its purpose is to help users develop a familiarity with various conceptualizations of these geometries.
The purpose of this collection of applets and activities is to make students familiar with the basic principles of complex numbers. Combining explanatory text, exercises and interactive GeoGebra applets, this resource is suitable for both classroom lectures and distance learning.
Users toss a virtual coin or die to investigate the law of averages. The outcomes of multiple experiments (consisting of 10000 tosses each) can be graphed on the same plot to facilitate visualization of trends. An activity is provided to facilitate thinking about the law of averages with the applet.
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Silvestre FranAois Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume TraitA(c) du calcul diffA(c)rentiel et du calcul intA(c)gral (1797-1800; 2nd ed. 1810-1819) a" an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through... more...
Documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on the development based on interaction between geometric function and measure theory and other branches of mathematical analysis. more...
Discusses a discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such branches of mathematics, variational analysis provides a uniform theoretical base that represents a tool for the applications. more...
Introduces geometric measure theory through the notion of currents. This book provides background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. more...
Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance. more...
When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and... more...
A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending... more...
Get ready to master the principles and operations of calculus! Master Math: Calculus is a comprehensive reference guide that explains and clarifies the principles of calculus in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, the book helps clarify calculus using... more...
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Linear Algebra With Application - 8th edition
Summary: Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that...show more gives the course the desired flavor.Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R(n) (make sure it is superscript n), matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions.Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text.Key Features of the Eighth Edition:-- Updated and revised throughout with new section material and exercises included in every chapter. -- Each section begins with a motivating introduction, which ties material to the previously learned topics. -- Carefully explained examples illustrate key concepts throughout the text. -- Includes such new topics such as QR Factorization and Singular Value Decomposition.-- Includes new app
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Intro Algebra Review
A Quick Refresher
Class Summary
This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.
What Will I Learn?
At the end of this course students will have reviewed the core topics of introductory algebra. Students will be comfortable with the concepts and procedures of introductory algebra, and be able to apply their knowledge to other coursework and real-world problems.
What Should I Know?
This is a review course, it is expected that students will have some previous knowledge of most topics covered in the course.
Made possible through a grant from the Bill and Melinda Gates Foundation.
Syllabus
Topic 1: Integer Operations
Properties of Integers
Absolute Value
Adding, Subtracting, Multiplying & Dividing
Order of Operations
Perimeter and Area of Rectangles, Squares & Triangles
Topic 2: Fractions and Decimals
Simplifying Fractions
Mathematical Operations with Fractions
Rounding Decimals
Decimals and Applications
Fraction to Decimal Conversion
Scientific Notation
Topic 3: Rates, Ratios, and Conversions
Ratios
Rates
Unit Conversions
Percents
Topic 4: Algebraic Expressions and Equations
Algebraic Expressions
Solving a Linear Equation
Pythagorean Theorem
Topic 5: Graphing Linear Equations
Graphing a Linear Equation
Slope of a Line
Writing a Linear Equation
Slope and Slope-Intercept Form
Course Instructors
Kelly Vetter
Instructor
Kelly Vetter is an instructor at Wake Technical Community College. She has a B.S. in Mathematics Education and a Certificate in E-Learning from North Carolina State University. She has taught math for a total of 17 years and has been teaching developmental math for 12 of those years. She has taught in various formats including the classroom, online, and hybrid courses.
Sue Ann Austin
Instructor
Sue Ann Austin is an instructor at Wake Technical Community College. She has taught developmental math for 4 years and prior to that was a high school math teacher. She has a B.S. in Applied Mathematics from Carnegie-Mellon University and completed the NC Teach program at North Carolina State University. She was a software engineer for 15 years prior to entering the field of education.
Andy Brown
Course Developer
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This is a sub-page of the large and comprehensive Eric Weisstein's World of Mathematics site which is separately reviewed...
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This is a sub-page of the large and comprehensive Eric Weisstein's World of Mathematics site which is separately reviewed elsewhere on MERLOT. At the time of review this probability and statistics area listed 19 subtopics including Bayesian analysis, descriptive statistics, probability, random numbers, random walks, and statistical tests. Approximately 350 separate items on probability and statistics were included.
Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of...
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Quoted from the site: [This site contains...] "Free mathematics tutorials to help you explore and gain deep understanding of math topics." The math topics covered include 1) Precalculus Tutorials 2) Calculus Tutorials and Problems 3) Geometry Tutorials and Problems 3) Trigonometry Tutorials and Problems for Self Tests 4) Elementary statistics and probability tutorials 5) Applications of mathematics in physics and engineering. And much more, including many applets.
The Probability/Statistics Object Library is a virtual library of objects for use by teachers and students of probability and...
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The Probability/Statistics Object Library is a virtual library of objects for use by teachers and students of probability and statistics. The library contains objects of two basic types, applets and components.An applet is a small, self-contained program that runs in a web page. Applets are intended to illustrate concepts and techniques in an interactive, dynamic way. A teacher or student can download an applet, drop it in a web page, and then add other elements of her own choice (such as expository text, data sets, and graphics). The applets in the library contain essentially no mathematical theory and thus can be used by students at various levels. The applets are intended to be small "micro worlds" where students can run virtual versions of random experiments and play virtual versions of statistical games.Components are the building blocks of applets and of other components. The Java objects are of three basic types: virtual versions of physical objects, such as coins, dice, cards, and sampling objects; virtual versions of mathematical objects, such as probability distributions, data structures, and random variables; user-interface objects such as custom graphs and tables. The Java objects can be used by teachers and students with some programming experience to create custom applets or components without having to program every detail from scratch, and thus in a fraction of the usual time. In addition, the components are extensively documented through a formal object model that specifies how the components relate to each other.Each object can be downloaded as a Java "bean" that includes all class and resource files needed for the object. An object in the form of a Java bean can be dropped into a builder tool (such as JBuilder or Visual Cafe) to expose the properties and methods of the object. Each object can also be downloaded in the form of a zip file that includes the source files and resource files for the object.
This site provides about 35 graphical applets on topics relative to Algebra, Precalculus, Calculus, and Statistics. These...
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This site provides about 35 graphical applets on topics relative to Algebra, Precalculus, Calculus, and Statistics. These are designed for classroom demonstrations of various mathematical/statistical concepts introductory probability book, published by the American Mathematical Society, is available from AMS bookshop. We are...
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This introductory probability book, published by the American Mathematical Society, is available from AMS bookshop. We are pleased to announce that our book has now been made freely redistributable under the terms of the GNU Free Documentation License (FDL), as published by the Free Software Foundation. Briefly stated, the FDL permits you to do whatever you like with a work, as long as you don't prevent anyone else from doing what they like with it.The book emphasizes the use of computing to simulate experiments and make computations. We have prepared a set of programs to go with the book. We have Mathematica, Maple, and TrueBASIC versions of these programs.
Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math...
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice type.
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Freedownload. The most recent version of this book is maintained by Information Age ... The ability tosolve problems." (GeorgePolya; math researcher and educator; 1877–1985.) "What science can there be more noble, more excellent, more
GeorgePolya, one of the foremost twentieth-century mathematicians. Polya devoted much ... ceive a free movie video for every three videos she rents. ... Solve each inequality in exercises 16 and 17, ...
John Dewey (1933) GeorgePolya (1988) Stephen Krulik and Jesse Rudnick (1980) ... students the heuristic and set their students free upon the problems of everyday life. Rather, ... Polya, G. (1988). Howtosolveit: A new aspect of mathematical method (2nd ed.).
GeorgePolya, "HowtoSolveIt," Princeton University Press, Princeton (1945) • Ask questions in class! There are usually other students wanting to know the table, consider a special case, look for a pattern, guess and test, draw a
GeorgePolya ... and the book can be read free from the Website listed in the reference. On September 30, 2004 the National Science Foundation announced it had committed $36.5 ... solve the types of math problems that arise in (3) above.
This is GeorgePolya's 10 commandments for teachers: 1. Be interested in ... Have you read "HowToSolveIt"? 2 months ago • Like Erlina Ronda • Yes, great little book ... 2 months ago • Like ... and can free students
GeorgePolya's General Problem-Solving Strategy.....18 Modeling and ... As you work tosolve a problem or accomplish a task, ... Here is a quote from ...
writings of GeorgePolya, ... receive a free movie video for every three videos she rents. ... Solve word problems 22 to 24 by writing an equation with a variable to represent the given information and then solve the equation. 22.
Out of print; full text available for free at Excerpted from Concrete Abstractions; ... [40] GeorgePolya. HowtoSolveIt: A New Aspect of Mathematical Method. Prince-ton, NJ: Princeton University Press, 2nd edition, 1971.
The mathematician GeorgePolya divided the problemsalv- ing ... and understand- Continued an next page Now that's what I call user friendly! ing the problem, making a plan for howtosolveit, trying out the plan or alternative ... can free the ecologist and the city planner to ...
Another technique for releasing the flow of ideas is free writing. Free writing helps a writer turn off his or her mental "editor" (who is ... by the mathematician GeorgePolya in HowtoSolveIt. Polya frames a series of questions directed toward four goals: (1) ...
It is now more than thirty years ago when GeorgePolya wrote his "Howtosolveit.", and I can only recommend his works to everyone who is inter- ested in the process of discovery by the human minds. Polya is very much concerned ...
requirements or that its operation will be uninterrupted or error free. ... GeorgePolya, did much in the area of problem solving. His book, ... When you solve an equation, remove parentheses first, combine like terms (i.e., ...
fulfilled lives in a country free of violence, discrimination and prejudice". ... solve problems and learn this subject through memorisation. ... According toGeorgePolya, problem solving consists of four basic steps
... to paraphrase GeorgePolya, is a trick I use twice. This book builds, ... This book complements works such as HowtoSolveIt [37], Mathematics and Plausible Reasoning [35, 36], ... Then solve the free-fall differential equation to find the exact vi, ...
2006–2008 George Pólya Lecturer by the MAA. ... Feel freeto use the year codes from the chart. 3. August 3, 2000 4. ... Solve the following mental addition problems by calculating from left to right. For an added challenge, ...
Polya counting theory, partially ordered sets, Mobius inversion, ... free for download at . ... but it is recommended that you first try tosolve them on your own. You must write your own solutions, ...
The mathematician GeorgePolya distinguished heuristics from analytical methods: For instance, ... heuristics that can solve problems that logic and probability cannot, such as NP-complete ... Free Markets, and the Sinking of the World Economy. New York: Norton Sunstein CR. 2005. Moral heuristics.
Is mathematics culture free? Some people say that mathematics is a set of ... mathematician GeorgePolya (1887–1985), a strong ... problem solving. He wrote "An essential ingredient of the problem is the desire, the will and the resolution tosolveit. The problem that you are supposed to do ...
(Original by GeorgePolya.) 3. A vicar and his curate, ... the new queen ordered the guards tofree certain prisoners based on the following scheme. ... Solve for x and y: 1x + 2y = 3 4X + 5y = 6 Generalize the above using two unknowns.
GeorgePolya (2004). Howtosolveit: A New Aspect of Mathematical Method. Princeton University Press . ... what "Gibbs free energy" means and howto use this con-cept. In the laboratory framework, students learn howto meas-
•GeorgePolya outlines the essence of problem solving, ... features are required to properly solve the problem? ... patient information in the database but they can download and use local copies of patient records when they are disconnected. 35.
... Joel Scambray, and George Kurtz, and Hacking Web Applications Exposed by Joel Scambray and Mike Shema. ... • HowtoSolveIt, by GeorgePolya. • Cognition in the Wild, by Edwin Hutchins ... is either free or a free trial; ...
According toGeorgePolya, we can think of two kinds of aims for school education: a good and narrow aim, that of turning out employable adults who ... tosolve such problems, that teachers and students find it worth their time and energy addressing these
Pólya, George Poncelet, Jean-Victor Ptolemy, Claudius Pythagoras of Samos ... tempted tosolve the quintic equation, an out- ... 1821, and was granted a free room due to his ex-treme poverty. The faculty even supported him
HowtoSolveIt. G. Polya, Princeton Science Library. ... You might also download and look at, Lecture Notes in Microeconomic theory, ... University press, 2006. Online and free at: /rubinstein/ Of these five, Kreps is probably my favorite. Varian is a very good book and
The most commonly used problem-solving model is GeorgePolya's four-step model: under-stand the problem; ... First published in Polya's HowtoSolveIt, 1945. ... potential,the curriculum must be free from bias and all students must be provided with a safe
| 677.169 | 1 |
This lesson plan has students create a confidence interval based on the historic snowfall records of a town in Ohio, the data for which is available online. The class will calculate the mean and standard deviation,...
This mathematics tutorial gives users an introduction to functions, functional notation and terminology. The site explains how a function is defined, and the correct way to read and write functional notation. Resources...
These roughly 200 lesson plans are related to mathematical problem solving and are provided by the non-profit Education Development Center. The lesson plans are designed to help students develop both deep conceptual...
This website lists terms specific to mathematical programming, as well as some terms from other disciplines, such as economics, computer science, and mathematics. Of note is the Notation section that provides all sorts...
This British website provides a listing of symbols used in mathematics as well as other useful information. The website is published by the Institute of Physics, which maintains a range of websites to support physics...
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College Mathematics: Student Support Edition: An Applied Approach
The Student Support Edition of Basic College Mathematics, 8/e, brings comprehensive study skills support to students and the latest technology tools ...Show synopsisThe Student Support Edition of Basic College Mathematics, 8 With its interactive, objective-based approach, Basic College Mathematics provides comprehensive, mathematically sound coverage of topics essential to the basic college math course. The Eighth Edition features chapter-opening Prep Tests, real-world applications, and a fresh design--all of which engage students and help them succeed in the course. The Aufmann Interactive Method (AIM) is incorporated throughout the text, ensuring that students interact with and master concepts as they are presented
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Compact Calculator - CompactCalc You can build linear, polynomial and nonlinear equation set. You are not limited by the size or the complexity of your mathematical expressions. CompactCalc has almost hundred of physical and mathematical constants built in, which can be easily accessed and used in calculations. No longer do you have to search the physic textbook for that common physical constant
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Scientific/Graphing Calculator Workshop
The Academic Support Center is offering scientific and graphing calculator (TI 84 and TI 84 plus) workshops. The workshop will focus on basic use of scientific and graphing calculators to the more advanced uses of the graphing calculator. The workshop will be helpful for all mathematics students who would like to know specific functions of the calculator and how they can be helpful in specific mathematics courses.
Workshops will be held in the Academic Support Center's satellite location in Anderson Library room 2120 at the times listed below. To register, click on the time and fill out the registration form. An email will be sent to you to confirm your attendance for the workshop. Keep in mind that the workshop's capacity is 12 students, so sign up early to reserve your spot!
If none of these times work for you, keep checking back because additional sections may be offered in the future.
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Today at Central Library Cooperative of Knowledge
Many students across the enter universities in hopes of getting a Bachelor in Administration, or even a Master's degree (MBA). Their intention is to obtain a high paying business management job. Business management careers can be very lucrative for the right people.
There are however, different types of business management...
Geometry topics contain a very long and extensive list, far too many to refer within the confines of a few lines. However, each of the topics or sub topics is in a specific classification grouped together with other like signs, symbols, and reasoning. The main header topics are of course,...
If you have done your pre algebra homework from your text book, but your book doesn't have an answer key, you can find the answers to those math problems. There are websites you can go to for the answers to your pre algebra problems. Type the words "pre...
Military Boarding School education is an excellent choice, as it can discipline and train you or your child well for future tasks in life. Presently prestigious military boarding schools have been introduced with up-to-date curriculums and new teaching methods giving opportunities even for female students to join them starting from...
Physics online is an interesting, innovative and very creative in the style and presentation for young students of all ages. Most of the physics online courses separate into three categories with the sub-categories listed for the convenience of the students. These main categories are mechanics, light and waves, and electricity....
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Prentice hall gold algebra
Prentice hall gold algebra worksheet answers downloads. I dont know but you shoud do the work yourself cause if theres a test or sumthin you wont be able to use a answer key! and if you use an answer key. Prentice hall geometry practice workbook answers key. Prentice hall worksheets answer sheets answers.
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Introduction to Analysis
9780821847879
ISBN:
0821847872
Edition: 5 Pub Date: 2009 Publisher: American Mathematical Society
Summary: Gaughan, Edward is the author of Introduction to Analysis, published 2009 under ISBN 9780821847879 and 0821847872. Three hundred eight Introduction to Analysis textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $47.12, or buy new starting at $55.00.
Ships From:Boonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. Introduction to Analysis is designed to bri... [more][ experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multi-step process requiring assistance for the beginner student
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Elementary Algebra by Schaums Outlines
393
Practice Questions
2
Quizzes
1056
Lessons
216
Flashcards
Overview
Covering everything from Signed Numbers, to Quadratic Equations, Schaum's Outline in Elementary Algebra is so thorough, both struggling and confident students can expect to achieve their personal best on exams. Equipped with 433 practice questions, 2 mini-tests and 216 flashcards, students will get the thorough review they need to better acquaint them with Elementary Algebra.
Topics Covered
Topics and concepts covered in Elementary Algebra by Schaums Outlines
From Arithmetic To Algebra
Representing Numbers By Letters
Representing Numbers By Letters
Stating Products Without Multiplication Signs
Changing Verbal Statements To Algebraic Equations
Interchanging Numbers In Addition
Interchanging Numbers In Addition
Interchanging Addends To Simplify Addition
Rearranging Addends
Interchanging Numbers In Multiplication
Interchanging Numbers In Multiplication
Simplifying Multiplication
Rearranging Factors
Symbolizing The Operations In Algebra
Symbolizing The Operations In Algebra
Symbols In Multiplication
Division By Zero
Expressing Addition And Subtraction Algebraically
Expressing Addition And Subtraction Algebraically
Expressing Addition Algebraically
Expressing Subtraction Algebraically
Changing Verbal Statements Into Algebraic Expressions
Expressing Multiplication And Division Algebraically
Expressing Multiplication And Division Algebraically
Representing Multiplication Or Division
Division And Its Relationship To Multiplication
Expressing Two Or More Operations Algebraically
Expressing Two Or More Operations Algebraically
Expressing Two Operations Algebraically
More Difficult Expressions
Changing Verbal Statements Into Algebraic Expressions
Order In Which Fundamental Operations Are Performed
Order In Which Fundamental Operations Are Performed
To Evaluate A Numerical Expression Not Containing Parentheses
To Evaluate An Algebraic Expression Not Containing Parentheses
Evaluating Numerical Expressions
Evaluating Algebraic Expressions
Evaluating When A Letter Represents
The Uses Of Parentheses
Changing The Order Of Operations
To Evaluate An Algebraic Expression Containing Parentheses
Evaluating Numerical Expressions Containing Parentheses
Evaluating Algebraic Expressions Containing Parentheses
Evaluating When A Letter Represents Zero
Multiplying Factors In Terms Numerical And Literal Coefficients
Multiplying Factors In Terms Numerical And Literal Coefficients
Expressions Containing Terms
Factors Of Terms
Numerical And Literal Coefficients
Repeated Multiplying Of A Factor Base Exponent And Power
Repeated Multiplying Of A Factor Base Exponent And Power
Table Of Powers
Literal Bases Squares And Cubes
Reading Powers
Writing As Bases And Exponents
Writing Without Exponents
Evaluating Powers
Evaluating Powers Of Fractions And Decimals
Evaluating Powers Of Literal Bases
Combining Like And Unlike Terms
Combining Like And Unlike Terms
To Combine Like Terms Being Added Or Subtracted
Combine Like Terms
Simplifying Expressions By Combining Like Terms
Combining Like Terms With Fractional And Decimal Coefficients
Combining Like Terms Representing Line Segments 9
Supplementary Problem 10
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 18
Supplementary Problem 22
Supplementary Problem 23
Supplementary Problem 24
Supplementary Problem 25
Simple Equations And Their Solutions
Kinds Of Equalities
Equations And Identities
Checking An Equation
Checking An Identity
Translating Verbal Statements Into Equations
Translating Verbal Statements Into Equations
Translating Statements Into Equations
Matching Statements And Equations
Representing Unknowns
Solving Simple Equations By Using Inverse Operations
Solving Simple Equations By Using Inverse Operations
Addition And Subtraction Are Inverse Operations
Multiplication And Division Are Inverse Operations
Solving By Using Inverse Operations
Rules Of Equality For Solving Equations
Rules Of Equality For Solving Equations
The Rule Of Equality For All Operations
Using Rules Of Equality
Using Division To Solve An Equation
Division Rule Of Equality
Division Rule Of Equality
To Solve An Equation By Using The Division Rule Of Equality
Solving Equations With Integral Coefficients
Division In Equations With Decimal Coefficients
Solving Equations With Percents As Coefficients
Solving Equations With Like Terms On One Side
Division Rule In A Wage Problem
Division Rule In A Commission Problem
Using Multiplication To Solve An Equation
Multiplication Rule Of Equality
Multiplication Rule Of Equality
To Solve An Equation By Using The Multiplication Rule Of Equality
Dividing By A Fraction
Dividing By A Fraction
To Solve An Equation Whose Unknown Has A Fractional Coefficient
Solving Equations With Integral Divisors
Solving Equations With Decimal Divisors
Solving Equations With Fractional Coefficients
Solving Equations With Percents As Coefficients
Multiplication Rule In Distance Problem
Multiplication Rule In Investment Problem
Using Subtraction To Solve An Equation
Subtraction Rule Of Equality
Subtraction Rule Of Equality
To Solve An Equation By Using The Subtraction Rule Of Equality
Subtraction Rule In Equations Containing Integers
Subtraction Rule In Equations Containing Fractions Or Decimals
Subtraction Rule In Problem Solving
Using Addition To Solve An Equation
Addition Rule Of Equality
Addition Rule Of Equality
To Solve An Equation By Using The Addition Rule Of Equality
Addition Rule In Equations Containing Integers
Addition Rule In Equations Containing Fractions Or Decimals
Addition Rule In Problem Solving
Using Two Or More Operations To Solve An Equation
Using Two Or More Operations To Solve An Equation
To Solve Equations By Using Two Inverse Operations
Using Two Inverse Operations To Solve An Equation
Solving Equations With Like Terms On The Same Side
Solving Equations With Like Terms On Both Sides
Solving Equations In Which The Unknown Is A Divisor
Solving Equations In Which The Unknown Is Being Subtracted
Solving Equations Whose Unknown Has A Fractional Coefficient
Using Two Operations In Problem Solving 18
Supplementary Problem 19
Supplementary Problem 20
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 23
Signed Numbers
Understanding Signed Numbers Positive And Negative Numbers
Understanding Signed Numbers Positive And Negative Numbers
Words Opposite In Meaning
Expressing Quantities As Signed Numbers
Absolute Value Of Signed Numbers
Using Number Scales For Signed Numbers
Using Number Scales For Signed Numbers
Number Scales
Two Meanings Of Signed Numbers
Comparing Signed Numbers
Use A Number Scale To Solve Problems
Adding Signed Numbers
Adding Signed Numbers
Rules For Adding Signed Numbers
Combining By Means Of Signed Numbers
Adding Signed Numbers With Like Signs
Adding Signed Numbers With Unlike Signs
Adding Signed Numbers Which Are Opposites Of Each Other
Adding Signed Numbers
Simplifying The Addition Of Signed Numbers
To Simplify The Writing Used In Adding Signed Numbers
To Simplify The Writing Used In Adding Signed Numbers
To Simplify Adding Signed Numbers
Simplifying The Addition Of Signed Numbers
Adding Positives And Negatives Separately
Using Signed Numbers And Number Scales To Solve Problems
Subtracting Signed Numbers
Subtracting Signed Numbers
Using Subtraction To Find The Change From One Position To Another
Using Subtraction To Find The Change From One Position To Another
Rule For Subtracting Signed Numbers
Subtracting A Positive Number
Subtracting A Negative Number
Subtracting Vertically
Subtracting Signed Numbers
Combining Addition And Subtraction Of Signed Numbers
Finding The Change Between Two Signed Numbers
Finding The Distance Between Two Levels
Finding A Temperature Change
Multiplying Signed Numbers
Rules For Multiplying Two Signed Numbers
Rules For Multiplying More Than Two Signed Numbers
Multiplying Signed Numbers With Like Signs
Multiplying Signed Numbers With Unlike Signs
Multiplying Signed Numbers
Multiplying More Than Two Signed Numbers
Using Signed Numbers To Solve Problems
Finding Powers Of Signed Numbers
Rules For Finding Powers Of Signed Numbers
Finding Powers When Base Is Positive
Finding Powers When Base Is Negative
Finding Powers Of Signed Numbers
Finding Bases Exponents Or Powers
Dividing Signed Numbers
Rules For Dividing Signed Numbers
Combining Multiplying And Dividing Of Signed Numbers
Dividing Signed Numbers With Like Signs
Dividing Signed Numbers With Unlike Signs
Dividing Signed Numbers
Combining Multiplying And Dividing Signed Numbers
Zero In Dividend Or Divisor
Evaluating Expressions Having Signed Numbers
Evaluating Expressions Having Signed Numbers
Evaluating Expressions Having One Letter
Evaluating Expressions Having Two Letters
Evaluating Expressions Having Three Letters
Summary Of Rules For Computations Involving Signed Numbers
Supplementary Problems
Supplementary Problem 1
Supplementary Problem 5
Supplementary Problem 7
Supplementary Problem 9
Supplementary Problem 14
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 24
Supplementary Problem 25
Supplementary Problem 26
Supplementary Problem 27
Introduction To Monomials And Polynomials
Understanding Monomials And Polynomials
Understanding Monomials And Polynomials
Selecting Like Terms
Adding Monomials
Adding Monomials
Adding Like Terms
Adding Like Terms Horizontally
Adding Like Terms Vertically
Adding Like And Unlike Terms
Arranging And Adding Polynomials
Arranging The Terms Of A Polynomial In Descending Or Ascending Order
To Add Polynomials
Arranging Polynomials And Combining Like Terms
Adding Arranged Polynomials
Adding Polynomials
Checking The Addition Of Polynomials
Subtracting Monomials
Subtracting Monomials
Subtracting Like Terms
Different Subtraction Forms
Combining Adding And Subtracting Of Like Terms
Subtracting Polynomials
To Subtract Polynomials
Subtracting Arranged Polynomials
Arranging Polynomials And Subtracting
Different Subtraction Forms
Checking The Subtraction Of Polynomials
Using Parentheses And Other Grouping Symbols To Add Or Subtract Polynomials
Using Parentheses And Other Grouping Symbols To Add Or Subtract Polynomials
Rules For Removing Parentheses And Grouping Symbols
Removing Parentheses Preceded By A Plus Sign
Removing Parentheses Preceded By A Minus Sign
Brackets Containing Parentheses
Using Grouping Symbols To Add Or Subtract Polynomials
Removing Symbols Of Grouping
Multiplying Monomials And Powers Of The Same Base
Multiplying Monomials And Powers Of The Same Base
Multiplying Powers Of The Same Base
Finding The Power Of A Power Of A Base
Multiplying Monomials
Multiplying A Polynomial By A Monomial
Multiplying A Polynomial By A Monomial
Multiplying A Polynomial By A Monomial Horizontally
Multiplying A Polynomial By A Monomial Vertically
Removing Parentheses
Removing Brackets Containing Parentheses
Removing Symbols Of Grouping
Multiplying Polynomials
To Multiply Polynomials
Multiplying Polynomials
Checking Multiplication
Extended Multiplication
Dividing Powers And Monomials
Dividing Powers And Monomials
To Divide Monomials
To Divide Monomials
To Check Division Of Monomials
Dividing Powers Of The Same Base
Dividing Monomials
Checking Division
Dividing A Polynomial By A Monomial
Dividing A Polynomial By A Monomial
Dividing A Polynomial By A Monomial
Checking Division
Multiplying And Dividing Polynomials By A Monomial
Dividing A Polynomial By A Polynomial
To Divide Polynomial
To Divide Polynomial
To Check The Division
Dividing A Polynomial By A Polynomial No Remainder
Arranging Polynomials And Dividing
Terms Missing In Dividend
Dividing Polynomials With Remainder 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 20
Supplementary Problem 22
Supplementary Problem 23
Supplementary Problem 25
Supplementary Problem 27
Supplementary Problem 28
Supplementary Problem 32
Supplementary Problem 33
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 37
Supplementary Problem 38
Supplementary Problem 39
Supplementary Problem 40
Supplementary Problem 41
First Degree Equations
Reviewing The Solution Of First Degree Equations Having Positive Roots
Reviewing The Solution Of First Degree Equations Having Positive Roots
Inverse Operations
Using Subtraction S To Undo Addition A
Using Addition A To Undo Subtraction S
Using Division D To Undo Multiplication M
Using Multiplication M To Undo Division D
Using Two Operations To Solve Equations
Equations Containing More Than One Term Of The Unknown
Equations Having Fractional Coefficients
Number Problems Leading To First Degree Equations
Solving First Degree Equations Having Negative Solutions
Solving First Degree Equations Having Negative Solutions
Using Addition Or Subtraction To Solve Equations
Using Multiplication Or Division To Solve Equations
Using Two Operations To Solve Equations
Equations Having Fractional Coefficients
More Difficult Equations
Problems Having Negative Roots
Solving Equations By Transposing
Rule Of Transposition
Rule Of Transposition
To Solve Equations By Transposing Terms
Transposing Terms In An Equation
More Difficult Equations
Solving Equations Containing Parentheses
To Solve Equations By Removing Parentheses
Removing Parentheses To Solve Equations
More Difficult Equations With Parentheses
Problems Leading To Equations With Parentheses
Solving Equations Containing One Fraction Or Fractions Having The Same Denominator
To Solve Equations Having Same Denominator By Clearing Of Fractions
Fractional Equations Having The Same Denominator
Fractional Equations Having Binomial Numerator Or Denominator
Solving Equations Containing Fractions Having Different Denominators
Lowest Common Denominator
To Solve Equations Having Different Denominators By Clearing Of Fractions
Fractional Equations Having Numerical Denominators
Fractional Equations Having Literal Denominators
Fractional Equations Having Binomial Numerators
Fractional Equations Having Binomial Denominators
Solving Equations Containing Decimals
Solving Equations Containing Decimals
To Solve An Equation Having Decimals
Equations With One Decimal
Solving Equations Without Clearing Of Decimals
Equations With Two Or More Decimals
Equations Containing Percents
Equations Containing Decimals And Parentheses
More Difficult Decimal Equations
Solving Literal Equations
Solving Literal Equations
Solving Literal Equations By Using One Operation
Solving For One Of The Letters In A Formula
Solving And Checking Literal Equations
Solving A Literal Equation For Each Letter
Solving More Difficult Literal Equations
The Graphing Calculator
Graphing Calculators Are Used To Solve Equations. 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 18
Supplementary Problem 19
Supplementary Problem 20
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 23
Formulas
Points And Lines
Points And Lines
Undefined Terms Of Geometry Point Line And Plane
Point
Line
Planes
Line Segments
Dividing A Line Segment Into Parts
Congruent Segments
Understanding Polygons Circles And Solids
Understanding Polygons In General
Understanding Circles
Understanding Triangles
Understanding Quadrilaterals
Understanding Solids
Formulas For Perimeters And Circumferences Linear Measure
Formulas For Perimeters And Circumferences Linear Measure
Perimeter Formulas For Triangles And Quadrilaterals
Perimeter Formulas For Polygons
Finding A Side Of An Equilateral Polygon
Finding Perimeters Of Regular Polygons
Finding Perimeters Of Quadrilaterals
Finding The Perimeter Of A Rectangle
Finding The Length Or Width Of A Rectangle
Perimeter Of An Isoceles Triangle
Circumference And Arc Formulas
Circumference Of A Circle
Perimeters Of Combined Figures
Formulas For Areas Square Measure
Formulas For Areas Square Measure
Area Formulas Using A For Area Of Figure
Area Formulas For Solids Using T For Total Area Of Solid
Relations Among Square Units
Finding The Area Of Squares
Finding Areas
Area Of Circle Formulas
Area Of A Circle
Formulas For Combined Areas
Formulas For Reduced Areas
Finding Total Areas Of Solids
Formulas For Volumes Cubic Measure
Formulas For Volumes Cubic Measure
Volume Formulas
Relations Among Cubic Units
Finding Volumes Of Cubes
Finding Volumes Of Rectangular Solid Prism And Pyramid
Finding Volumes Of Sphere Cylinder And Cone
Deriving Formulas From V Bh
Formulas For Combined Volumes
Deriving Formulas
To Derive A Formula For Related Quantities
Obtaining Formulas From A More General Formula
Deriving A Coin Formula
Deriving Coin Formulas
Deriving Time Formulas
Deriving Length Formulas
Obtaining Formulas From D and Rt
Transforming Formulas
Transforming Formulas
Use Inverse Operations To Transform Formulas
Transformations Requiring Division
Transformations Requiring Multiplication
Transformations Requiring Addition Or Subtraction
Transformations Requiring Two Operations
More Difficult Transformations
Finding The Value Of An Unknown In A Formula
Finding The Value Of An Unknown In A Formula
Finding The Value Of An Isolated Unknown
Finding The Value Of An Unknown That Is Not Isolated
More Difficult Evaluations Using Transformations
Finding An Unknown In A Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17 31
Supplementary Problem 32
Supplementary Problem 34
Supplementary Problem 35
Graphs Of Linear Equations
Understanding Graphs
Reviewing Number Scales
Forming A Graph By Combining Number Scales
Comparing A Map And A Graph
Locating Points On A Graph
Locating Positions On A Map
Coordinates Of Points In The Four Quadrants
Coordinates Of Points Between The Quadrants
Graphing A Quadrilateral
Graphing A Triangle
Graphing Linear Equations
Graphing Linear Equations
To Graph A Linear Equation
To Graph A Linear Equation
To Graph A Linear Equation By Using Intercepts
Equations Of The First Degree
Making Tables Of Coordinate Values
Graphing Linear Equations
Graphing Linear Equations Using Intercepts
Graphing Equations Of First Degree In Only One Unknown
Coordinate Values Of Any Point On A Line
Coordinate Values Of Any Point Not On A Line
Intercepts And Points Of Intersection
Solving A Pair Of Linear Equations Graphically
Solving A Pair Of Linear Equations Graphically
Consistent Inconsistent And Dependent Equations
To Solve A Pair Of Linear Equations Graphically
Finding Common Solutions Graphically
Consistent Equations And Their Graphic Solution
Inconsistent Equations
Dependent Equations
Deriving A Linear Equation From A Table Of Values
Deriving A Simple Linear Equation By Inspection
Deriving A Linear Equation By The Ratio Method
Deriving Simple Linear Equations By Inspection
Deriving Linear Equation Of Form By Ratio Method
Midpoint Of A Segment
Midpoint Of A Segment
Applying The Midpoint Formula
Determining If Segments Bisect Each Other
Distance Between Two Points
Distance Between Two Points
Finding The Distance Between Two Points By Using The Distance Formula
Applying The Distance Formula To A Triangle
Applying The Distance Formula To A Parallelogram 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 19
Supplementary Problem 20
Introduction To Simultaneous Equations
Solving A Pair Of Equations By Addition Or Subtraction
To Solve A Pair Of Equations By Adding Or Subtracting
Using Addition Or Subtraction To Eliminate One Unknown
Solutions Not Requiring Multiplication
Solutions Requiring Multiplication
Solutions Requiring Rearrangement Of Terms
Fractional Pairs Of Equations
Decimal Pairs Of Equations
Solving A Pair Of Equations By Substitution
To Solve A Pair Of Equations By SubstitutionProblem Solving And Mathematical Modeling
Problem Solving And Mathematical Modeling
Number Problems Having One Unknown
Number Problems Having One Unknown
To Solve A Number Problem Having One Unknown
Translation Of Statements Into Equations
Verification Or Check In Original Statement
Complete Solutions Of Number Problems
Number Problems Having Two Unknowns
Number Problems Having Two Unknowns
To Solve A Number Problem Having Two Unknowns
Representing Two Unknowns By Using One Letter
Using One Equation For Two Unknowns
Using Two Equations For Two Unknowns
Complete Solution Of Number Problem Having Two Unknowns
Consecutive Integer Problems
Consecutive Integer Problems
Representation Using N For First Integer
Representation Using N For Middle Integer
Translation In Consecutive Integer Problems
Translation In Consecutive Even Integer Problems
Complete Solutions Of An Integer Problem
Age Problems
Age Problems
Representing Ages On Basis Of Present Age
Representing Ages
Using One Equation For Two Unknowns In Age Problems
Using Two Equations For Two Unknowns In Age Problems
Complete Solution Of An Age Problem Two Methods
Ratio Problems
Ratio Problems
Ways Of Expressing A Ratio
General Principles Of Ratios
Ratio Of Two Quantities With Same Unit
Ratio Of Two Quantities With Different Units
Continued Ratio Of Three Quantities
Numerical Ratios
Algebraic Ratios
Representation Of Numbers In A Fixed Ratio
Ratio In Number Problems
Ratio In A Triangle Problem
Ratio In A Money Problem
Ratio In A Will Problem
Ratio In A Wage Problem
Angle Problems
Pairs Of Angles
Using One Equation For Two Unknowns In Angle Problems
Using Two Equations For Two Unknowns In Angle Problems
Three Angles Having A Fixed Ratio
Supplementary Angles Problem
Sum Of Angles Of A Triangle Problem
Perimeter Problems
Perimeter Problems
One Equation Method Perimeter Of Rectangle
Two Equation Method Perimeter Of Triangle
One Equation Method Perimeter Of Trapezoid
Perimeter Of A Quadrilateral Ratio Of Sides
Perimeter Of An Isosceles Triangle Problem
Perimeter Of A Square Problem
Coin Or Stamp Problems
Coin Or Stamp Problems
Finding Total Values
Representation In Coin Or Stamp Problems
Using One Equation In Coin Or Stamp Problems
Using Two Equations In Coin Or Stamp Problems
Complete Solution Of Coin Problem
Complete Solution Of A Change Problem
Complete Solution Of A Fares Problem
Cost And Mixture Problems
Cost And Mixture Problems
Representation In Mixture Problems T and Nv
Representation In Cost Problems
Translation In Value And Cost Problems
Complete Solution Blending Coffee Problem
Complete Solution Selling Tickets Problem
Investment Or Interest Problems
Investment Or Interest Problems
Representation In Interest Problems I and Pr
Translation In An Interest Problem
Complete Solution Ratio In An Interest Problem
Alternate Methods In An Investment Problem
Alternate Methods In A Profit And Loss Investment Problem
Complete Solution Adding A Third Investment
Motion Problems
Motion Problems
Representation Of Distance
Representation Of Time
Separation Situation
Closure Situation
Round Trip Situation
Gain Or Overtake Situation
Motion Problem A Trip In Two Stages
Mathematical Modeling
Mathematical Modeling
Example 10
Supplementary Problem 11
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15 33
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 36
Supplementary Problem 38
Supplementary Problem 39
Supplementary Problem 40
Supplementary Problem 43
Supplementary Problem 44
Supplementary Problem 45
Supplementary Problem 46
Supplementary Problem 47
Supplementary Problem 48
Supplementary Problem 49
Supplementary Problem 50
Supplementary Problem 51
Supplementary Problem 52
Supplementary Problem 54
Supplementary Problem 55
Supplementary Problem 56
Supplementary Problem 58
Supplementary Problem 60
Supplementary Problem 62
Supplementary Problem 64
Supplementary Problem 65
Supplementary Problem 66
Products And Factoring
Understanding Factors And Products
A Product And Its Factors
Finding The Product Of Monomial Factors
Finding The Product Of Two Factors A Monomial And A Polynomial
Finding Products Involving Fractions And Decimals
Factoring A Polynomial Having A Common Monomial Factor
Factoring A Polynomial Having A Common Monomial Factor
To Factor A Polynomial Having A Common Monomial Factor
Factoring Polynomials Having A Common Monomial Factor
Factoring Numerical Polynomials
Squaring A Monomial
Squaring A Monomial
Squaring Numbers
Squaring Monomials
Finding Areas Of Squares
Finding The Square Root Of A Monomial
Finding The Square Root Of A Monomial
Finding Principal Square Roots
Finding Sides Of Squares
Finding The Product Of The Sum And Difference Of Two Numbers
Finding The Product Of The Sum And Difference Of Two Numbers
Multiplying The Sum Of Two Numbers By Their Difference
Multiplying Two Numbers By The Sum Product Method
Multiplying A Monomial By Sum And Difference Factors
Factoring The Difference Of Two Squares
Factoring The Difference Of Two Squares
To Factor The Difference Of Two Squares
Procedure For Factoring The Difference Of Two Squares
Complete Factoring Involving The Difference Of Two Squares
Finding The Product Of Two Binomials With Like Terms
Finding The Product Of Two Binomials With Like Terms
To Multiply Two Binomials By Inspection
Products Of Binomials By Steps
Products Of Two Binomials Mentally
Representing Areas Of Rectangles
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
To Factor A Trinomial In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomial In Form Of Ax2 Bx C
To Factor A Trinomial In Form Of Ax2 Bx C
Factoring Trinomials In Form Of Ax2 Bx C
Squaring A Binomial
Squaring A Binomial
To Square A Binomial
Factoring A Perfect Square Trinomial
Factoring A Perfect Square Trinomial
To Factor A Perfect Square Trinomial
Factoring A Perfect Square Trinomial
Representing The Side Of A Square
Completely Factoring Polynomials
Completely Factoring Polynomials
Procedure To Completely Factor Expressions Having Common Monomial Factor
Procedure To Completely Factor Expressions Having No Common Monomial Factor
Factoring Completely Expressions Having Common Monomial Factor
Factoring Completely Expressions Having No Common Monomial Factor
The Variable Direct And Inverse Variation
The Variable Direct And Inverse Variation
Measuring The Change In A Variable
Using Division To Measure The Change In A Variable
Multiplying Or Dividing Variables
Understanding Direct Variation
Understanding Direct Variation
Multiplication And Division In Direct Variation
Direct Variation In Formulas
Multiplication And Division In Direct Variation
Applying Direct Variation To Statements
Finding Values For Directly Varying Variables
Applying Direct Variation To A Motion Problem
Applying Direct Variation To An Interest Problem
Understanding Inverse Variation
Understanding Inverse Variation
Multiplication And Division In Inverse Variation
Inverse Variation In Formulas
Multiplication And Division In Inverse Variation
Applying Inverse Variation To Statements
Finding Values For Inversely Varying Variables
Supplementary Problems
Supplementary Problem 1
Supplementary Problem 2
Supplementary Problem 3
Supplementary Problem 4
Supplementary Problem 5
Supplementary Problem 6
Supplementary Problem 8
Supplementary Problem 9
Supplementary Problem 10
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16 26
Supplementary Problem 27
Supplementary Problem 28
Supplementary Problem 29
Supplementary Problem 30
Supplementary Problem 31
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 36
Fractions
Understanding Fractions
Understanding Fractions
Zero Numerators Or Zero Denominators
Fractions Meaning Division
Fractions Meaning Ratio
Fractions Meaning Parts Of A Whole Or Of A Group
Fractions Having Zero Numerators
Fractions Having Zero Denominators
Changing Fractions To Equivalent Fractions
Changing Fractions To Equivalent Fractions
Using Multiplication To Obtain Equivalent Fractions
Using Division To Obtain Equivalent Fractions
Obtaining Missing Terms
Reciprocals And Their Uses
Reciprocal Of A Number
Rules Of Reciprocals
Are Reciprocal Of Each Other
The Product Of Two Reciprocals Is 1
Using Reciprocals To Change Division To Multiplication
Using Reciprocals To Solve Equations
Reducing Fractions To Lowest Terms
Reducing Fractions To Lowest Terms
To Reduce A Fraction To Lowest Terms
Binomials Which Are Negatives Of Each Other
Reducing Fractions Whose Terms Have Common Monomial Factors
Reducing Fractions Whose Terms Have A Common Binomial Factor
Reducing Fractions Having Binomial Factors Which Are Negatives Of Each Other builtPerfect for beginning math students, this program is designed by curriculum experts and experienced teachers to bring students up to speed in the most challenging areas of early-level algebra. Concepts include real…
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Mathematics in Fun and in Earnest
A world-renowned mathematician takes a lighthearted look at the philosophy, form, and recreations of mathematics in this fascinating book. In lucid and witty language, he discusses and illustrates the charm of mathematics as well as the science's vast practical utility and its vital significance to our cultural history. 1958 edition.
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Essential Mathematics for Economics and Business has become established as one of the leading introductory textbooks on mathematics for students of these subjects. It combines a non-rigorous approach ...
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Translation Of Geometric Figures Pdf
Math by Design Lesson Plan Transformations to describe this transformation lead a discussion about ways to describe the transformation of a figure encourage descriptions that include up down and right left Math by Design Lesson Plan Transformations
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year students often use a functional language in their introductory programming classes today. Experiences gained in this way allows them to build mathematical concepts quickly and properly. On the other hand, modern algebra systems, such as MATLAB, accelerate advanced calculation and offer an excellent platform for experimentation, but they do not facilitate understanding of fundamental concepts. It is proposed to use jointly the functional approach and a modern algebra system (in this instance, the MATLAB software). This would reduce a danger of creating a clutter of unrelated procedures in place of a coherent system of concepts.
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Basic Engineering Mathematics
Synopses & Reviews
Publisher Comments: level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult.
Now in its fifth edition, Basic Engineering Mathematics is an established textbook, with the previous edition selling nearly 7500 copies. All students that require a fundamental knowledge of mathematics for engineering will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering, the Diploma, and the BTEC First specifications. Level 3 students will also find this text to be a useful resource for getting to grips with essential mathematics concepts, because the compulsory topics in BTEC National and A Level Engineering courses are also addressed.
• Numerous worked examples supported by 600 worked problems and 1050 further problems within exercises included throughout the text. Additionally, there are 15 assignments included at regular intervals.
• Free instructor's manual available for download, which includes solutions to assignments.
AboutRoyal Naval School of Marine Engineering, HMS Sultan, Gosport; formerly University of Portsmouth and Highbury College, UK
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Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra& Introductory Algebra, Third Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for successUsed - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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...
More About
This Book
problems, and practice exercises to test your skills.
This Schaum's Outline gives you
1,000 fully solved problems
Complete review of all course fundamentals
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time—and get your best test scores!
Topics include: Number Systems; The Earliest Mathematics;
Additive Systems;
The Egyptian Number System;
Alphabetic Systems;
Positional Systems on a Fixed Base;
Historical Examples of Positional Systems with a Base Different from Ten;
The Babylonian Number System;
The Mayan Number System;
Method for Translating Base Ten into Base Two;
The Algebra of Sets;
Set Theoretic Exponentiation;
Cardinal Numbers;
Theory of Numbers;
Mathematical Induction;
Complete Induction;
Prime Numbers;
The Division Theorem;
Testing for Primality;
The Greatest Common Divisor;
Irrational Numbers;
Factorization into Primes;
The Least Common Multiple;
The Euclidean Algorithm;
Some Famous Unsolved Problems (Perfect numbers,
Fermat primes, The Goldbach Conjecture);
Linear Diophantine Equations;
Fractions (How is a fraction represented in diagrams?
How are fractions represented on a number line?
What is the "unit"?
What is the "shifting unit"?
What is the multiplicative identity element for fractions?
What is a proper fraction?
What is an improper fraction?
When is a fraction larger than one whole?
What is a unit fraction?
How are fractions "simplified" (or "reduced")?
When is a fraction in "simplest form" (or "lowest terms")?
How are mixed numbers changed to improper fractions?
What are equivalent fractions?
How can we determine when fractions are equivalent?
How are fractions ordered from largest to smallest or from smallest to largest? How are fractions compared to find the largest or smallest value?
How is the least common denominator (LCD) determined?
How is the numerator determined once the LCD or common denominator is known?
How are fractions added and subtracted?
What are the properties of fraction addition?
How are fractions multiplied?
What are the properties of fraction multiplication?
Why is the product of two proper fractions smaller in value than either fraction factor?
What is the "multiplicative inverse," or "reciprocal" of a fraction?
How are fractions divided?
Why does the "invert-and-multiply" rule "work" when dividing fractions?
What are complex fractions?
How are complex fractions simplified?);
Decimals, Ratios, Proportions, and Percents (
What is a decimal fraction?
What is a mixed decimal?
What are the place values for decimals?
How are decimals written in expanded form?
What are terminating decimals?
What are equivalent decimals?
What are repeating (or recurring) nonterminating decimals?
What are nonepeating, nonterminating decimals?
How can common fractions be written as decimals?
How can decimals be written as common fractions?
How are mixed numbers written as decimals?
How are decimals ordered and compared?
How are decimals rounded?
How are decimals added and subtracted?
How are decimals multiplied?
Why is the placement of the decimal point in the product of two decimals determined by counting the number of decimal places in the factors?
How is decimal multiplication the same as whole number multiplication? How is decimal multiplication different from whole number multiplication?
How are decimals divided?
How is decimal division different from whole number division? How is decimal division the same as whole number division?
What does it mean to "add a zero" to the end of a decimal fraction?
What is scientific notation and how is it used?
What is a ratio?
What is a rate?
How are ratios and rates the same? How are they different?
How are ratios expressed as decimals? As percents?
When are two ratios equal?
What is a proportion?
What is a scaled drawing?
How are scales used to calculate actual quantities?
What does percent mean?
How are percents changed to decimals?
How are decimals changed to percents?
How are percents changed to common fractions?
How are common fractions changed to percents?
What does a percent greater than 100% mean?
What does a percent less than 1% mean?
How is a percent of a number calculated and what does it mean?
What are the aliquot parts of 100?
How is the percent of a number calculated?
When finding the percent of a number, when is it appropriate to use the fraction form of a rational number and when is it appropriate to use a decimal form of a rational number?
How can we find a number when a percent of it is known?
How is the percent of increase or decrease found?);
Algebra, Patterns, and Functions (What is a variable?
How are a "variable" and an "unknown" the same? How are they different?
What does the equal sign mean?
What is an algebraic expression?
What is an equation?
What is a linear equation?
How are linear equations solved?
What is an inequality?
How are linear inequalities solved?
What is the absolute value of a number?
What is a pattern? How are patterns used to solve problems?
What is a function?
What is the slope of a line?
What is the y-intercept of a line?
How is a linear equation graphed?
What is factoring?
How are algebraic expressions factored?
What is the Pythagorean Theorem?
What are Pythagorean triples?
What is a quadratic equation?
What is covariation?
What is direct variation?
What is inverse variation?);
Geometry and Measurement; Combinatorics and Probability; The Multiplication Principle; Terminology of Sets;
Probability; The Meaning of Probability;
Basic Ideas of Probability Theory: Probability Spaces
Events;
Conditional Probability;
Independent Events;
Random Variables and Expected Values;
; Statistics; Distributions and Types of Data
(What is a distribution?
What is a normal distribution?
What is a skewed distribution?
What are discrete data (also known as "categorical data") and how are they analyzed?
What are continuous data (sometimes also called, numerical data) and how are they analyzed?);
Populations and Samples (
What is the difference between a population and a sample?
What is convenience sampling?
What is systematic sampling?
What is voluntary-response sampling?
What is random sampling?
What is a biased sample?
What is a simulation?
What are frequency tables and how are they constructed?
What is relative frequency?
What is a picture graph (also known as a pictograph, pictogram, or pictorial graph) and how is it constructed?
What is a bar graph (also known as a bar chart) and how is it constructed?
What is a double or multiple bar graph and how is it constructed?
What is a stacked bar graph and how is it constructed?
What is a histogram and how is it constructed?
How are bar graphs and histograms the same? How are they different?
What is a line graph (also known as a broken line graph) and how is it constructed?
What is a double line graph and how is it constructed?
What is a circle graph (also known as a pie graph, pie chart, pie diagram, area graph) and how is it constructed?
What is a line plot?
What is a stemplot (also known as a stem-and-leaf plot) and how is it constructed?
What is a back-to-back stem-and-leaf plot and how is it constructed?
What is a scatterplot and how is it constructed?
What is correlation?
What is a line of best fit and how can it be found?);
Measures of Center (What are measures of central tendency?
What is the mean of a set of data (also known as the arithmetic mean or arithmetic average) and how is it determined?
What is the median of a set of data and how is it found?
What is the mode of a set of data?);
Measures of Spread (What are measures of dispersion?
What is the range of a set of data and how is it calculated?
What is the variance of a set of data and how is it calculated?
What is the standard deviation of a set of data and how is it calculated?
What are percentiles?
What are quartiles and how are they determined?
What is the interquartile range?
What is a boxplot (also known as a box-and-whisker plot) and how is it constructed?
Table of Contents
Chapter 1: Number Systems
The Earliest Mathematics
Additive Systems
The Egyptian Number System
Alphabetic Systems
Positional Systems on a Fixed Base
Historical Examples of Positional Systems with a Base Different from Ten
The Babylonian Number System
The Mayan Number System
Method for Translating Base Ten into Base Two
Chapter 2: Sets
The Algebra of Sets
Set Theoretic Exponentiation
Cardinal Numbers
Chapter 3: Theory of Numbers
Mathematical Induction
Complete Induction
Prime Numbers
The Division Theorem
Testing for Primality
The Greatest Common Divisor
Irrational Numbers
Factorization into Primes
The Least Common Multiple
The Euclidean Algorithm
Some Famous Unsolved Problems (Perfect numbers, Fermat primes, The Goldbach Conjecture)
Linear Diophantine Equations
Chapter 4: Fractions
Introduction
Try These First
4.1 What is a "fraction"?
4.2 How is a fraction represented in diagrams?
4.3 How are fractions represented on a number line?
4.4 What is the "unit"?
4.5 What is the "shifting unit"?
4.6 What is the multiplicative identity element for fractions?
4.7 What is a proper fraction?
4.8 What is an improper fraction?
4.9 When is a fraction larger than one whole?
4.10 What is a unit fraction?
4.11 How are fractions "simplified" (or "reduced")?
4.12 When is a fraction in "simplest form" (or "lowest terms")?
4.13 How are mixed numbers changed to improper fractions?
4.14 What are equivalent fractions?
4.15 How can we determine when fractions are equivalent?
4.16 How are fractions ordered from largest to smallest or from smallest to largest? How are fractions compared to find the largest or smallest value?
4.17 How is the least common denominator (LCD) determined?
4.18 How is the numerator determined once the LCD or common denominator is known?
4.19 How are fractions added and subtracted?
4.20 What are the properties of fraction addition?
4.21 How are fractions multiplied?
4.22 What are the properties of fraction multiplication?
4.23 Why is the product of two proper fractions smaller in value than either fraction factor?
4.24 What is the "multiplicative inverse," or "reciprocal" of a fraction?
4.25 How are fractions divided?
4.26 Why does the "invert-and-multiply" rule "work" when dividing fractions?
4.27 What are complex fractions?
4.28 How are complex fractions simplified?
End of Chapter Exercises
Sample Certification Test Items
Chapter 5: Decimals, Ratios, Proportions, and Percents
Introduction
Try These First
5.1 What is a decimal fraction?
5.2 What is a mixed decimal?
5.3 What are the place values for decimals?
5.4 How are decimals written in expanded form?
5.5 What are terminating decimals?
5.6 What are equivalent decimals?
5.7 What are repeating (or recurring) nonterminating decimals?
5.8 What are nonepeating, nonterminating decimals?
5.9 How can common fractions be written as decimals?
5.10 How can decimals be written as common fractions?
5.11 How are mixed numbers written as decimals?
5.12 How are decimals ordered and compared?
5.13 How are decimals rounded?
5.14 How are decimals added and subtracted?
5.15 How are decimals multiplied?
5.16 Why is the placement of the decimal point in the product of two decimals determined by counting the number of decimal places in the factors?
5.17 How is decimal multiplication the same as whole number multiplication? How is decimal multiplication different from whole number multiplication?
5.18 How are decimals divided?
5.19 How is decimal division different from whole number division? How is decimal division the same as whole number division?
5.20 What does it mean to "add a zero" to the end of a decimal fraction?
5.21 What is scientific notation and how is it used?
5.22 What is a ratio?
5.23 What is a rate?
5.24 How are ratios and rates the same? How are they different?
5.25 How are ratios expressed as decimals? As percents?
5.26 When are two ratios equal?
5.27 What is a proportion?
5.28 What is a scaled drawing?
5.29 How are scales used to calculate actual quantities?
5.30 What does percent mean?
5.31 How are percents changed to decimals?
5.32 How are decimals changed to percents?
5.33 How are percents changed to common fractions?
5.34 How are common fractions changed to percents?
5.35 What does a percent greater than 100% mean?
5.36 What does a percent less than 1% mean?
5.37 How is a percent of a number calculated and what does it mean?
5.38 What are the aliquot parts of 100?
5.39 How is the percent of a number calculated?
5.40 When finding the percent of a number, when is it appropriate to use the fraction form of a rational number and when is it appropriate to use a decimal form of a rational number?
5.41 How can we find a number when a percent of it is known?
5.42 How is the percent of increase or decrease found?
End of Chapter Exercises
Sample Certification Test Items
Chapter 6: Algebra, Patterns, and Functions
Introduction
Try These First
6.1 What is algebra?
6.2 What is a variable?
6.3 How are a "variable" and an "unknown" the same? How are they different?
6.4 What does the equal sign mean?
6.5 What is an algebraic expression?
6.6 What is an equation?
6.7 What is a linear equation?
6.8 How are linear equations solved?
6.9 What is an inequality?
6.10 How are linear inequalities solved?
6.11 What is the absolute value of a number?
6.12 What is a pattern? How are patterns used to solve problems?
6.13 What is a function?
6.14 What is the slope of a line?
6.15 What is the y-intercept of a line?
6.16 How is a linear equation graphed?
6.17 What is factoring?
6.18 How are algebraic expressions factored?
6.19 What is the Pythagorean Theorem?
6.20 What are Pythagorean triples?
6.21 What is a quadratic equation?
6.22 What is covariation?
6.23 What is direct variation?
6.24 What is inverse variation?
End of Chapter Exercises
Sample Certification Test Items
Chapter 7: Geometry and Measurement
Chapter 8: Combinatorics and Probability
Let Us Count the Ways
The Multiplication Principle
Terminology of Sets
Probability
The Meaning of Probability
Basic Ideas of Probability Theory: Probability Spaces Events
Conditional Probability
Independent Events
Random Variables and Expected Values
Chapter 9: Statistics
Introduction
Try These First
Distributions and Types of Data
9.1 What is a distribution?
9.2 What is a normal distribution?
9.3 What is a skewed distribution?
9.4 What are discrete data (also known as "categorical data") and how are they analyzed?
9.5 What are continuous data (sometimes also called, numerical data) and how are they analyzed?
Populations and Samples
9.6 What is the difference between a population and a sample?
9.7 What is convenience sampling?
9.8 What is systematic sampling?
9.9 What is voluntary-response sampling?
9.10 What is random sampling?
9.11 What is a biased sample?
9.12 What is a simulation?
9.13 What are frequency tables and how are they constructed?
9.14 What is relative frequency?
9.15 What is a picture graph (also known as a pictograph, pictogram, or pictorial graph) and how is it constructed?
9.16 What is a bar graph (also known as a bar chart) and how is it constructed?
9.17 What is a double or multiple bar graph and how is it constructed?
9.18 What is a stacked bar graph and how is it constructed?
9.19 What is a histogram and how is it constructed?
9.20 How are bar graphs and histograms the same? How are they different?
9.21 What is a line graph (also known as a broken line graph) and how is it constructed?
9.22 What is a double line graph and how is it constructed?
9.23 What is a circle graph (also known as a pie graph, pie chart, pie diagram, area graph) and how is it constructed?
9.24 What is a line plot?
9.25 What is a stemplot (also known as a stem-and-leaf plot) and how is it constructed?
9.26 What is a back-to-back stem-and-leaf plot and how is it constructed?
9.27 What is a scatterplot and how is it constructed?
9.28 What is correlation?
9.29 What is a line of best fit and how can it be found?
Measures of Center
9.30 What are measures of central tendency?
9.31 What is the mean of a set of data (also known as the arithmetic mean or arithmetic average) and how is it determined?
9.32 What is the median of a set of data and how is it found?
9.33 What is the mode of a set of data?
Measures of Spread
9.34 What are measures of dispersion?
9.35 What is the range of a set of data and how is it calculated?
9.36 What is the variance of a set of data and how is it calculated?
9.37 What is the standard deviation of a set of data and how is it calculated?
9.38 What are percentiles?
9.39 What are quartiles and how are they determined?
9.40 What is the interquartile range?
9.41 What is a boxplot (also known as a box-and-whisker plot) and how is it constructed?
9.42 What is an outlier and how is it determined?
9.43 What is a cluster?
9.44 What is a gap?
9.45 What is a z-score (also standard score) and how is it calculated?
End of Chapter Exercises
Sample Certification Test Items
Bibliography
Answer KeyIndex
| 677.169 | 1 |
This geometry lesson from Illuminations uses the model of the orbits of Mars and Earth relative to the sun to illustrate parametric equations. As an interdisciplinary learning activity, the material may be used in...
Based at the University of Plymouth, the Centre for Innovation in Mathematics Teaching has developed many instructional materials designed to help both novice and experienced math teachers. This particular area of the...
This document from SpaceTEC National Aerospace Technical Education Center is one of three handbooks for people preparing for mechanic certification with airframe or powerplant ratings, or both. This particular volume...
This site uses the example of Native American building design to demonstrate the mathematical concepts of angles, coordinates and parabolas. Tutorials on arc geometry and arc coordinates are included. This...
The Center for Cultural Design presents this site on breakdancing as a way of teaching mathematical concepts. Specifically, rotation and sine function are demonstrated. The cultural and social background of breakdance...
| 677.169 | 1 |
Conic
Sections Movie - Animated moved
shows how slicing through a cone with a plane produces the various
conic sections. The movie goes a bit too fast to follow both the left
and right images and see their relationship. Try advancing it a frame
at a time.
Conics
- Some interesting interactive demonstrations of drawing conics and
their reflective properties.
Financial
Calculator -- The site will
perform a variety of mortgage-related
calculations including how much house you can afford and amortization
schedules. It will even show you how much can be saved by making
biweekly payments or extra payments toward principal.
KnotPlot Site
- Here you
will find a collection of knots and links, viewed from a (mostly)
mathematical perspective. Nearly all of the images here were created
with KnotPlot, a fairly elaborate program to visualize and manipulate
mathematical knots in three and four dimensions. You can download
KnotPlot and try it on your computer.
"Magic" Tricks
- With a
little logic you can figure out how it's done. It the meantime, it's
intriguing fun.
Math
Dictionary for Kids - Contains a
clickable alphabetical listing
of over 400 mathematical terms beginning with abacus and ending with
zero.
Math
Help -
links to a variety of online resources compiled by students at Chalmers
University of Technology in Sweden.
Math is
Power is the theme of the public service
advertising campaign of NACME, The National Action Council for
Minorities in Engineering, Inc. If no one has told you how math
classes can improve your future, call NACME at 1-800-97NACME. They
will tell you.
MathNerds
- A free service providing hints, direction, references, or guidance
(not necessarily answers) in many areas of mathematics. The MathNerds
team members are unpaid volunteers whose only compensation for their
efforts are the "Thank You" messages from our clients.
3DXplorMath
This is a Mac OS X program for creating all sorts of math graphs. This
program is very versatile (and a little overwhelming). It can graph 2D
(including polar, parametric, and implicitly defined funcions) and 3D.
Click on all the pull-down menus to see what your options are, or even
better if you have the time, read the manual.
| 677.169 | 1 |
Microsoft Math Product Guide
"Microsoft Math provides a space for nurturing student learning in
mathematics with dynamic visualizations. The program provides essential
ingredients for classroom environments designed to challenge all students
to engage in visual thinking."
— Margaret L. Neiss
Professor of Mathematics Education,
Oregon State University
Microsoft® Math is a set of mathematical tools that can help students get
their work done quickly and easily while promoting a better understanding
of mathematical concepts. The primary tool in Microsoft Math is a full-
featured scientific calculator with extensive graphing and equation-solving
capabilities. It is designed to work just like a handheld calculator, but offers
a wide range of additional tools that deepen students' knowledge of
complex mathematics.
Overview
Microsoft Math provides students and teachers with a wide range of tools, including the following:
• A 2-D and 3-D graphing calculator to graph complex equations
• A Step-by-step Equation Solver to walk students through math problems
• An Equation Library, which puts more than 100 common equations and formulas in a single
location
• A Triangle Solver that helps students explore the relationships between the parts of triangles
• A Unit Conversion Tool for fast, easy conversion of different measurements
• An Ink Handwriting Support feature for added flexibility in how students work
Microsoft Math features a host of math tools designed to help students learn mathematical
concepts. This collection of tools, tutorials and instructions helps students tackle math and
science problems in one central location.
Teachers say that students need more help with their homework. In addition, the majority of those
teachers believe the quality of work and overall performance are enhanced when students use
technology both at home and at school. And, as any child will admit, math is often a stumbling
block to student success.
The easy-to-use interface of Microsoft Math looks like a calculator — a familiar tool — but with a
difference: It moves the emphasis from solving mathematical equations to increasing
understanding of math and promoting lifelong skills.
Microsoft Math gives students a worksheet and a graphing space. Combined, these features
enable students to explore mathematical functions to better understand them. In addition, these
abilities provide an invaluable tool for teachers, who can use Microsoft Math to create visual
images of many mathematical ideas. As just a few examples, students can do any of the following
activities:
• Walk through the steps necessary to solve common algebra problems
• Dynamically manipulate graphs of functions and equations
• Visualize systems of inequalities to identify regions for solutions to problems
• Conduct explorations in three dimensions
• Enter multiple data sets and search for patterns from the visual graphics
Graphing Calculator
A major component of Microsoft Math, the graphing calculator is a groundbreaking complement to
the calculators already required by most schools. It is designed primarily to help students
visualize and solve difficult math and science problems, whether trigonometry, statistics, algebra,
or calculus. Support for calculus includes functions on limits, series, derivatives and integrals.
By graphing complex equations, students get not only a better way to solve their homework
problems, but also help in gaining a deeper understanding of the reasoning behind those
problems. This ability is enhanced through sophisticated graphing capabilities that allow students
to view, rotate and animate large 2-D and enhanced 3-D color graphs. An animated slider
enables them to make changes to the equation and see the effect on the graph.
In addition, reusing common numbers and expressions can save time when there are multiple
problems to solve. With the graphing calculator, it's simple to add and store variables.
Step-by-Step Equation Solver
The Step-by-step Equation Solver generator gives students the support they need by providing
them with complete walk-through solutions to many math problems in middle-school and high-
school pre-algebra, algebra I, algebra II, and trigonometry classes.
In addition to supporting students when they are learning on their own, this feature is also ideal
within a classroom setting because it allows a teacher to quickly display a particular solution
method applied to a specific math problem.
Equation Library
With more than 100 interactive common math equations and formulas in a single location,
students can find and interact with the right equations necessary to solve problems. If they want,
they can quickly graph these equations using the graphing calculator.
Triangle Solver
The Triangle Solver helps students explore triangles and the relationships between their parts. As
a student enters the values for sides and angles, the displayed triangle changes shape to reflect
those values. Once enough values are entered, the remaining sides and angles are completed
and the trigonometric rules used are called out.
Unit Conversion Tool
The Unit Conversion Tool makes it easy for students to quickly convert units of measure such as
length, area, volume, weight, temperature, pressure, energy, power, velocity and time.
Ink Handwriting Support
New support for Tablet and Ultra-Mobile PCs means that students can do their math homework
more naturally, by writing it out. Microsoft Math contains handwriting recognition software tailored
to math, giving it high recognition accuracy. As a result, students can enter mathematical
expressions as they would on paper.
System Requirements
Microsoft Math requires the following:
• A personal computer with a Pentium 600MHz or faster processor (1GHz or faster processor
recommended)
®
• Windows XP Service Pack 2 or later
• 256 MB of RAM (512 MB or more recommended)
• 450 MB of available hard disk space
• Microsoft .NET Framework 2.0 (requires between 200 MB and 450 MB of hard disk space)
• VGA-capable or better video card with a minimum 640x480 resolution (1024x768
recommended)
"When solving a quadratic equation, Microsoft Math doesn't just churn and
spit out one of the solutions. Instead, it shows you both solutions and how
to obtain them using square completion or the quadratic equation."
— Jonathan Briggs
Math Teacher, Eastside Preparatory School
Kirkland, Wash
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More About
This Textbook
Overview
Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox's Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel's theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.
Related Subjects
Meet the Author
DAVID A. COX, PhD, is Professor in the Department of Mathematics at Amherst College. He has published extensively in his areas of research interest, which include algebraic geometry, number theory, and the history of mathematics. Dr. Cox is consulting editor for Wiley's Pure and Applied Mathematics book series and the author of Primes of the Form x2 + ny2
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Advanced Mathematical Concepts - 06 edition
Summary: Advanced Mathematical Concepts, 2006 provides comprehensive coverage of all the topics covered in a full-year Pre-calculus course. Its unique unit organization readily allows for semester courses in Trigonometry, Discrete Mathematics, Analytic Geometry, and Algebra and Elementary Functions. Pacing and Chapter Charts for Semester Courses are conveniently located in the Teacher Wraparound Edition.
Advanced Mathematical Concepts lessons develop mathematics us...show moreing numerous examples, real-world applications, and an engaging narrative. Graphs, diagrams, and illustrations are used throughout to help students visualize concepts. Directions clearly indicate which problems may require the use of a graphing calculator.
New Features: " A full-color design, a wide range of exercise sets, relevant special features, and an emphasis on graphing and technology invite your students to experience the excitement of understanding and applying higher-level mathematics skills. " Graphing calculator instructions is provided in the Graphing Calculator Appendix. Each Graphing Calculator Exploration provides a unique problem-solving situation. " SAT/ACT Preparation is a feature of the chapter end matter. The Glencoe Web site offers additional practice: amc.glencoe.com " Applications immediately engage your students; interest. Concepts are reinforced through a variety of examples and exercise sets that encourage students to write, read, practice, think logically, and review. " Calculus concepts and skills are integrated throughout the course50 +$3.99 s/h
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Mathematicians seek deep truths about a purely formal world, one that may or may not have much to do with the physical world we inhabit. Through our readings, seminar discussions, and writing assignments, we'll explore that connection, the existential status of mathematical objects (What is mathematics? Do mathematical objects actually exist, and if so, where? Are mathematical systems discovered or created?), and surrounding issues as we learn more about modern mathematical practice.
This course coincides with the seminar portion of the Mathematical Systems program, so students in this course will share seminars with students in that program.
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Over the next few years, advanced level mathematics will undergo dramatic changes, as the Department of Education and Science introduces new syllabuses and methods of assessment. Because A-level mathematics has scarcely altered in a generation, many see the changes as long overdue. They will go some way towards making A level more compatible with GCSE mathematics, and will include an increase in the use of coursework for assessment, a greater emphasis on reading maths texts for comprehension, more use of problem solving and practical work, and a higher profile being given to the history of mathematics.
It is into this changing climate that Mathematics Review has been launched. When I received the advance publicity for it, my first reaction was one of amazement that no publisher had
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Textbook
Text Topics
Chapter 1 – Sections 1.1-1.4
Chapter 2 – Sections 2.1-2.5
Chapter 3 – Sections 3.1-3.4
Chapter 4 – Sections 4.1-4.5 (The coverage of Section 4.2 should
deal primarily with the
recursive definitions of number sequences such as the Fibonacci and Lucas
Numbers.)
Elementary proofs dealing with number theory seemed to go quite
well last year for everyone, I believe. Hopefully, we'll see the
same level of
success this time around.
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The user reviews definitions of important algebra terms. After viewing further explanations and some examples, users can interactively test their understanding of the definitions of important algebra... More: lessons, discussions, ratings, reviews,...
The 3-D animated video helps students understand the wordings in the following distance, rate, and time word problem: Two space jets named Dragon and Eagle start from Mars and fly in opposite dire... More: lessons, discussions, ratings, reviews,...
The user reads about the definition of an equation, the use of variables, and how to write an equation from a sentence. Examples are given as well as an online quiz to practice the skill of matching
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97800713901 of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing the author's acclaimed and patented fail-safe methodology for making mathematics easy to understand, Bob Miller's Basic Math and Pre-Algebra for the Clueless enhances students' facility in these techniques and in understanding the basics.
This valuable new addition to Bob Miller's Clueless series provides students with the reassuring help they need to master these fundamental techniques, gives them a solid understanding of how basic mathematics works, and prepares them to perform well in any further mathematics courses they take
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Getting Started with "Math in ONE"
Code use for Windows, Android versions
(AG) - Applies to Android graphing version.All (A) functions are included in (AG)
(AP) - Applies to Android programing Calculator version. All (AG) functions are included in (AP).
If no symbol is indicated, then instructions apply to both Windows and Android products.
(W)
There are two main resources to help you learn about "Math in ONE" which are found in the "Reference Manual" and the convenient descriptions built into the program. Two examples are presented below.
When using "Math in ONE", these descriptions appear with the right click of your mouse on an object (e.g. checkbox, button,...), then left click on the pop up button. Refer to the example on the left.
For all the pull down menus (e.g."Functions"), simply place your mouse over an item to review its description. Refer to the example on the right.
(AP) Help Options: For an explanation of the features underlying each button, press and hold the button of interest for one second, a new window with a description of the button function will appears.
(AP) Sliding finger in arrow direction will display new functions assign to the buttons.
(A) To get to 'Help Index or Setting' window, from main view press 'option menu (om or Op Men)' button then select 'help' or 'Setting'.
Thank you for your interest in "Math in ONE"! Please refer to this reference manual for further guidelines. We appreciate all of your feedback regarding this site and the "Math in ONE" program. We will make all the effort to satisfy you. We hope you enjoy working with this product!
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J.P. McCarthy: Math Page Marks
Pending…
Week 6. Then we started Laplace Methods.
Week 7
In Monday's tutorial we will look at doing some partial fractions. I am going to rob and adapt these exercises, this and this question are looking for but not finding intuitive ways to think about the Laplace transform 6
We finished our of vectors by looking at the application to work and moments. We also did a review of MATH6015 differentiation.
Week 7 understanding the dot and cross productLATE EDIT: I just realised that I included no questions like Q.1 on P.32 of the notes… they are also examinable (matrix arithmetic). Also Q. 7 should read "Verify your answer for using Cramer's Rule"
The test will be from 7.05-8 pm in Week 8 (Wednesday 19 March). I won't give a sample but instead look here for a selection of test & exam questions. You can find a summary of Chapter 1 methods here.
Also I explained that some questions involving finding the inverse of 3×3 matrices using the Gauss-Jordan Algorithm can end up very messy in terms of the numbers. Questions like P. 44 Q.1-5 are fine as are P. 52 Q. 2, 3 (iv)-(vi) 6
We solved a number of linear systems using the inverse matrix method. Note however that this cannot work if the solution is not unique… we used a property of matrices called the determinant to decide in advance if a certain class of linear system, homogenous systems, had a unique solution or not. If the matrix (of coefficient) is invertible then the solution has to be unique and we saw that the matrix (of coefficients) is invertible if and only if the determinant is non-zero. Finally we will looked at Cramer's Rule: a method for solving for only one of the variables of a linear system. We then began talking about statistics and got as far as discussing the difference between the mean, the median and the mode.
Week 7
We will go as far into the chapter on statistics as possible. In Maple I will allow you to revise for the test with the aid of Maple. I will write a worksheet which includes the sample questions. Remember Maple runs from 6-7.10 and 8.50-10. The theory class runs from 7.15-8.45the sample questions
p.52 Q. 3 (iv)-(vi)
P.62 Q. 1 and 4
P. 68 Q. 1-4 the determinantHomework
Will be discussed in class on Monday.
Week 9
Week 10
Exercises
For the Week 10 tutorial you should look at Q.44, 45, 52, 53, 56-60 solving a complex numbers problem geometrically 5… the answer is we have to do partial pivoting. We also began the section on the powerful theory of the Laplace Transform.
Week 6
In Monday's tutorial we should be looking at our sample paper — you should print off a copy for yourself. Otherwise look at the sample in the notes but replace the partial pivoting question by a Jacobi/Gauss-Siedel question answer which says that partial pivoting can actually be really bad in theory (give inaccurate solutions), but almost always works well 5
We continued working with the dot product and then introduced the cross product.
Week 6 generalising the vector product to more than three dimensionsDue to the lost night in the storm, I am now putting the test in Week 8. Ye will get a sample test (format only) in week 6. It will be on Chapter 1. 5
We found some matrix inverses using the Gauss-Jordan Algorithm and saw how matrix inverses are useful in solving matrix equations. In particular, we saw that we can rewrite a linear system as a matrix equation. In Maple, we saw how Maple handles linear systems with no and infinite solutions. We also used the Maple Tutor to help us do some matrix manipulations.
Week 6
We will solve a number of linear systems using this inverse matrix method. Note however that this cannot work if the solution is not unique… we will use a property of matrices called the determinant to decide in advance if a certain class of linear system, homogenous systems, have a unique solution or not. If the matrix (of coefficient) is invertible then the solution has to be unique and we will see that the matrix (of coefficients) is invertible if and only if the determinant is non-zero. Finally we will look at Cramer's Rule: a method for solving for only one of the variables of a linear systemp.44 exercises
p.46 exercises
p. 52 Q. 1, 3(i),(ii) & 4 matrix inversesMCQ Results
As discussed previously, the MCQ results will come out the day you hand in the homework: 11 April 2014. I will send the homework next week.
Week 8
Week 9
Exercises
I have emailed ye a copy of the exercises. For the Week 9 tutorial you should look at Q.46 and Q. 47 the iterates of the tangent function 4
In the tutorials we looked at Gaussian Elimination. Also if you download Maple (see below), there is a Maple Tutor that is easy to use and will help you. Open up Maple and go to Tools -> Tutors ->Linear Algebra -> Gaussian Elimination which asks what are the applications of linear systems Learning
| 677.169 | 1 |
Engineers require a solid knowledge of the relationship between engineering applications and underlying mathematical theory. However, most books do not present sufficient theory, or they do not fully explain its importance and relevance in understanding those applications. Advanced Engineering Mathematics with Modeling Applications employs a balanced approach to address this informational void, providing a solid comprehension of mathematical theory that will enhance understanding of applications – and vice versa. With a focus on modeling, this book illustrates why mathematical methods work, when they apply, and what their limitations are. Designed specifically for use in graduate-level courses, this book: Emphasizes mathematical modeling, dimensional analysis, scaling, and their application to macroscale and nanoscale problems Explores eigenvalue problems for discrete and continuous systems and many applications Develops and applies approximate methods, such as Rayleigh-Ritz and finite element methods Presents applications that use contemporary research in areas such as nanotechnology Apply the Same Theory to Vastly Different Physical ProblemsPresenting mathematical theory at an understandable level, this text explores topics from real and functional analysis, such as vector spaces, inner products, norms, and linear operators, to formulate mathematical models of engineering problems for both discrete and continuous systems. The author presents theorems and proofs, but without the full detail found in mathematical books, so that development of the theory does not obscure its application to engineering problems. He applies principles and theorems of linear algebra to derive solutions, including proofs of theorems when they are instructive. Tying mathematical theory to applications, this book provides engineering students with a strong foundation in mathematical terminology and methods.
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Starting at $30Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available yet coversallrelevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.
Table of Contents
Preface
ix
Preliminaries
1
(54)
Real Numbers, Estimation, and Logic
1
(7)
Inequalities and Absolute Values
8
(8)
The Rectangular Coordinate System
16
(8)
Graphs of Equations
24
(5)
Functions and Their Graphs
29
(6)
Operations on Functions
35
(6)
Trigonometric Functions
41
(10)
Chapter Review
51
(4)
Review and Preview Problems
54
(1)
Limits
55
(38)
Introduction to Limits
55
(6)
Rigorous Study of Limits
61
(7)
Limit Theorems
68
(5)
Limits Involving Trigonometric Functions
73
(4)
Limits at Infinity; Infinite Limits
77
(5)
Continuity of Functions
82
(8)
Chapter Review
90
(3)
Review and Preview Problems
92
(1)
The Derivative
93
(58)
Two Problems with One Theme
93
(7)
The Derivative
100
(7)
Rules for Finding Derivatives
107
(7)
Derivatives of Trigonometric Functions
114
(4)
The Chain Rule
118
(7)
Higher-Order Derivatives
125
(5)
Implicit Differentiation
130
(5)
Related Rates
135
(7)
Differentials and Approximations
142
(5)
Chapter Review
147
(4)
Review and Preview Problems
150
(1)
Applications of the Derivative
151
(64)
Maxima and Minima
151
(4)
Monotonicity and Concavity
155
(7)
Local Extrema and Extrema on Open Intervals
162
(5)
Practical Problems
167
(11)
Graphing Functions Using Calculus
178
(7)
The Mean Value Theorem for Derivatives
185
(5)
Solving Equations Numerically
190
(7)
Antiderivatives
197
(6)
Introduction to Differential Equations
203
(6)
Chapter Review
209
(6)
Review and Preview Problems
214
(1)
The Definite Integral
215
(60)
Introduction to Area
215
(9)
The Definite Integral
224
(8)
The First Fundamental Theorem of Calculus
232
(11)
The Second Fundamental Theorem of Calculus and the Method of Substitution
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This textbook is used by the Department of Mathematics at College of the Redwoods in Eureka, California for instructional purposes in their Math 120 course, Intermediate Algebra. This text was... More > written by the department specifically for use in Math 120.< Less
This is a complete curriculum for the second semester of algebra. It is designed to be used with the first semester book as well as the student workbook and teacher workbook. All these books are... More > available is a complete curriculum for the second semester of pre algebra. It is designed to be used with the first semester book as well as the student workbook with keys. All these books are available... More > collection of cards provides students with the essential information about key topics in high school mathematics and algebra. Each card provides a visual representation of the concept to assist... More > in remembering the formulas, definitions, and procedures needed to succeed in math class. From square roots to measurements and graphing linear equations to test-taking strategies, these cards use visual cues so students can relate the images to the concepts.
To better prepare your student for math class, visit to see other research-based books to organize, motivate, and prepare your students to be successful on math assessments, homework, and problem solving. For students transitioning to high school, we offer a self-guided book to ease the transition and improve grades.< Less
Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of... More > Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals, which is the content of Discrete Structures I at UMass Lowell.
Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit Less
Open source MTH 164 textbook for the Virginia Community College System, remixed from "Precalculus: An Investigation of Functions," by David Lippman and Melonie Rasmussen and "College... More > Algebra," by Carl Stitz and Jeff Zeager.< Less
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Computational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This textbook provides students with a versatile and accessible introduction to the subject. It assumes only a background in high school algebra, enables instructors to follow tailored pathways through the material, and is the only textbook of its kind designed specifically for an introductory course in the computational science and engineering curriculum. While the text itself is generic, an accompanying website offers tutorials and files in a variety of software packages.
This fully updated and expanded edition features two new chapters on agent-based simulations and modeling with matrices, ten new project modules, and an additional module on diffusion. Besides increased treatment of high-performance computing and its applications, the book also includes additional quick review questions with answers, exercises, and individual and team projects.
The only introductory textbook of its kind--now fully updated and expanded
Features two new chapters on agent-based simulations and modeling with matrices
An online instructor's manual with exercise answers, selected project solutions, and a test bank and solutions (available only to professors)
An online illustration package is available to professors
Angela B. Shiflet is the Larry Hearn McCalla Professor of Mathematics and Computer Science and director of computational science at Wofford College. George W. Shiflet is the Larry Hearn McCalla Professor of Biology at Wofford College.
Review:
Praise for the previous edition: "The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application. . . . [This book] has been carefully and thoughtfully written with students clearly in mind."--William J. Satzer, MAA Reviews
Praise for the previous edition: "Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding."--Wouter van Joolingen, Physics Today
Praise for the previous edition: "A masterpiece. I know of nothing comparable. I give it five stars."--James M. Cargal, UMAP Journal
Praise for the previous edition: "This is an important book with a wonderful collection of examples, models, and references."--Robert M. Panoff, Shodor Education Foundation
Praise for the previous edition: "This is a very good introduction to the field of computational science."--Peter Turner, Clarkson University
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Chapter Summary
Image Attributions
Description
In this chapter, students will plot points in a polar coordinate system, graph and recognize limaçons and cardiods, and work with real-world applications involving polar coordinates and polar equations.
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Find a Hempstead, NY MathScientific calculators and/or graphing calculators are integrated throughout the course. Elementary math includes number theory, which is the study of whole numbers and relations between them. This unit includes in-depth instruction on factors, multiples, primes, composites, divisibility tests, and exponents
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Centennial, CO Geometry/homework is essential. Hope to hear from you soon. JohnI completed math in college through Differential EquationsThis is at least partly true. The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems!
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97815595300Key To Algebra Book 1: Operations On Integers
Too many students end their study of mathematics before ever taking an algebra course. Others attempt to study algebra, but are unprepared and cannot keep up. Key to Algebra was developed with the belief that anyone can learn basic algebra if the subject is presented in a friendly, non-threatening manner and someone is available to help when needed. Some teachers find that their students benefit by working through these books before enrolling in a regular algebra course--thus greatly enhancing their chances of success. Others use Key to Algebra as the basic text for an individualized algebra course, while still others use it as a supplement to their regular hardbound text. Allow students to work at their own pace. The Key to Algebra books are informal and self-directing. Book 1 covers Operations on Integers. Format: PaperbackPublisher: Key Curriculum Press
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Mathematics for Teachers: Interactive Approach for Grade K-8
9780495561668
ISBN:
0495561665
Edition: 4 Pub Date: 2009 Publisher: Brooks/Cole
Summary: Sonnabend, Thomas is the author of Mathematics for Teachers: Interactive Approach for Grade K-8, published 2009 under ISBN 9780495561668 and 0495561665. Five hundred ninety two Mathematics for Teachers: Interactive Approach for Grade K-8 textbooks are available for sale on ValoreBooks.com, one hundred twenty four used from the cheapest price of $70.75, or buy new starting at $189
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$105Ratti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding.
With a new addition to the series, Precalculus Essentials, this text offers the best of both worlds: fast-paced, rigorous topics and a friendly, "teacherly" tone. This text is developed with a focus on key topics for calculus preparation.
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Intermediate Algebra - 8th edition
ISBN13:978-0495117940 ISBN10: 0495117943 This edition has also been released as: ISBN13: 978-0495118022 ISBN10: 0495118028
Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, INTERMEDIATE ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anxiety. Their proven five-step problem-solving strategy helps break ea...show morech problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the jobSellBackYourBook Aurora, IL
0495117943
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More About
This Textbook
Overview
When Julie Miller began writing her successful developmental math series, one of her primary goals was to bridge the gap between preparatory courses and college algebra. For thousands of students, the Miller/O'Neill/Hyde (or M/O/H) series has provided a solid foundation in developmental mathematics. With the Miller College Algebra series, Julie has carried forward her clear, concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area.
The main objectives of the college algebra series are three-fold:
• Provide students with a clear and logical presentation of the basic concepts that will prepare them for continued study in mathematics.
• Help students develop logical thinking and problem-solving skills that will benefit them in all aspects of life.
• Motivate students by demonstrating the significance of mathematics in their lives through practical applications.
Product Details
Meet the Author
Julie Miller has been on the faculty in the School of Mathematics at Daytona State College for 20 years, where she has taught developmental and upper-level courses. Prior to her work at DSC, she worked as a Software Engineer for General Electric in the area of Flight and Radar simulation. Julie earned a Bachelor of Science in Applied Mathematics from Union College in Schenectady, New York, and a Master of Science in Mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for College Algebra, Trigonometry, and Precalculus, as well as several short works of fiction and nonfiction for
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Precalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the ...Show synopsisPrecalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today's instructors and students. New co-author Callie Daniels has experience in all classroom types including traditional, hybrid and online courses, which has driven the new MyMathLab features. For example, MyNotes provide structure for student note-taking, and Interactive Chapter Summaries allow students to quiz themselves in interactive examples on key vocabulary, symbols and concepts. Daniels' experience, coupled with the long-time successful approach of the Lial series, has helped to more tightly integrate the text with online learning than ever before ***NOTICE! ! ! This book is a Brand New Annotated...New. ***NOTICE! ! ! This book is a Brand New Annotated Instructor Edition (same textbook content as the student edition, may have extra answers or notes).
Description:Fine. 0321783808 ANNOTATED INSTRUCTOR'S EDITION contains the...Fine. 0321783808 ANNOTATED INSTRUCTOR'S EDITION contains the COMPLETE STUDENT TEXT with some instructor comments or answers
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Scientific Calculator Precision 63 for scientists, engineers, teachers, and students. Calculates mathematical formulas of any length and complexity. Calculation history can be stored into text file or printed. There are ten...
Free English4Today studyGuide: Number 1 in the series with more than 2000 downloads per week! Guide to English language verbs and tenses with optional online support materials and exercises. Part of a series...
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of...
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
Undergraduate computer lab designed to teach quantitative thinking in the context of neurobiology. Ideally, this lab would...
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Undergraduate computer lab designed to teach quantitative thinking in the context of neurobiology. Ideally, this lab would be taught as a supplement to a concurrent lecture course. Students are assumed to have completed one year of undergraduate calculus.Topics include Nernst equation, GHK equation, passive electrical spread, voltage clamp, action potentials, synaptic currents, reciprocal inhibition, lateral inhibition, and the swimming circuit of Tritonia. Math skills used include graphing, logarithms, differential equations, and discrete-time models.The modules are designed to be self-contained lab exercises. They are Mathcad documents that the students complete for credit. Thus, students must have access to Mathcad (version 13 or higher). PDF versions of the modules are also provided for demonstration purposes.
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This quick-reference dictionary for math students, teachers, engineers, and statisticians defines more than 700 terms related to algebra, geometry, analytic geometry, trigonometry, probability, statistics, logic, and calculus. It also lists and defines mathematical symbols, includes a brief table of integrals, and describes how to derive key theorems. Filled with illustrative diagrams and equations.
Dictionary of Mathematics Terms, 3rd Edition
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It helps you improve your skills in Edexcel GCSE mathematics and achieve your highest potential. This book targets the key areas of mathematics as identified by Edexcel examination data and senior exa...
Title: EDEXCEL GCSE SCIENCE EXTENSION UNIT STUD. By continuing with this checkout and ordering from Speedy Hen, you are accepting our current Terms and Conditions. Details of which can be found by cli...
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Brand New Edexcel GCSE Modular Mathematics Text Book. This perfect for students stuying GCSE Mathematics either with Edexcel or another exam board. It has lots of exercises, examples and how to do thi...
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Other GCSE books for sale. Very good item and been kept well. Does have signs of wear and tear on cover and corners and had writing of names on first page in ink and i have had a flick through and the...
Written specifically for Edexcel's InternationalGCSE Physics qualification in a clear and engaging style that students find easy to understand, this book includes a wide range of activities and exerci...
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Sight Enhancement Systems
Manufacturers of large display scientific calculators with speech output, and of large display calculators that allow people with low vision to perform scientific, statistical and trigonometric calculations. Download brochures and manuals for the Sci-Plus
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The Silicon Mirror and Kaleidoscope - Elliot Leonard
The Silicon Mirror is an interactive tool for creating tessellations. It
operates on the same principles as a kaleidoscope. The Silicon Kaleidoscope is a screen saver that uses the Silicon Mirror to create kaleidoscopic images that flow in real time.
...more>>
The Siluroid Curve - Dario de Judicibus
Formulas, graphs, compass-and-straightedge constructions, derivatives, and more about this bi-quadratic, trilobate curve. Among the torpedo- or fish-shaped curve's curious properties: connecting its intersection with the generatrix or goniometric circle
...more>>
SIMATH - Marc Conrad
A computer algebra system, especially for number theory. Try out the online version of the SIMATH calculator simcalc; a more detailed overview is available as a .dvi file or you can download the TeX-Source of this file.
...more>>
SIMMS IM LEVEL I - Research Project Help - T. DeBuff
High School freshman-level integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that will
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Simple Math Problems - Ki Woo Song
Selected math problems from a variety of sources. Solutions may either be requested via e-mail or looked up from the source (references to articles are provided.) Topics include algebraic expressions; probability; physics, geometry, proofs, and brain
...more>>
Simplified Solutions for Math
Curricula (lesson plans, pratice work sheets and tests) for Algebra, CAHSEE, and General Math, aligned to the California Department of Education's Mathematics Framework for California Public Schools.
...more>>
SingaporeMath.com Inc.
Formerly "Family Things," this family business located in Oregon, USA provides information, sample pages, and ordering information for the Singapore mathematics and science curricula, with sample placement tests for the New Elementary Math Series, sample
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singingbanana.com - James Grime
YouTube videos, "lazy microblog," and social networking hub of Enigma Project Officer James Grime, who "hopes to explain to kids and general audiences why he love his maths so much, to challenge some of the public's misconceptions, and to explain why
...more>>
SINUS transfer - University of Bayreuth
Spurred by the outcome of the Trends in International Mathematics and Science Study (TIMSS), Germany launched a nation-wide "model programme for increasing efficiency in mathematics and science education." Between 1998 and 2007, more than 1800 of the
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Sir Roger Penrose - World of Escher
Recreational math is the passion of Sir Roger Penrose, who was recently knighted for his outstanding contributions to mathematics. Penrose is a professor of mathematics at the University of Oxford in England, where he pursues an active interest in recreational
...more>>
A Site For Cyber Eyes - BZLeonard
Fractals, graphics, photos and altered photos, 3D graphics, links, Sherman's Humor Column, and Ginger's Diary (A teenager describes being bombed by the Japanese on December 7, 1941).
...more>>
Sites with Problems Administered by Others - Math Forum
Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, color-coded for the level(s) of the problems
...more>>
SketchMad - Nathalie Sinclair
An archived resource, not currently updated: A resource center devoted to using The Geometer's Sketchpad in the classroom. Includes tips, strategies, lesson plans, and sketches for beginning and intermediate Sketchpad teachers, stories from the classroom
...more>>
Skydome Unit Plan - Ruth Carver, Margaret Sinclair
A unit suitable for grades 7-11 with the objectives: to review many different mathematical skills; to work on a unit that connects with the "real world"; to improve reading for information skills. Questions include: What is the lowest price for a seat
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Skymath National Weather Report Module
An overview of an instruction unit in which students produce a national weather report and a report on their understanding of various weather phenomena. The unit ties together number sense, symbols, and graphics; emphasizes sorting and counting and making
...more>>
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Helping Children Learn Mathematics
9780470403068
ISBN:
0470403063
Edition: 9 Pub Date: 2008 Publisher: Wiley, John & Sons, Incorporated
Summary: Reys, Robert E. is the author of Helping Children Learn Mathematics, published 2008 under ISBN 9780470403068 and 0470403063. Three hundred eight Helping Children Learn Mathematics textbooks are available for sale on ValoreBooks.com, one hundred sixty seven used from the cheapest price of $0.46 guarantee for ancillary materials(Such as CDs, Online access code).Ships today or the next business day. Cover and binding maybe well-worn. Text may contain ex [more]
No guarantee for ancillary materials(Such as CDs, Online access code).100% BRAND NEW ORIGINAL US PAPERBACK STUDENT 9th Edition / with sealed WEB REGISTRATION CARD / ISBN-10: 0470403063 / Mint condition / Never been read / ships out in one business day with free tracking.[less]
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NEW-LIFE OF FRED BEGINNING ALGEBRA and ZILLIONS OF PRACTICE PROBLEMS FOR BEGINNING ALGEBRA. Need a lot of practice or stuck on a particular kind of problem? This book has been requested by many reader...
And even some algebra and economics. Fred begins his summer vacation. Why Fred couldn't be a movie star. How to get rid of snakes in sugar cane fields. Learn . The difference between freedom and liber...
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This is an outstanding two dimensional plotting program that produces smooth, textbook quality output. Several features make...
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This is an outstanding two dimensional plotting program that produces smooth, textbook quality output. Several features make it easy to generate pictures including, for example, tangent lines, Riemann rectangles, trapezoid approximations. The original version is French and there is an English version. The public domain version allows the use of all features except printing/exporting graphics.
This applet is used to calculate the solution set to a linear system of equations. Type in the number of equations (this...
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This applet is used to calculate the solution set to a linear system of equations. Type in the number of equations (this should be thesame as the number of unknowns) and then press "Enter Equations.״A window should pop up with blank text fields where you may enter the coefficients for each variable in the system of equations.The column on the right is for adding the solution values for each of the equations. This table should contain the same values as thecoefficient matrix. After you have filled out each of the text fields, press "done.״Finally, a new window will pop up providing that all of the fields had values entered. This window will contain the values of eachof the unkonwns that the computer solved for.
QuickMath is an automated service for answering common math problems over the internet. ...
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QuickMath is an automated service for answering common math problems over the internet. Think of it as an online calculator that solves equations and does all sorts of algebra and calculus problems - instantly and automatically! When you submit a question to QuickMath, it is processed by Mathematica, the largest and most powerful computer algebra package available today. The answer is then sent back to you and displayed right there on your browser, usually within a couple of seconds. Best of all, QuickMath is 100% free!
Here is Zona Land's graphics calculator, EZ Graph. With it you should be able to graph almost any polynomial, rational,...
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Here is Zona Land's graphics calculator, EZ Graph. With it you should be able to graph almost any polynomial, rational, exponential, logarithmic, or trigonometric function. It will allow you to enter variables into your function definition so that you can see the effect of changing coefficients easily.
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Formules mathématiques is the French version of the Math Formulary App that covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic better.
SD-Card Installation is supported. Bug reports related to the content and the app itself are more than welcome. Proposals for new features would be great.
This is the free version of the Formules mathématiques Pro app that you can getA convenient, and very simple list of mathematics, with more'than 800 of the most important formulas of algebra, trigonometry, analytic geometry, limits, derivatives, integrals, matrices, vectors ... and now the graphs of the main functions.
The best synthesis in stores! Constantly updated. (App replaces the "Formula 2012" with 50000 downloads.)
******************** In the market for € 0.50 formulePRO version with the addition of physics, chemistry, exercises and MUCH more!
Available in many languages, this is a perfect app on Google Play that provides all basic many tools to calculate the geometric shapes or find the roots of equations. Users can also share any formulas with friends by many ways: email, message, or facebook. Not only for smartphones, this app is also suitable for tablets with compatible interfaces.
New features of the app: - Multiple languages support: English, French, Vietnamese, Chinese, Japanese, SpanishBest math tool for school and college! If you are a student, it will helps you to learn geometry!
Note: Trigonometric functions are used for computing unknown lengths and angles in triangles (in navigation, engineering and physics). The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators.
Math Formula Reference is a simple application that helps you access a vast collection of math formulas, with thousands of mathematical equations. This app can help you as a quick reference (cheat sheet) so you can access math formulas whenever and wherever you want. This math formulary app is one of the most comprehensive of its kind.
Your children will learn essentials mathematical principles and practice spanish while having fun playing with their new friends Dikie and Dukie!
*** EDUCATIONAL GAME COLLECTION FOR KIDS FROM 3 TO 10 YEARS OLD ***
You need internet conection for play with this free version!
Through these 18 educational games your children will explore the basics concepts of calculus. While playing the child will learn to identify numbers, sum, subtract, multiply and divide. Likewise the child will also develop his creativity and memory, helping him intuitively to become familiar with the device. All of this while having fun playing in spanish!
The cute characters Dikie and Dukie will be guiding and advising the child with full voices in Spanish.
CONTENTS The game is structured in 3 worlds of different difficulty: 1. The Garden of the Numbers: 7 games to become familiar with numbers and their characteristics. 2. The Kitchen of the Addition and Subtraction: 6 games to learn basic arithmetic operations like addition and subtraction. 3. The Room of Multiplication: 5 games to develop more advanced arithmetic operations such as multiplications and divisions.
FEATURES - 18 EDUCATIONAL GAMES IN ONE! - Complete Locution in Spanish! - Fun graphics and animations. - Interface adapted for children! - Games with random outcomes, games change every time you play!
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Monday, May 25, 2009
Far be it from the bunny to be serious, but have you folk realized that algebra and calculus are in pretty much the same position that arithmetic was in 1970 when HP's calculator killed it. Why sweat integrating functions when Mathematica/MathLab/Maple can do it for you? To the same extent, you have to know the rules in order to spot problems (ill stated inputs, etc), but you don't necessarily have to master the minutia.
.
I've long forgotten the calculus I learned in high school, but if I had learned it at the same time that I had easy and continuing access to useful software, I might still be able to do something with it.
I was awful at calculus when it was memorizing rules, but as soon as it was applied and used to answer a question, or when I could play with MathLab, it made sense and I learned it. I am all for being able to understand and use concepts, and being able to use a computer for calculation. It still requires you to figure out if the output was reasonable or the result of an error on your part.
Hmm. My teaching experience is not favorable to the calculators. When they first came out, I figured that no big deal whether one arrived at 2+2 = 4 by way of device or pencil. One (echoing Anne) still had to know what to be adding, why you were adding, rather than some other operation, and to consider whether the output was reasonable.
Instead, what I saw was a transition to GIGO meaning 'garbage in, gospel out'. Once an answer came up on the screen, it must be correct. Significant digits? However many the calculator carries. Sanity checking? Nonsense, if the calculator says 2+2 = 1, that must be the answer. (Hitting the / instead of the +? Nahh, can't happen. Besides, the test has too many questions to check your work. After all, you can work so much faster with a calculator.)
The outcome seems to be that those who can get good answers by calculator are exactly and only those who could get them by hand as well. But the fraction who can't get them by hand is staggering.
I'm currently studying maths and physics (first year Uni). I'm enjoying it a lot. I don't see the calculator affecting the work I do - I use it all the time in physics, but it's bleedingly obvious when the answer is wrong due to input error. In maths, I don't use it much. Text book writers seem to have this habit of making answers come out in rational fractions :)
"."
Heaven forbid that anyone that ever takes physics should ever have to solve a real problem in the real world without a computer at hand.
Frankly, I find that when the shit hits the fan, computers are the first thing to stop working. Then some basic math skills can help you pump the water out and get the power back on. Nobody has good data at that point, so the calcs do not have to be too precise, and understanding the math lets you do "quick and dirty" calcs. The guy with math skills says, "Send me an 8 inch pump." The guy without math skills says "send me the biggest pump you got." Is that the 4 inch pump that is already on the helo, or the 16 incher back at HQ?
So we will compensate for lack of math by just passing a law that says, "Mother Nature is not allowed to do anything that will impair computer functions or telecommunications in the vicinity of critical infrastructure or large populations." While we are at it lets go ahead and outlaw hurricanes and global warming.
-A good collection of electromechanical desk calculators, like the Marchants or Fridens used (en masse) to help design the first A-bombs. Ah, back in the good old days, when a "computer" was the person who operated the calculator ...
Still have my slide rule, and my grandfather's :-)Hmm. My teaching experience is not favorable to the slide rule. When they first came out, I figured that it was no big deal whether one arrived at 2+2 is about 4 by way of device or pencil. One (echoing Anne) still had to know what to be adding, why you were adding, which scale on the rule to use, and to consider whether the output was reasonable.
Instead, what I saw was a transition to GIGO meaning 'garbage in, gospel out'. Once an answer came up on the slide rule, it must be correct... ----- (and you should see what the old fart mathematicians said about the invention of pencil and paper!)
Mechanical assistance for doing arithmetic or calculus is a Good Thing. Engineers or scientists who can't reliably do arithmetic or calculus without mechanical assistance are No Bloody Good. Schools which grant degrees to such people, purporting to indicate that they have a grounding in useful mathematical skills, are also No Bloody Good.
As an employer, I can and do insist on basic mental mathematical skills. If you can't reliably multiply two-digit numbers in your head, or differentiate cos cos on paper, or tell me instantly - within 20%, say - how many microseconds a computation takes if we do 17 thousand of them in 2.5 seconds, don't bother applying.
I'd like to add mental extraction of square roots, but it's a fairly obscure and nowadays little-used skill, so only true geeks bother to learn it.
A few examples from other areas, not all exactly the same issue, but related:
1) History. Merely knowing (historical, for example) facts might once have been good enough, as it implied you'd spent enough time chasing them down in libraries for much to have soaked in.
Now: OK, Google. How do you find things? How do you assess conflicting interpretations? What sources are likely to be more accurate?
Old skill:find the data and sort out what's important. New skill: even more crucial to be able to sort out what's important.
2) Art. A decade ago, I attended a talk for supporters of a local art museum. John Lasseter (Pixar; event was at SGI, so we could get him) spoke. During questions, someone asked him "We have a nephew dying to get into this area. Which computer tools should he know?"
Lasseter: (Sigh): doesn't matter much, we have a lot of our own internal tools, but tell him to be able to see, draw, and tell a story. Computers can take care of the mechanics, but if he can't do those other things, he'll have a tough time working on the creative side.
Old animation skill: good drawing, day-in, day-out. New skill: use the tools, but apply creativity other ways.
Needless to say, Lasseter's worldview has something to do with Pixar's track record.
3) Spreadsheets. Everyone is now a programmer. I see no end of business plans where someone generates growth forecasts just by plugging in a growth percentage. VCs are unimpressed.
4) Programming. A decade ago, they asked me to give a talk for a computer class at Penn State, then answer questions from students about "programming in the real world."
A student asked: "We've studied C, C++, Java, etc. In the real world, which language is most important in business?"
me: "you're not going to like the answer... English." *(student surprised) "Everyone programs at much higher levels than they used to, and that's great, but if you cannot talk to people, figure out requirements, express your ideas, present them, no matter how good a coder you are, you will not be very effective."
So long as students can understand the how and the why of the basic rules of calculus, including limits, then how they actually compute the integrals is not terribly important - any more.
On the other hand, at university level I would expect serious mathematics or physics students to be comfortable at manipulating expressions involving integrals and derivatives. Otherwise they aren't going to have much hope at proving things or developing new ideas (that rely upon calculus). If they use a computer algebra package to assist with this and to reduce the human error-rate, then good on them. Still, some practice with pencil and paper helps burn in the rules; having a well-developed gut knowledge of these things helps motivate the more abstract topics that follow
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Builds on the author's tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' ...Show synopsisBuilds on the author's tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' proficiency and conceptual understanding of algebra. This text continues coverage and integration of geometry in examples and exercises
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More About
This Textbook
Overview
This is the second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws (the Noether theorem), the quark model, and gauge theory in elementary particle physics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus
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Descriptions and Ratings (1)
Date
Contributor
Description
Rating
3 Sep 2011
MathWorks Classroom Resources Team
Recorded webinar by Loren Shure, MathWorks.
This webinar discusses the use of MATLAB in curriculum and shows demonstrations from a real course on mathematical modeling that includes math and visualization as common denominators for MATLAB users. Features demonstrated include:
• cell execution mode
• using MATLAB as a presentation tool with HTML links
• publishing to HTML
• introduction to programming with MATLAB
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Mathematica is widely used in many areas of education. These applications can be extended to web-based education tools with webMathematica. The Integrator, is a Research-developed web site that solves integration problems. Another use of webMathematica in education is Calc101, which mixes free and pay-per-use calculators that lead precollege and college students through integration and differentiation problems, as seen here.
1.4.3 Publishing
Many publishers are developing web-based supplements to textbooks, manuals, and journals. webMathematica provides a suitable technology to support these efforts in technical subjects. The Mathematical Explorer, an interactive text from Wolfram Research, covers a wide range of topics from Escher patterns and square wheels to Fermat's Last Theorem and the Riemann Hypothesis. A web-based supplement to The Mathematical Explorer, built with webMathematica, is available at as shown in the following.
1.4.4 Research
Researchers all over the world use Mathematica to investigate their fields of interest and develop techniques and algorithms for solving problems. All the Mathematica work they develop can now be delivered with live interactive web sites, vastly increasing the number of people who can use and learn from their results. A typical web site that plots surfaces of constant curvature is
1.4.5 Hobbyist
webMathematica allows individual users to showcase their personal interests with web-based interactive calculations and visualizations. AnalyticCycling.com, is a recreational web site that takes advantage of the webMathematica engine. Designed for technically oriented cyclists, AnalyticCycling.com offers web-based calculators that take a no-compromise, textbook approach to computing cycling performance.
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... read more
Undergraduate Topology by Robert H. Kasriel This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 edition.
Combinatorial Enumeration by Ian P. Goulden, David M. Jackson Graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems, from elementary to research level, for discrete structures and their substructures. Full solutions to 350 exercises.
Introduction to Topology: Third Edition by Bert Mendelson Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Product Description:
well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index
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MA 208 Discrete Mathematics Maldonado, Aldo Rene My philosophy is based on the constructivist view of mathematics learning. Students construct their own schema. Instructor provides guidance like lectures, HW assignment and tutoring but learning task is placed entirely on student's shoulders. Full use of technology is one of the ways instructor guides students
Classroom Rules of Conduct: Cell phones and pagers must be turned off to prevent unnecessary disruptions during the class. Disruptive behavior, racist, or sexist speech out of context will not be tolerated
Class Activities
Assignments
Week 1
Introduction to Combinatorial Problems and Techniques, Introduction to Logic and Proofs
1.1,1.2, 1.4 and Appendix A3
Week 2
Sets, Relations and Functions
2.1, 2.2, 2.3
Week 3
Graphs
3.1-3.5 Appendix B
Week 4
Trees
4.1,4.2,4.4
Week 5
Counting Theory, MIdterm
7.1-7.5
Week 6
Recurrence relations and Generating Functions
8.1, 8.2, 8.3
Week 7
Combinatorial Circuits, Finite State Machines
9.1,9.2,9.4
Week 8
Review and FInal
Review and final
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Lectures on Classical Differential Geometry: Second Edition by Dirk J. Struik Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, envelopes, more. Many problems and solutions. Bibliography.
Fundamental Concepts of Geometry by Bruce E. Meserve Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrationsChallenging Problems in Geometry by Alfred S. Posamentier, Charles T. Salkind Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and more. Arranged in order of difficulty. Detailed solutions.
Advanced Euclidean Geometry by Roger A. Johnson This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.Analytical Geometry of Three Dimensions by William H. McCrea Geared toward advanced undergraduates and graduate students, this text covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations, quadric in Cartesian coordinates, and intersection of quadrics. 1947 editionA Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961 edition.
Euclidean Geometry and Transformations by Clayton W. Dodge This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 editionFrom Geometry to Topology by H. Graham Flegg Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.
The Geometry of René Descartes by René Descartes The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.
History of Analytic Geometry by Carl B. Boyer This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical bibliography. Index.
A Modern View of Geometry by Leonard M. Blumenthal Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.
Proof in Geometry: With "Mistakes in Geometric Proofs" by A. I. Fetisov, Ya. S. Dubnov This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problemsA Vector Space Approach to Geometry by Melvin Hausner This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.
Product Description:
conics and quadrics developed within the context of metrical, affine, and projective transformations. The algebraic treatment is occasionally exchanged for a synthetic approach, and the connection of the geometrical material with other fields is frequently noted. Prerequisites for this treatment include three semesters of calculus and analytic geometry. Special exercises at the end of the book introduce students to interesting peripheral problems, and solutions are provided
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Developmental Mathematics for College Students - Text Only - 02 edition
Summary: Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. In this text, students get a thorough review of arithmetic and geometry along with all the topics covered in a standard elementary algebra course. The authors build the strong mathematical foundation necessary to give students confidence to apply their newly acquired skills in further mathematics cour...show moreses, at home, or on the job
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Linear Algebra
9780201119497
ISBN:
0201119498
Publisher: Addison-Wesley Longman, Incorporated
Summary: Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness, and overall usability. Its inclusion of calculus-related examples, true/false problems, section summaries, integrated applications, and coverage of Cn make it a superb text for the sophomore or junior-level linear algebra course. This Third Edition retains the features that have made it successful over ...the years, while addressing recent developments of how linear algebra is taught and learned. Key concepts are presented early on, with an emphasis on geometry. KEY TOPICS: Vectors, Matrices, and Linear Systems; Dimension, Rank, and Linear Transformations; Vector Spaces; Determinants; Eigenvalues and Eigenvectors; Orthogonality; Change of Basis; Eigenvalues: Further Applications and Computations; Complex Scalars; Solving Large Linear Systems MARKET: For all readers interested in linear algebra.
Fraleigh, John B. is the author of Linear Algebra, published under ISBN 9780201119497 and 0201119498. Twenty three Linear Algebra textbooks are available for sale on ValoreBooks.com, twenty two used from the cheapest price of $0.01, or buy new starting at $544.04
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CLASS – XI MATHEMATICS General instructions: All questions are divided into three Parts. Attempt Part A and either of Part B Or Part C. 1. What is a power set? ... CBSE Sample Paper MathematicsClass XI (11th) 2006 Keywords:
The Problem Solving Assessment will be conducted for all students of class IX in Jan – Feb 2013 and the details are available in a separate circular. The `Problem Solving Assessment' (CBSE-PSA) will be counted towards FA-4 which ... Mathematics (047) Class IX
Mathematics for Class XII by M.L. Aggarwal 7 R.D.P.S. Final Exam 100 28.09.13 to 17.11.13 Ch 10 : Vectors ... Grades will be sent to CBSE on the basis of continuous and comprehensive evaluation. Topic : Contemporary Problems & Indian Society • Meaning of Culture • Evolution of Indian Culture
CENTRAL BOARD OF SECONDARY EDUCATION ... Admission of CBSE students in Class XI for academic year 2010-11 after Introduction of ... Mathematics and Science (b) For Commerce based Courses with Mathematics : Candidates obtaining higher CGPA ...
CBSE for classes IX-X ... class. (i v)Subjects like Home Science, Drawing, Music, SUPW will be assessed on Five point Grading system as suggested by CBSE (An nexure III) Assessment is to be recorded twice in a year in each class ... 4.Mathematics 5.Science 6.Social Science
Central Board of Secondary Education, PA to DIR(Trg) ... solve application based problems in Mathematics and Science, ... (CBSE-PSA) for students of Class XI from the second term of this session 2012-13.
In mathematics, the word, ... In previous class, we have studied about arithmetic progression (A.P). In this Chapter, besides discussing more about A.P.; arithmetic mean, geometric mean, relationship between A.M.
level particularly the standard set by the CBSE and has vertical linkage with under graduate courses ... A Textbook of Mathematics for class XI published by NCERT, New Delhi JAMMU AND KASHMIR STATE BOARD OF SCHOOL EDUCATION SYLLABUS CLASS XI 50
In the mathematics, the new syllabi emphasise reasoning and conceptual grasp at every stage. In the ... The syllabus for Environmental Studies (EVS) upto Class V has been perceived as an integrated curricular area for the entire primary stage. The syllabus is woven around six common themes close to
CBSECLASS X: ENGLISH WRITING: BIOGRAPHICAL SKETCH ... especially mathematics. After school, Kalam ... won the 2002 presidential election and served as the 11th President of India, from 2002 to 2007. During his term as President, ...
Dates of AIEEE offline exam for 11thclass will be held on by CBSE: 29th April 2012 4. ... with an aggregate of 50 % marks with Physics and mathematics as the compulsory ... Central Board of Secondary Education PS 1-2, Institutional Area IP Extension, Patparganj,
classes in the Central Board of Secondary Education (CBSE ... ogy and mathematics were made mutually exclusive immediately after the 8th class. However, some years ago the CBSE qui-etly introduced computer science as an alternative to biology at the 11th and 12th class levels. Thus students ...
The new format of education by CBSE is an initiative to address holistic learning, ... (English or Hindi), Mathematics, Science and Social Science w.e.f the session 2013-2014 for class IX and 2014-15 ... order to promote 'Best Out of Waste' on 11th April. Class IX : Making Magazine holder ...
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A First Course in Mathematical Modeling:
Description: OffMore...
Off modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling
| 677.169 | 1 |
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