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College Algebra: Concepts through Functions, Second Edition embodies Sullivan/Sullivan 's hallmarks-- accuracy, precision, depth, strong student support, and abundant exercises--while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals: preparing for class, practicing their homework, and reviewing the concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus.
Essentials of Statistics Plus NEW MyStatLab with Pearson eText -- Access Card Pa , New, Free Shipping ALERT: Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN . Several versions of Pearson's MyLab Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID , provided by your instructor, to register for and use
Michael Sullivan's Statistics: Informed Decisions Using Data, Fourth Edition, connects statistical concepts to students' lives, helping them to think critically, become informed consumers, and make better decisions. Throughout the book, Putting It Together features help students visualize the relationships among various statistical concepts. This feature extends to the exercises, providing a consistent vision of the bigger picture of statistics. This book follows the Guidelines for Assessment and Instruction in Statistics Education (GAISE), as recommended by the American Statistical Association, and emphasizes statistical literacy, use of real data and technology, conceptual understanding, and active learning.
Weiss's Elementary Statistics, Eighth Edition is the ideal textbook for introductory statistics classes that emphasize statistical reasoning and critical thinking. Comprehensive in its coverage, Weiss's meticulous style offers careful, detailed explanations to ease the learning process. With more than 2,000 exercises, most using real data, there is a wealth of opportunity for students to apply their knowledge and develop statistical literacy. The text is suitable for a one-semester course. Elementary Statistics, Eighth Edition, contains parallel presentation of critical-value and p-value approaches to hypothesis testing. This unique design allows both the flexibility to concentrate on one approach or the opportunity for greater depth in comparing the two. This edition of Elementary...
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Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book. From SAT scores to job search methods, statistics influences and shapes the world around us. Marty Triola's text continues to be the bestseller because it helps students understand the relationship between statistics and the world, bringing life to the theory and methods. Elementary Statistics raises the bar with every edition by incorporating an unprecedented amount of real and interesting data that will help instructors connect with students today, and help them connect statistics to their daily lives. The Twelfth Edition contains more than 1,800 exercises, 89% of which use real data | 677.169 | 1 |
Description100s of problems!
Hundreds of practice exercises and helpful explanations
Explanations mirror teaching methods and classroom protocols
Focused, modular content presented in step-by-step lessons
Practice on hundreds of Algebra I problems
Review key concepts and formulas
Get complete answer explanations for all problems
About the author
Mary Jane Sterling is the author of Algebra I For Dummies, 2nd Edition, Trigonometry For Dummies, Algebra II For Dummies, Math Word Problems For Dummies, Business Math For Dummies, and Linear Algebra For Dummies. She taught junior high and high school math for many years before beginning her current 30-years-and-counting tenure at Bradley University in Peoria, Illinois. Mary Jane especially enjoys working with future teachers and trying out new technology3 total
KristinPrydn
Read this review This book is great for concepts, but it has absolutely no problems to work if you want to see if you actually understand the concept. I am returning to college and bought this as a refresher because I
User reviews
KristinP
BordersRead this review This book is great for concepts, but it has absolutely no problems to work if you want to see if you actually understand the concept. I am returning to college and bought this as a refresher because I
Similar"1,001 Algebra I Practice Problems For Dummies," with free access to online practice problems, takes you beyond the instruction and guidance offered in "Algebra I For Dummies," giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find: One year free subscription to all 1,001 practice problems On-the-go access any way you want it-from your computer, smart phone, or tablet Multiple choice questions on all you math course topics Personalized reports that track your progress and help show you where you need to study the most Customized practice sets for self-directed study Practice problems categorized as easy, medium, or hard
Whether you're studying algebra at the high school or college level, the practice problems in "1,001 Algebra I Practice Problems For Dummies" give you a chance to practice and reinforce the skill s you learn in the classroom and help you refine your understanding of algebra. Note to readers: "1,001 Algebra I Practice Problems For Dummies, "which only includes problems to solve, is a great companion to "Algebra I For Dummies, 2nd Edition" which offers complete instruction on all topics in a typical Algebra I course." testPrepare for calculus the smart way, with customizable pre-calculus practice
"1,001 Pre-Calculus Practice Problems For Dummies" offers 1,001 opportunities to gain confidence in your math skills. Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, or computer, the online component works in conjunction with the book to polish your skills and confidence in preparation for calculus.
Calculus-level math proficiency is required for college STEM majors. Pre-calculus introduces you to the concepts you'll learn in calculus, and provides you with a solid foundation of methods and skills that are essential to calculus success. "1,001 Pre-Calculus Practice Problems For Dummies" gives you the practice you need to master the skills and conquer pre-calculus. Companion website includes: All 1,001 practice problems in multiple choice format Customizable practice sets for self-directed study Problems ranked as easy, medium, and hard Free one-year access to the online question bank
Math is notorious for giving students trouble, and calculus is the #1 offender. Fear not! Pre-calculus is the perfect calculus prep, and "1,001 Pre-Calculus Practice Problems For Dummies" gives you 1,001 opportunities to get it right.From angles to functions to identities - solve trig equations with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with angles, circles, triangles, graphs, functions, the laws of sines and cosines, and more! 100s of Problems! * Step-by-step answer sets clearly identify where you went wrong (or right) with a problem * Get the inside scoop on graphing trig functions * Know where to begin and how to solve the most common equations * Use trig in practical applications with confidence
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More from authorWith its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, "Algebra I Essentials For Dummies" provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into." testNow, it is easier than ever before to understand complex mathematical concepts and formulas and how they relate to real-world business situations. All you have to do it apply the handy information you will find in "Business Math For Dummies." Featuring practical practice problems to help you expand your skills, this book covers topics like using percents to calculate increases and decreases, applying basic algebra to solve proportions, and working with basic statistics to analyze raw data. Find solutions for finance and payroll applications, including reading financial statements, calculating wages and commissions, and strategic salary planning.
Navigate fractions, decimals, and percents in business and real estate transactions, and take fancy math skills to work. You'll be able to read graphs and tables and apply statistics and data analysis. You'll discover ways you can use math in finance and payroll investments, banking and payroll, goods and services, and business facilities and operations. You'll learn how to calculate discounts and markup, use loans and credit, and understand the ins and outs of math for business facilities and operations. You'll be the company math whiz in no time at all! Find out how to: Read graphs and tables Invest in the future Use loans and credit Navigate bank accounts, insurance, budgets, and payroll Calculate discounts and markup Measure properties and handle mortgages and loans Manage rental and commercial properties
Complete with lists of ten math shortcuts to do in meetings and drive your coworkers nuts and ten tips for reading annual reports, "Business Math""For Dummies" is your one-stop guide to solving math problems in business situations. | 677.169 | 1 |
You may need more than one source to cover all the topics listed for any one level. The information below provides guidelines, but you will need to check that all the topics listed for the courses above are covered.
Try the practice test. The other button tells you the solutions. Keep in mind that MUM does not permit a calculator to be used on a placement test. Also we do not require you to know about complex numbers.
Website with free lessons:
Click on Lessons index in the upper right hand corner. In the page you get next, click on Lessons in order in the top right hand corner. Make sure you are on the Lessons in order page or the following won't make sense.
For our Intermediate Algebra: Start with Solving Radical Equations and Graphing Radical Equations from Beginning Algebra Topics; then go to Intermediate Algebra Topics – omit the first two items (Graphing systems of linear inequalities and Linear programming) and start with Inequalities: Absolute Value. Continue to the end of the Intermediate Algebra Topics, but skip Function Transformations and the last topic Sequences and Series. Then do the first few sections of Advanced Algebra Topics, namely, Complex Fractions, Rational Expressions: Simplifying, Adding Rational Expressions, and Multiplying Rational Expressions. Also from "…and the beginnings of trig". Everything up to Special Angle Values. You will need to find the Law of Sines and the Law of Cosines in another trigonometry book.
For our Functions and Graphs 1: Start with Function Transformations from the Intermediate Algebra Topics. Then it won't hurt to start Advanced Algebra Topics from the beginning. Omit Complex numbers and Partial-Fraction Decomposition. Work all the topics down to "Systems-of-equations word problems." Omit the matrices and determinants and all the rest.
For our Functions and Graphs 2: Composition of functions and Inverse functions from Advanced Algebra Topics will be useful, but the rest of the course is not covered in Purplemath, namely trigonometry. You will need to look elsewhere for help with trigonometry.
Purplemath also has advice about what books would be helpful in reviewing (but not necessarily helpful for studying the topics from scratch). And lots of links to other helpful websites.
At Khan Academy you will find worked examples and lectures on all the topics.
Website with lessons on mathematics that you have to pay for:
Aleks.com provides a great analysis of where you are and what topics you need to study. You get a pie chart of the analysis and then you begin to fill in the areas you need to work on. Click on course products.
Our Elementary Algebra course corresponds to: Beginning Algebra OR Prep for Intermediate Algebra. It would also help to review the section called Descriptive Statistics in the course Prep for Statistics.
Our Intermediate Algebra: Intermediate Algebra OR Prep for College Algebra with Trigonometry OR Prep for Pre-Calculus
Our Functions and Graphs 2: Pre-Calculus (omit sequences, series, and probability) OR College Algebra with Trigonometry
Books available from the MUM Library for review
Important Advice: Don't just start reading a book! You won't get very far if you do. First work through the relevant chapter reviews and chapter tests. Only then read the sections of the book pertaining to problems you had trouble with. The key to doing well on the test is to work problems, work problems, work problems. Note that you may need more than one book to cover all the topics listed in the "Topics to Review" page of the website Be sure to check that you have covered all the topics on that list. | 677.169 | 1 |
Synopses & Reviews
Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:
Prealgebra, 5/e, is a consumable worktext that helps students make the transition from the concrete world of arithmetic to the symbolic world of algebra. The Aufmann team achieves this by introducing variables in Chapter 1 and integrating them throughout the text. This text's strength lies in the Aufmann Interactive Method, which enables students to work with math concepts as they're being introduced. Each set of matched-pair examples is organized around an objective and includes a worked example and a You Try It example for students. In addition, the program emphasizes AMATYC standards, with a special focus on real-sourced data. The Fifth Edition incorporates the hallmarks that make Aufmann developmental texts ideal for students and instructors: an interactive approach in an objective-based framework; a clear writing style; and an emphasis on problem solving strategies, offering guided learning for both lecture-based and self-paced courses. The authors introduce two new exercises designed to foster conceptual understanding: Interactive Exercises and Think About It exercises.
About the Author
Richard Aufmann is Professor of Mathematics at Palomar College in California. He is the lead author of two best-selling developmental math series, a best-selling college algebra and trigonometry series, as well as several derivative math texts. The Aufmann name is highly recognized and respected among college mathematics faculty.Vernon Barker has retired from Palomar College where he was Professor of Mathematics. He is a co-author on the majority of Aufmann texts, including the best-selling developmental paperback series.Joanne Lockwood is co-author with Dick Aufmann and Vernon Barker on the hardback developmental series, Business Mathematics, Algebra with Trigonometry for College Students, and numerous software ancillaries that accompany Aufmann titles. She is also the co-author of Mathematical Excursions with Aufmann | 677.169 | 1 |
Introduction to Mathematical Reasoning Numbers, Sets and Functions
9780521597180
ISBN:
0521597188
Pub Date: 1998 Publisher: Cambridge Univ Pr
Summary: Eccles, Peter J. is the author of Introduction to Mathematical Reasoning Numbers, Sets and Functions, published 1998 under ISBN 9780521597180 and 0521597188. Three hundred sixty seven Introduction to Mathematical Reasoning Numbers, Sets and Functions textbooks are available for sale on ValoreBooks.com, fifty nine used from the cheapest price of $33.49, or buy new starting at $40.44.
May include moderately worn cover, writing, markings or slight discoloration. SKU:978052159718097 | 677.169 | 1 |
08
Comment:There is a newer edition of this item:--This text refers to an out of print or unavailable edition of this title.
--This text refers to an out of print or unavailable edition of this title.
Editorial Reviews
From the Back CoverSpecial emphasis on the central role of propositional & predicate logic
Full chapters on algorithm analysis & complexity theory
Introductory coverage of formal machines & coding theory
Over 700 exercises
Flexible structure so that the material can be easily adapted for different teaching styles.
New to this Edition
Improved treatment of induction
Coverage of more 'basic' algebra
List of symbols including page references for definition/explantion
Modern text design and new exercises to aid student comprehension
0201360616B04062001
--This text refers to an out of print or unavailable edition of this title.
About the Author
John Truss has taught at Oxford University, Paisley College of Technology and currently at the University of Leeds. He has been a committee member of the British Logic Colloquium since 1990, and has recently been appointed an editor of the Journal of the London Mathematical Society. He wrote Foundations of Mathematical Analysis in 1997 and has authored 40 research papers.
0201360616AB04062001 teacher's assistant for an undergraduate computer science course that uses this book. I have to say that it really is a terrible book for students to learn from who have never had much exposure to non-calculus math and the concept of the "mathematical proof". It skims over topics without providing enough exposition on the topics to allow students to have a fair grasp on the subject. This may just be the nature of teaching discrete math, but there seem to be far too many topics that Truss is trying to squeeze into too small of a space. He tries to throw in some more advanced topics such as formal machines and complexity theory, but only at the cost of having the overall quality of the material be watered down. Sadly, though, from what I have heard, this is the best current intro discrete math book out there.
I will have to agree with the other reviewer that it seems as if Truss is trying to cram lots and lots of discrete mathematics into an indiscrete stack of 500pp but i think he has done very well. At least in addressing those who need to skim over the material quickly, though they would love instead to relish on Grimaldi's. | 677.169 | 1 |
On learning mathematics from scratch, again.
How would you chart a course for math studies? I've read in various places that you can possibly self-teach yourself math from just dover books and schaum's outlines,
Background: I've got a formal math education up through calc 2. Unfortunately, I never really "got" the math, and mostly just went to get a grade and get out. This sucks, especially since I'd like to really learn more about physics and my lack of true calculus "understanding" seemed to hold me back. Granted, my math is probably a lot more advanced than most of the population, I'm just not satisfied with it. I want to go back to Algebra, Geometry, Trigonometry and then move into Calculus, Linear Algebra, Diff Eq, etc, more like an engineering math background, spending as little money as possible (hell, I'll probably be able to find Dover books at the library, you know?.. and yes, this means Stewart & the like are right out..), andYou don't want to spend money, which is fine, but how flexible is your time? If you can fit it in, you are likely to be able to audit classes at your local university free of charge. I always just walked in on the first day and asked the professor if they minded me auditing. I haven't had a single one turn me down (although I was mostly auditing high level - read "small" - classes, calculus is likely to be a packed lecture hall). The money is for the grade/degree, not the education.
There's always the original source material. It's all old enough that you can get it for free (even in translation to English), and it has to explain the principles to as a new line of thinking. Since you're relearning the material, you should have the background to follow it. It's a very proof heavy way to do it, but it would definitely get you there.
Quite true. This is fairly ridiculous but that's how world works now. You are supposed to be going to university to become competent enough to do a well paying job (for example), but in practice you're just doing it to get a paper that correlates somewhat (but far from perfectly) with competence, and gets you through the door; the companies just eat up the losses caused by incompetence, or go belly up if losses are too great, or rely on their own testing, at least in the software industry.
The universities bundle the certification with education, that's just a marketing tactic that works far better for them than offering education and certification as separate products. Very small percentage of their customers are interested in education per se, so the education itself is easily obtainable for freeThanks for the offer, but I had Stewart in school. Man that book gave me a headache. :/
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You don't want to spend money, which is fine, but how flexible is your time?
Not very right now. I'm signed up for some film classes in the spring starting mid-february, but no math/physics. This is more of just an exercise to try and "right" something I feel like I cheated myself out of (or was cheated out of by my instructors who were more interested in passing students than teaching them). who knows where it will lead later.
I figure I'll work through the above to try and get that foundation I want, then return to my physics interests.
Some areas I'll suggest you look into aren't covered in Mathematician's Delight.
One of them is generally termed 'discrete math' - as opposed to the continuum of trig/calculus. A little bit of combinatorics can go a long way in solving practical problems that in any way involve questions of "how many" - it's the study of counting. From there, graph theory can offer an interesting perspective on the world.
You may also want to poke at some abstract algebra or topology for fun. The former offers some very nice views of how to understand everything else you'll see in a more coherent framework.
I'll also suggest at least some study of formal logic, and the attendant rigor in proofs that comes with it. The basic premise is that anything we can prove can be described in a form that can be verified entirely syntactically - solely checking whether each step followed the rules, rather than the reader having to understand the meaning (semantics) of each step.
It starts with basic school arithmetics and takes you all the way through the foundations of engineering maths (discrete mathematics, logic, calculus etc.), at least for a BS it is all that you will need.
I haven't read dio's suggestion, but I have to wonder whether an engineering math book is going to fit the "focusing on the WHYS not just the HOWS" requirement of the OP. I've used a few engineering math books as references in my day, and while they're good for that purpose, they tend to be light on theory.
Stroud is an excellent textbook i own both basic and the advance version. Very simple to learn what you need out of.
BUT ITS NOT WHAT YOU ARE AFTER
Stroud plays fast and loose with many things my lecturers (Mech Eng at a good uni) recommended Erwin Kreyszig's Advanced Engineering Mathematics and were very disparaging of stround saying it cheated. Then again i learnt of stroud becuase it was easy when it counted and that is why i own. Got doing second order differentials in a day took me 5 days with kreyszig when I relearnt it for the 3rd time. But with Kreyszig i understood what I was doing more so that is what i would go with.
Engineering Maths books sound like they might be pitched at the right level for you. They start at Calc and work their way up and they are designed for us dumb engineers.
I Wish you luck in your quest. There are many things i would like to do with hot pokers than learn maths again.
What is your overall goal? Having in mind something like "I want to learn topic X" is a much better goal than "I want an engineering level math background". There are a lot of things wrong with the standard engineering level mathematics curriculum (beginning with the fact that there even is such a thing as a standard curriculum).
A even better goal is "I wanted to solve problem Y" or "understand phenomenon Y". I always used signal processing as a goal since I was into recording music.
I'm in a similar boat...having recently experienced a new interest in mathematics after hating it pretty much my entire life.
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andI can't help you for algebra or trig, but for calculus, I definitely recommend MIT's OpenCourseware. I downloaded the PDF from the Intro to Calculus course and it pretty much has the "why" of calculus in the first few pages.
That depends on what you end up needing to use the maths for? I'm guessing physics, and if you mean degree-level physics that's some serious ball-achin' mathematics if you get into the heavy stuff...
I think Stroud is great for engineering students, who are of course his target audience, but maybe not so hot for maths/physics students. I also used Kreyzig, as it was the recommended book for my degree, but still don't feel that it helped with the WHYs which is what you say you are interested in.
When it really comes to understanding maths and developing your intuition and insight, I would first of all say go back to absolute basics and revisit even the basics such as arithmetic. Really build up your familiarity with the fundamentals. Many mathematicians express great familiarity with numbers themselves and I think that's worth exploring. Secondly, practise and practise and practise. Dont' just learn methods of solution, but practise your mental arithmatic too. Familiarity comes with practise but often taught courses pressure you to keep advancing your topic of study, which can be lethal to your chances of success the moment you over-advance... Thirdly, try reading books that explore mathematical techniques, styles of thinking and which also examine the various *different* ways to approach problems. It should help you find your natural approach to mathematics (everyone thinks differently) and help you start to see past the mechanics of 'solutions'. I must confess I'm a bit short of good suggestions for this, but in general I'd say try to read and explore as widely on each topic as possible.
Lastly, try reading about mathematicians themselves, their stories and the stories of their work and discoveries. It's really very interesting to see how they each understood maths, how they felt and what drove them. It should help you begin to feel about maths as a *human* endeavour and not just make you feel like a human calculating machine This freaks out a lot of people, because they are used to subjects that are understandable on day 1, and students often get complexes about "not understanding it" and seriously shortchange themselves.
I've often wondered why that was only in the teacher's guide, and not routinely told to students. For me, I found the knowledge that blundering around doing problems mechanically for the first few weeks is normal, and since I often "got it" within a week or so, I was actually above average, not struggling to keep up.
My guess is that going back, you will "get it" tremendously faster, since you have covered it once. Plus, having seen other material that uses the math, you won't ever struggle with the "this is dumb. I'll never use this." cop-out
I'm not convinced we all "got" Geometry on Day 1, let alone Shakespeare... but the basic point is probably a good one.
I'm a class away from starting Linear Algebra and Diff equations, and I went back to school in my late 20's, so I had to take a lot of remedial stuffI really, really like math, I just admit to myself I'm not particularly good at it and do lots and lots of homework. I eventually got it with a hell of a lot of road bumps in the way.
One other resource I didn't see mentioned in the thread is Khan Academy. They cover everything from elementary arithmetic to Linear Algebra, and everything is broken down into easy to digest 10-15 minute videos, so it's easy to go back and review something you might have missed or forgotten. What I find especially nice is that he tends to explain concepts in intuitive terms rather than just giving rote instructions for solving formulaic problems, and makes it easier to connect one concept to another. If you're feeling extra frisky, there are exercises that accompany the lessons with some nice progress-tracking toolsTHIS IS EXACTLY HOW I FELT IN CALC I and lead me to create this thread, actually. I passed Calc I & II but I felt extremely out-gunned and over-my-head because I forgot all the building blocks up to it. Even though I managed to pass, I was never satisfied with my performance and it still eats at me to this dayYou used that for your calc class? Nice, the math program where I went didn't pick that up until Real Analysis. We did use Spivak's Calculus text, though, and it did give a serious treatment to the principles and derivation of calculus[quote=MilleniX]We did use Spivak's Calculus text, though, and it did give a serious treatment to the principles and derivation of calculus.[/quote]
Oops, I forgot. We also used Spivak. It's good, I think a clean introduction to multi-variable calculus and manifolds haveI find myself caught on all sides of the rigor wall, currently. I'm taking a numerical analysis class taught by an engineering professor. I already have an understanding of the "big picture" of the field, so I find the lack of rigor in the class super frustrating. I don't need someone telling me "real life" examples or explaining conceptual bits, I want the gory details. On the flip side, I have to keep up in algebra by shear memorization. High power tools are wielded without regard to life or limb. The logic is super precise. But, I could get the same treatment in a textbook versus copying well-worn notes from the board. So it feels like a giant waste of time (for all parties involved) not gaining any perspective from the professor's presentation.
I still don't understand precisely what the OP wants out of his experience. If it's mathematics for mathematics sake, people have made the "classical" suggestions of learning calculus through Spivak and Rudin (I'll also toss out Apostol for calculus and Arnol'd for ODE). All I see in the original message is a list of courses you'd find on the resume of any vanilla engineering graduate. It gives no feel for where the true interests lie. What precise problems motivate you?
I went into math trying to figure out the mathematics behind music technology. I learned differential geometry to understand general relativity and electromagnetism. I continued with analysis to deepen my understanding of signal processing. I simply learn mathematics better if I have a solid, nontrivial application in mind. (This is probably a reflection of my philosophy of mathematics.)
I recently did a similar thing. I got all the way through Linear Algebra/Diff. Equations and a few upper-level physics classes before dropping out, and now I'm back trying to get my bachelor's and eventually a master's. I'm currently enrolled in Calc II and Physics I.
First, it's easy to learn enough to pass a regular university-level course without sufficiently learning the material if you're intelligent. Auditing a course is a good way to keep you on track and give you information if you're self-learning, but it's all about the self-motivation and self-discipline if you want to master the materialSo it all depends on where your skills are at and what your ultimate goal is. If your math skills are better than mine were, or if you just want to learn some new interesting things you can take a different approach and do well at it. But if you're looking to get an expert level understanding, or a job in the field (or if you're looking to apply what you learn to a different field like engineering), you'd definitely be best off relearning *everything* and putting a good amount of work into it.
If your really want to move into the field and *excel* at it (or if you're just a giant nerd and you want to learn as much out of it as you can ) you're going to need to revisit most of the stuff you've learned in the past. It's frustrating, but that's my experienceMilleniX wrote:
We did use Spivak's Calculus text, though, and it did give a serious treatment to the principles and derivation of calculus.
Oops, I forgot. We also used Spivak. It's good, I think a clean introduction to multi-variable calculus and manifolds.
Not that one. Again, I'm pretty sure that's intended for upper-division math majors ("The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course"). I mean CalculusHere. This absolutely killed me. The teacher would go over a subject in class. Cool. I got it. Didn't bother with homework. When it was time to take the test, I easily passed and moved on. I never did learn how to study. Didn't need to, until algebra II. Now, I'm in the same place as MongoMania
The key thing is that integration by parts is a heuristic, there's no algorithmic iteration that always leads you to the solution. You need to strategically pick u and v based on what simplifies the problem. The goal is to turn an integral you can't solve into some stuff minus an integral you can solve.
Don't iterate unless absolutely necessary. If you don't immediately see how to solve the resultant integral (by substitution or whatever), go back and pick a different u and v, rather than trying to use integration by parts again. Sometimes it is helpful to do it more than once, but it is easy to make a mess trying, so don't do it unless you have exhausted the other possibilities.
Ah, yeah, there's a cute trick with that. Do it twice and you should end up with some stuff plus something that looks like the original integral. Set it equal to the original integral, move that term to the other side, divide off the constant, and voila.
If you don't get it in the next 10 min or so let me know and I'll latex it up. | 677.169 | 1 |
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The lessons in this book introduce basic algebraic concepts to students in the primary grades. Manipulative materials, problem-solving investigations, games, and real-world and imaginary contexts support arithmetic learning while introducing ideas basic to algebra, including patterns, equivalence, and graphing. | 677.169 | 1 |
Books à la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book. Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make better decisions every day. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts. This Package Contains: Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition, (à la Carte edition) with MyMathLab/MyStatLab Student Access Kit | 677.169 | 1 |
Queueing theory (the mathematical theory of waiting lines in all its configurations) continues to be a standard major area of operations research on the stochastic side. Therefore, universities with an active program in operations research sometimes will have an entire course devoted mainly or entirely to queueing theory, and the course is also... more... | 677.169 | 1 |
Office Hours: Tuesday and Thursday
9:50-10:30 (Darwin 122, our classroom); by discovery; or by
appointment. Please come to office hours if you have any
questions about the course material or your progress.
We're
going to work on many concepts of early algebra, including some
background in fractions that is often a stumbling block for students.
Our goal is to become fluent in algebraic manipulations, to allow you
to succeed in later courses which count on your algebra skills.
"In its
most common form, algebra is just an extension of the number system.
For example, algebraic formulas often describe how one quantity
depends on another. Determining gas mileage, predicting the amount of
food needed for a party, and figuring the costs of renting videos are
all examples of daily situations that require algebra.
"Not
every student needs to be able to derive the quadratic formula. But
all should understand how a change in one quantity affects another
and how to make decisions based on these relationships. In this
sense, every student needs to master algebra.
"Learning
how to read, write, and do arithmetic may seem more important than
learning algebra. But a lack of algebraic understanding can be just
as debilitating as deficiencies in reading or arithmetic when ...
trying for a good job."
Course
particulars
CALCULATOR
policy: Calculators are not to be used in this course. While they
are valuable tools in many endeavors, they won't help you learn the
concepts we'll be studying.
ASSIGNMENTS: Homework will be
assigned at the end of each class meeting. Keep all homework in a
loose leaf binder. Indicate page of the text at the top of each page.
A completely worked solution presented is expected. When
drawing graphs use graph paper and a straightedge.
QUIZZES will be given on a
regular basis. They will include problems from your homework as well
as other problems. You will be allowed to use your homework binder
to answer questions on the quizzes. So it is important that the
homework binder is kept up to date. The quizzes cannot be made up but
you will be allowed to drop at least two of your lowest scores. A
completely worked solution neatly and legibly presented is
expected.
The weekly quizzes will include
problems based on prior weeks' material. The quizzes will take either
of the following two forms:
Form
1: You will be allowed to use your text homework binder to answer
questions on FORM 1 quizzes. These quizzes will consist of two
parts. The first part will consist of two or three problems taken
directly from your homework notebook. The second part will
consist of problems 'similar' to homework problems. You will be
allowed to use your text homework notebook to answer questions on
both parts of the quiz. So it is important that the binder,
i.e. homework, is kept up to date.
Form
2:These quizzes will be closed book and will be similar to
the homework problems. They will be unannounced and you will not be
allowed to use your homework notebook for these quizzes.
EXAMS cannot be made up.
You may replace your lowest exam score with your Final exam score.
The Final is cumulative and must be taken. A completely worked
solution neatly and legibly presented is expected.
Resources
Math Study Lab:Learning
Skills Services and the Tutorial
Program are co-sponsoring a Math 35 Study Lab for this semester.
It will be Mondays 2-4 p.m. and Thursdays 10 a.m. – noon. First
meeting is Thursday, September 2 in Salazar 1040. I highly
recommend that you take advantage of this free service! You can
just drop in on the occasions when you can make it.
ELM: If you feel that you are in Math 35 only because of a
bad test day – in other words, you believe you already know the
material or could pass the ELM with a little more studying –
you can take it again during the semester (October 9 and December 4).
The web site
has some information on the test (including description of the
content of the test, under "Focus on Math" link), and
is where you go to register. There is an $18 fee to take the test. If
you take the October 9 test and bring me your score reporting showing
a passing score prior to the final exam, then you don't have to take
the final and you will receive a C for this course. If you pass
either October 9 or December 4, then you won't have to take Math 45
in the Spring and can proceed directly to the GE math course of your
choice.
Online resources: The California State University has a new
website at
to help you if you want to take the ELM. This site has a practice
test, and additional practice problems, for you to work on. If you
want to do additional work to prepare, the ALEKS ELM tutorial which
you can purchase for $35 through this site is a great deal. ALEKS
also has a beginning algebra module, and you can use that for the
same $35 fee – the fee buys you an 18-week license to use all
of ALEKS. You can learn more about ALEKS, and try it out before you
buy, at
M*A*T*H
Colloquium: This is our weekly lecture on various
mathematical topics. The September 8 lecture will be particularly
relevant for some of us. 5 extra credit quiz points if you attend
and give me a 1-page writeup about the talk and what you learned. | 677.169 | 1 |
Product Description
Review
From the reviews:
MATHEMATICAL REVIEWS
"There are many books about the theory of prime numbers and a few about computations concerning primes. This book bridges the gap between theoretical and computational aspects of prime numbers. It considers such matters as how to recognize primes, how to compute them, how to count them, and how to test conjectures about them¿The book is clearly written and is a pleasure to read. It is largely self-contained. A first course in number theory and some knowledge of computer algorithms should be sufficient background for reading it…Each chapter concludes with a long list of interesting exercises and research problems."
BULLETIN OF THE AMS
"The book is an excellent resource for anyone who wants to understand these algorithms, learn how to implement them, and make them go fast. It's also a lot of fun to read! It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."
AMERICAN SCIENTIST
"…a welcome addition to the literature of number theory – comprehensive, up-to-date and written with style. It will be useful to anyone interested in algorithms dealing with the arithmetic of the integers and related computational issues."
SIAM REVIEW
"Overall, this book by Crandall and Pomerance fills a unique niche a deserves a place on the bookshelf of anyone with more than a passing interest in prime numbers. It would provide a gold mine of information and problems for a graduate class on computationl number theory."
From the reviews of the second edition:
"This book is a very successful attempt of the authors to describe the current state-of-the-art of computational number theory … . One of the many attractive features of this book is the rich and beautiful set of exercises and research problems … . the authors have managed to lay down their broad and deep insight in primes into this book in a very lucid and vivid way. … The book provides excellent material for graduate and undergraduate courses on computational theory. Warmly recommended … ." (H.J.J. te Riele, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006)
"An absolutely wonderful book! Written in a readable and enthusiastic style the authors try to share the elegance of the prime numbers with the readers … . Weaving together a wealth of ideas and experience from theory and practice they enable the reader to have more than a glimpse into the current state of the knowledge … . any chapter or section can be singled out for high praise. … Indeed it is destined to become a definitive text on … prime numbers and factoring." (Peter Shiu, Zentralblatt MATH, Vol. 1088 (14), 2006)
"This impressive book represents a comprehensive collection of the properties of prime numbers. … in the exercises at the end of each chapter valuable hints are given how the theorems have been attained. The chapters end with research exercises. The book is up to date and carefully written. … The volume is very vividly and even entertainingly written and is best suited for students and for teachers as well." (J. Schoissengeier, Monatshefte für Mathematik, Vol. 150 (1), 2007)
"The aim of this book is to bridge the gap between prime-number theory covered in many books and the relatively new area of computer experimentation and algorithms. The aim is admirably met. … There is a comprehensive and useful list of almost 500 references including many to websites. … This is an interesting, well-written and informative book neatly covering both the theoretical as well as the practical computational implementation of prime numbers and many related topics at first-year undergraduate level." (Ron Knott, The Mathematical Gazette, Vol. 92 (523), 2008)
From the Back Cover
Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added.
Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use.
From the reviews of the first edition:
"Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers."
<- L'Enseignement Mathématique
"...Prime Numbers is a welcome addition to the literature of number theory---comprehensive, up-to-date and written with style."
- American Scientist
"It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."
Most helpful customer reviewsRead more ›
This book has all the recent (2001) developments in factoring algorithms and related number theory. It has chapters on algorithms for large numbers. While graduate-level, much of it should be accessible by an undergraduate. It hasThe book content is quite fascinating; the only real readability difficuly is some rather obscure and undefined notation. The physical quality of the book is inexcusably bad. The brand new book started falling apart as soon as it was opened. Springer Verlag, the publisher, refused to correct the situation. I shan't again buy anything publishd by Springer-Verlag!
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
6 reviews
33 of 33 people found the following review helpful
Standard reference on the subject.April 21 2003
By
Decio Luiz Gazzoni Filho
- Published on Amazon.com
Format: Hardcover Unfortunately, modern factoing algorithms deserve a book on its own, and it's impossible to cover all the ground in the space alloted to them in this book. The authors do a pretty good job of introducing them, even if the explanation is unclear and a bit shallow at times, and they always reference other works on the field for further information they were unable to cover. Chapter 7, ``Elliptic Curve Arithmetic,'' is a great starting point for elliptic curve studies, with a no-nonsense introduction to the subject that is certainly enough for the algorithms that follow. These include Lenstra's Elliptic Curve Method of factorization; Shanks-Mestre's, Schoof's and Atkin-Morain's algorithms for assessing curve order; and Goldwasser-Kilian's and Atkin-Morain's primality proving algorithms. Almost as valuable as the rest of the book itself (at least for implementers) is the ninth and last chapter, ``Fast algorithms for large-integer arithmetic.'' Many of these can be carried over without effort to floating point, so the scope of the material is even broader than the authors claim. Having read parts of Knuth's ``The Art of Computer Programming: Seminumerical Algorithms,'' I can attest to the superb exposition of Crandall and Pomerance being a breath of fresh air in this field. This book belongs on the shelf of every programmer implementing multiprecision arithmetic for this chapter alone.
25 of 25 people found the following review helpful
A Factoring "Bible"March 6 2002
By
Ed Prothro
- Published on Amazon.com
Format: Hardcover
This book has all the recent (2001) developments in factoring algorithms and related number theory. It has chapters on algorithms for large numbers. While graduate-level, much of it should be accessible by an undergraduate. It has10 of 12 people found the following review helpful
advanced coverageSept. 22 2005
By
W Boudville
- Published on Amazon.com
Format: Hardcover
This is an advanced treatment of prime numbers. But it is not all abstract number theory. The recurrent theme is how to compute these and how to use primes in other computationally intensive tasks.
The book summarises centuries of effort. Notably with Goldbach's Conjecture about every even number>2 being the sum of two primes. But intriguing issues like the density of primes along the number line are gone into. Along with the Mersenne primes and prime producing formulae.
An entire chapter discusses cryptography and related matters. Primes are at the heart of PKI and its RSA implementation. There is even a section briefly covering quantum computing and a quantum Turing Machine. Rather sparse detail because, well, the experimental results are still very new. Only baby steps have been forthcoming. The phase coherence difficulties are formidable. But it is a potentially vast area of future work.
2 of 2 people found the following review helpful
This is not a book for casual reading, or indeed even for studious reading: it requires devotionMarch 30 2015
By
James Kenney
- Published on Amazon.com
Format: Hardcover
Verified Purchase
This book is one of obvious authority, written by men far beyond gifted. It is on a topic which has fascinated me for 55 years: prime numbers. It is clearly a book for a gifted few who can tread these sacred precincts; I only wish I were one of them.
2 of 5 people found the following review helpful
Cover a lot of aspects of the mathematics under encryption.March 14 2011
By
Amazon Customer
- Published on Amazon.com
Format: Paperback
Was really helpful for a course in computer security. You have details algorithms to play with prime number. It was a great buy to understand how security is made of calculus with Prime numbers. | 677.169 | 1 |
What Is Calculus?
Calculus was invented as a tool for solving problems. Prior to the development of calculus, there were a variety of different problems that could not be addressed using the mathematics that was available. For example, scientists did not know how to measure the speed of an object when that speed was changing over time. Also, a more effective method was desired for finding the area of a region that did not have straight edges. Geometry, algebra, and trigonometry, which were well understood, did not provide the necessary tools to adequately address these problems.
At the time in which calculus was developed, automobiles had not been invented. However, automobiles are an example of how calculus may be used to describe motion. When the driver pushes on the accelerator of a car, the speed of that car increases. The rate at which the car is moving, or the... | 677.169 | 1 |
help hold a Masters later math classes and the basis for all math that follows. | 677.169 | 1 |
Working Analysis
By
Jeffery Cooper, University of Maryland, U.S.A.
The text is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis.
Audience
Engineers and scientists who wish to see how careful mathematical reasoning can be used to solve applied problems; upper division students in Advanced Calculus
Book information
Published: September 2004
Imprint: ACADEMIC PRESS
ISBN: 978-0-12-187604-3
Reviews
"This is a solid, well-written advanced calculus book that deserves to be on the shelves of mathematics department offices when faculty are selecting course resources." -J. Feroe, Vassar College, in CHOICE, JUNE 2005 "...this textbook is based on a very healthy philosophy that it is easier to learn mathematical analysis when it is intertwined with meaningful applications. The book is fun to read and, I am sure, will be fun to learn from." -Victor Roytburd, Rensselaer Polytechnic Institute, in SIAM REVIEW "In my opinion the book by Cooper is a viable competitor to Strichartz...To summarize, this textbook is based on a very healthy philosophy that it is easier to learn mathematical analysis when it is intertwined with meaningful applications. The book is fun to read and, I am sure, will be fun to learn from." – Victor Roytburd, Rensselaer Polytechnic Institute | 677.169 | 1 |
Description
This app is a computer algebra module for computing real roots of polynomials, by first isolating them. The theorems by Sturm (1827) and Vincent (1834-36) are used. Additionally it computes lower and upper bounds on the values of the positive roots of the poly, factors it and determines whether it has any rational roots. All with the help of Bernard Parisse's open source library giac.
CAVEAT: During App installation, an auxiliary program called Ministro will ask permission to also be installed. Accept, because Ministro is needed to install the libraries handy tool for computing poles and zeros and plotting the pole -zero locations , given the numerator and denominator polynomial coefficients of a transfer function. The frequency response, magnitude as well as phase are also plotted. the format for entering the polynomial coefficients is: A(1)+A(2)z^-1+A(3)z^-2+...+A(n-1)z^-n Caution: Since the app uses Bairstow Alogrithm for computing the roots of polynomial, the convergence cannot be guaranteed for very high order polynomials.
12th Grade Polynomials for students is amazing fun, FREE and learning at same time for the serious students in 12th class. Its an excellent App for students to practice after school. It covers various aspects of Polynomials family in different ways and different style. And also is a starting point for parents and students alike who are keen on succeeding in the higher classes. This 12th Grade Polynomials math App for the 12th college class will supplement further education with what's already learnt at school and will be a fun and easy add-on tool to the kitty of the kids. They will enjoy practicing the various 12th standard levels of Polynomials for free, share the score with their 12th class peers and compete, share the score with their teachers and parents to keep them abreast of their maths and complex Polynomial skills. Good for Intermediate second year (10+2) students.
This app covers various levels like: >>>> Divide polynomials using long division >>>> Evaluate polynomials using synthetic division >>>> Write a polynomial from its roots >>>> Find the roots of factorised polynomials
Each level has at-least 20 questions and the locked level has additional 20 questions. Overall there are around 80 questions in the App. It also supports CBSE, NCERT, ICSE, State syllabus and USA Common Core and various other international standards, hence is an international App.
Download for free today and become a genius mathematician ! Remember, this is a Jinga production !
This App was created by Dimitris A. Sidiropoulos (under the supervision of Alkiviadis G. Akritas) as part of the required thesis for the degree of the Department of Electrical and Computer Engineering. Thanks are due to Sophia Liaskou for providing the theoretical background for this app. | 677.169 | 1 |
The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society. This book focus on these aspects. more...
Biometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have... more...
Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations." ? SIAM Review geometric invariance and asymptotic attraction for a... more...
Contains a set of black line masters for interesting math number games that can be reproduced on A3 card for practical use in the classroom, strengthening students? knowledge of times tables and number skills. Activities to suit Grades 1-7 students.
more...
Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more... | 677.169 | 1 |
An entertaining and captivating way to learn the fundamentals ofusing algorithms to solve problems
The algorithmic approach to solving problems in computertechnology is an essential tool. With this unique book, algorithmguru Roland Backhouse shares his four decades of experience toteach the fundamental principles of using algorithms to solveproblems. Using fun and well–known puzzles to gradually introducedifferent aspects of algorithms in mathematics and computing.Backhouse presents you with a readable, entertaining, and energeticbook that will motivate and challenge you to open your mind to thealgorithmic nature of problem solving.
Provides a novel approach to the mathematics of problem solvingfocusing on the algorithmic nature of problem solving
Uses popular and entertaining puzzles to teach you differentaspects of using algorithms to solve mathematical and computingchallenges
Features a theory section that supports each of the puzzlespresented throughout the book
Assumes only an elementary understanding of mathematics
Let Roland Backhouse and his four decades of experience show youhow you can solve challenging problems with algorithms!
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Since the topic itself has complexity in its DNA, it is presented well, makes it interesting (almost intriguing) for students in the first year of Computer Science ( the course on which the book is based).
The approach is a bit outside the box, since it presents examples first - almost all the typical courses in Italian universities do this after the mathematical theory/algebraic.
The book is divided into 2 parts practically of the same length and number of pages. In the first part the reader is exposed to: examples from games at the Tower of Hanoi, all with resolution explained in detail, both in words and through equations and algorithms. They are also offered exercises to be solved and ideas for projects. The first, fortunately, have solutions and answers in Appendix.
The second is the mathematical theory which acts as a glue to algorithms - from algebra to number theory of quantifiers.
Everything is explained in English but it is easy to understand by non-native English speakers (just a decent knowledge of language is necessary).Read more ›
a lot of exercises so you can practise what you've learned. i bought it a few months ago and only read the first 100 pages or so. did help me with my uni work but should've bought it earlier to have enough time to read all the content. but overall its a good book which covers interesting APS concepts
this book is hard to understand, the layout is bad and it jumps a lot! the logic could be better explained, rather than using boolean, and at times even the simplest things are said in the hardest way!!! | 677.169 | 1 |
College Algebra with Trigonometry : Graphs and Models with MathZone: MandatoryMathematical reform is the driving force behind the organization and development of this new text in college algebra and trigonometry. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate.The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. Proceeding in this way, students gain a broader, deeper, and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme.The second major objective of this book is the development of a library of elementary functions, including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review.The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications. | 677.169 | 1 |
Description
Hi Guys,
This is a Smart Worksheet covering circles, parabolas and ellipses. The sheet consists of nearly 80 questions with each having an individualized on-line video solution. I've also included a host of tools and resets so that you can track of your progress, Hope you enjoy the live worksheet and if you have any questions, then by all means give us a buzz and send us an email. Cheers, MarkIssue Description: Conic Section, Conics as Sections of a Plane and a Right Circular Cone, General equation of a Conic section when its Focus, Directrix and Eccentricity are given, Parabola, Standard Equation of Parabola, Some Terms Related to Parabola, Standard Forms of Parabola with Latus Rectum, Special form of parabola (y – k)2 = 4a(x – h), General Equation of a Parabola, Position of a Point (x1, y1) with Respect to a Parabola y2 = 4ax, Intersection of a Line and a Parabola, Equation of Tangent in Different Forms, Point of Intersection of Tangents at any Two Points on the Parabola, Equation of Pair of Tangen
A mush have series of books for all the JEE aspirants. JEE Prep series of books is available for Physics, Chemistry and Mathematics for JEE aspirants. Every book contains detailed theory and solved examples. Good number of problems from previous years IITJEE and AIEEE papers have been explained in detail. The books are written in a manner so that an individual student can understand the concepts and problems. Students are suggested to solve the problems on their own then match the solutions, It will boost their confidence to take this challenging exam. So go and get the books and give a boost to your JEE preparations! You can also mail your suggestions at admin@learnersplanet.com or call (91)9099020032 All the Best!Highly appreciated by teachers and parents; children are having fun classifying and matching 100 Food, Animals & House objects, while improving fine motor skills, acquiring new cognitive skills and building vocabulary.
The Sorting n' Learning game is a newest addition to our educational apps for toddlers and preschoolers - representing a balance between playing & learning. It is a vocabulary teaching aid and provides kids with a good foundation for future math and language skills. It is based on an incredible and innovative concept that will help them: * Improve categorization & classification skills * Focus on visual perception and concentration * Develop cognition and fine motor skills free app helps your children develop matching, tactile, spatial and fine motor skills while playing and exploring 30 different Tools puzzles. The Tools edition is specially developed for young boys, but can also be interesting for girls that like to help their dads around the home.
Watch them learn all the names of numerous fixing tools used in everyday life in the home, garden, yard or garage, through fun and play. A pleasant voice will always encourage and praise your kids and toddlers and motivate them to continue to build their vocabulary, memory, and cognitive skills while playing baby favorite, the best educational FREE puzzle game that will entertain and teach for hours. It will help your toddler learn his first words and alphabets while working on the development of fine motor and tactile skills - all this through matching different shapes. Animations, interaction & high-quality graphics with the addition of educational elements ranging from animal names, animal sounds & real-life animal pictures, fun facts & videos are what makes this game unique and hard-to-resist. Learning can be a lot of fun! A must-have puzzle for little children who loves playing in Water and on the Sea Beach. Learn who lives underwater, match the broken shapes and watch the cute animals come to life. This free kindergarten game is great for your baby toddler or preschooler and is appropriate for autistic children too. Having hours of fun will lead to development of fine motor skills, as well as improvement of speech and pronunciation while learning first words and lots of animal names, sounds & fun facts.
Gameplay & Features: - 37 hand-drawn animals from the Farm & Sea to play with AsDo you want your children to be educated through your or their smart devices? Hurrah! Intellectual Labs has done it again by providing you Kids Learner App. Kids Learner app educates kids, as young as 3 year old, to learn writing alphabets(ABC, abc), numbers (123) and English words in an entertaining as well as interactive way.
We have taken care of all the proper writing steps. Each word has few steps and kids have to follow them in order to put the correct letters. If a mistake is made, a buzz will be played to keep the child on the right path. To make it more interesting, your kids have to grab hungry bug with their finger, move along the path to take foods and letters will be drawn.
Animated letters, words and sounds will keep your children engaged for hours in this learning activity which involves writing, correcting and speaking different letters and words. The application is totally free, and following are a few key features:
★★★★★ ABC and 123 writing ★★★★★ Exquisite graphics ★★★★★ Helping Kids to learn and write words like BEAR, AIRPLANE, PARROT, FLAPPY BIRDS, in an interactive way. Beautiful letters animations and sounds will entertain your children and educating them. ★★★★★ Beautiful animations. ★★★★★ Vivid music is in harmony with the game
let us know about your feedback and helping us in updating next versions with more words for your kids :)
Designed to give you and your kids an outdoor painting experience and help develop creativity, as well as aesthetic development, work on your fine motor skills, stimulate a different form of self-expression and learn more about your emotions. Paint your favorite pets, cat & dog, the farm pig & cow, the jungle elephant, savannah lion, forest owl, zoo monkey and many more.
Painting is much more than just a simple activity, it is a way for children to do many important things: convey ideas, explore color, process and outcomes and create aesthetically pleasing works and experiences. With "Animals Painting 4 School Kids" now you can allow your little ones to freely work with paints and colour without worrying that you'll have to clean up a big mess after each fun creative session.
Features: • Numerous animations to make the app experience even more fun & addictive • 4 Amazing textures representing real brushes, markers, color pencils and crayons with different sizes to choose from • Slider color picker representing a vibrant 68 - color pallet • Start over with your painting in just one click or erase it partially, whichever works best for you • Built-in gallery to store all the coloring masterpieces & share them with friends and family via email or Facebook • Showcase your art on our Art Wall of Fame :)
* All the drawing illustrations in this game are created by iAbuzz, and all their copyright belongs solely to Abuzz D.O.O. Macedonia.
At Desmos, we imagine a world of universal math literacy and envision a world where math is accessible and enjoyable for all students. We believe the key is learning by doing.
To achieve this vision, we've started by building the next generation of the graphing calculator. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series. Sliders make it a breeze to demonstrate function transformations. It's intuitive, beautiful math. And best of all: it's completely free.
Features:
Graphing: Plot polar, cartesian, or parametric graphs. There's no limit to how many expressions you can graph at one time - and you don't even need to enter expressions in y= form!
Sliders: Adjust values interactively to build intuition, or animate any parameter to visualize its effect on the graph
Tables: Input and plot data, or create an input-output table for any function
Statistics: Find best-fit lines, parabolas, and more.
Zooming: Scale the axes independently or at the same time with the pinch of two fingers, or edit the window size manually to get the perfect window.
Points of Interest: Touch a curve to show maximums, minimums, and points of intersection. Tap the gray points of interest to see their coordinates. Hold and drag along a curve to see the coordinates change under your finger.
Scientific Calculator: Just type in any equation you want to solve and Desmos will show you the answer. It can handle square roots, logs, absolute value, and more.
Inequalities: Plot cartesian and polar inequalities.
Offline: No internet access required.
Visit to learn more and to see the free online version of our calculator.
Note: the app doesn't yet support saving & sharing of graphs. If you need to save and share, we recommend visiting on your device.
Enter an inequality that is <, <=, >, >= or = and this works out the solution for you. It basically does just what it says on the tin. So if you have homework that you need to check the answers for, then look no further.
This tool is taken from the selection of tools that appears on my live worksheet app on Inequalities and the Modulus Function, that appears on my wolfram alpha developer page.
This is a Smart Worksheet on Fractions. A lot of people, both young and old, often struggle with one aspect or another of working out fractions. The sheet covers, converting improper and proper fractions, addition and subtraction as well as multiplication and division.
It is designed so that you have a go first and then click on the question to open the video solution to check you answer. There are tutorial videos interspersed in the sheet just before you try the section of questions.
There are resets and a whole host of useful tools so that you can keep a track of your progress as you work through.
Hi Guys, Enter any algebraic expression and this simplies it. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further. The widget tool is taken from the selection of tools that appears on my live worksheet app that appears on my developer page. Hope it proves helpful. Cheers, Mark
This is a Smart Worksheet on second order linear differential equations covering both homogeneous and non-homogeneous types and including problems with initial conditions.
There are also some useful de solver tools where you can type in your own problems and obtain the worked solutions so you can check any homework that you have.
There's a PDF file for those who want to work on the sheet independently and an email math que, where you can jot down a questions and append it to an email. If I get time, I will write up a YouTube video solution and send you the link.
All the best with the worksheet and if you have any feedback just give us a buzz.
Enter two whole numbers and this does the long division, showing you it all step by step. It basically does just what it says on the tin. So if you have homework that you need to check the long division for, then look no further.
The widget tool is taken from the selection of tools that appears on my live worksheet app entitled Surds, Polyomials and the Remainder Theorem, that appears on my developer page.
Hi Guys, Enter any function and this works out any derivative at x or at any specific value. It basically does what it says on the tin. So if you have homework that you need to check the answers for, then look no further. This tool is taken from the selection of tools that appears on my Wolfram Alpha developer page. Hope it proves helpful. Cheers, Mark
Hi Guys, Enter any function and this works out the inverse along with plotting both the function and its inverse superimposed over each other. It basically does just what it says on the tin. So if you have homework that you need to check the answers for at any limit value and this calculates the value of the limit. And if you click on show steps it will break down the evaluation step by step. It basically does what it says on the tin. So if you have homework that you need to check the answers for, then look no further. Hope it proves helpful. Cheers, Mark
Hi Guys, Enter an equation or expression and this simplifies it often giving multiple versions. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further. The widget tool is taken from the selection of tools that appears on my live worksheet apps on my developer page. Hope it proves helpful. Cheers, Mark
Hi Guys, Enter any integral function and this will calculate the answer. It does just what it says on the tin. So if you have integration this will calculate the maximum domain and range. It does just what it says on the tin. So if you haveEnter a function and this evaluates the Laplace Transform or the Inverse Laplace Transform. It basically does just what it says on the tin. So if you have Laplace Transform questions that you need to work on, then look no further.
The widget tool is taken from the selection of tools that appears on my wolfram alpha developer page.
Enter any partial fraction functions and this generates the solution with a step by step outline solution. It basically does just what it says on the tin. So if you have homework that you need to check out, then look no further.
This tool is taken from the selection of tools that appears on my live worksheet app on Differentiation, that appears on my developer page.
This is a Live Worksheet on linear algebra covering finding eigenvalues and eigenvectors as well as the applications of Cayley-Hamilton Theorem. There are some useful tools along the bottom including a PDF worksheet. You can also choose to email me with your questions. | 677.169 | 1 |
Mathematics for the Fundamentals of Engineering Examination / Edition 1…
See more details below
Hardcover
Overview specialized areas of the discipline: chemical, civil, electrical, industrial, and mechanical engineering. With an emphasis on simple logic rather than abstract formulas, it clarifies concepts using every day terminology, 271 numerical examples, and 100 helpful diagrams. In addition, the book shows readers how to conserve time in the examination by making full use of the modern calculator. Reflecting the system that will be used exclusively in the PE Examination, this essential learning tool is written in SI Units. | 677.169 | 1 |
Originally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is... more...
Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition. more...
Don't be tripped up by trigonometry. Master this math with practice, practice, practice!
Practice Makes Perfect: Trigonometry is a comprehensive guide and workbook that covers all the basics of trigonometry that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples,... more...
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly... more...
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine,... more...
This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader's enjoyment and includes a concordance of trigonometric identities, enabling easy reference. Trig or Treat is a must-have for:. • every student of trigonometry, to find the proofs... more...
This volume offers a concise, highly focused review of what high school and beginning college undergraduates need to know to successfully solve the trigonometry problems they will encounter on exams. Rigorously tested examples and coherent, to-the-point explanations are presented in an accessible form and will provide valuable assistance in conquering... more... | 677.169 | 1 |
Oceanography at Fitchburg State University
Challenges to using math in introductory geoscience
Fitchburg State University is a four-year public institution with a diverse student population, which includes those traditionally underrepresented in higher education (first-generation, low-income, and students with disabilities). Approximately half of our incoming students require developmental math coursework, but often enroll in science classes prior to completing them. The result is that many students (mostly non-majors) in our courses lack requisite math skills, but they are taking these courses alongside science majors. The goal of implementing TMYN in Oceanography is to help those under-prepared students gain the math skills needed to succeed in the course, allowing more in-class time for content. The online format of the modules are also beneficial for our students, most of whom commute to campus or have off-campus employment.
More about your geoscience course
This course, which includes 2.5 hours of lecture and 1.25 hours of lab per week, is required for our majors and minors, but most students are enrolled to fulfill their Liberal Arts and Sciences Lab science elective. There are no prerequisites for the course. There are no TAs.
Inclusion of quantitative content pre-TMYN
Students encounter math frequently in this course. Previously, I would typically introduce a calculation in class, have them try it on their own/in groups during class time, and then have a similar calculation as a homework assignment or in lab. For students who had major difficulty with the calculations, I tried to work with them individually during class/lab, encouraged them to work with me outside of class time, and have encouraged some to visit the math help center - but students have reported that the math center is geared toward math classes and not math that is embedded in science classes. Since many of our students have off-campus employment - often full-time - scheduling additional time on campus presents a challenge for them. Incorporating TMYN into this course provides a math resource that can be accessed as a student's schedule allows.
Strategies for successfully implementing The Math You Need
Students complete the pre-test during the first week of class (delivered online, but completed during class). As an introduction to TMYN, students work through the Density modulein class. Density will be discussed during the following week as it relates to oceanic and continental crust and isostasy. The remainder of the modules (described below) were completed outside of class time, with a deadline immediately prior to their use in class/lab.
The first two labs cover seafloor spreading – during the first lab, students calculate spreading rate based on distance from the ridge axis and seafloor age and complete unit conversions (km/Myr to cm/y). The second lab revisits the seafloor spreading data from Lab 1, but students learn to use a spreadsheet to organize and graph data, determine the best fit line, and determine spreading rate from the best fit line. To incorporate TMYN, students will complete Rates and Unit Conversions for Lab 1, and Best Fit Line for Lab 2.
The sediments lab (Lab 4) includes rates again (sedimentation rates), but students will need to rearrange the equations to calculate the age of sediment layers based on sedimentation rate and depth. Students will therefore complete the Rearranging Equations Module before Lab 4.
During the remainder of the course, students can revisit the above modules (as outlined on the syllabus). Students would benefit from working through the unit conversions and rearranging equations modules two times at a minimum, so I encourage this by allowing them to replace a previous quiz score with one that comes later in the semester.
Assessment of their learning is based on pre- and post-test results, as well as quiz scores. The pre-test score does not count for the grade. The module quizzes and post-test are graded and incorporated into their 'Assignments' grade.
Reflections and Results (after implementing)
Overall, the first year of implementation seemed successful. Students improved their math
skills during the course of the semester, as evidenced by the pre- to post-test
gain (25% during fall, 10% during spring).
Students completed most of the modules early in the semester based on
how concepts come up, and they were encouraged to revisit them as necessary
later. TMYN was heavily integrated - I
mentioned TMYN in class almost every day during the first month, and it appeared
in their assignments and labs (e.g., "recall the TMYN rates module that
you just completed - use that information to complete the following calculation
. . . "). It was mentioned with
less frequency later since they had completed most of the modules, but I
reminded them about the modules when new calculations were heading their way. This integration established TMYN as the 'culture'
of the class, and most students responded favorably based on relatively high
participation rates on the modules and improvement in scores. Anecdotally, students also seemed more
willing to ask for additional assistance with calculations, and the fear factor
was less apparent. | 677.169 | 1 |
...
Show More taking place, identify and label important quantities, and set up coordinate axes. Shows readers how to analyze the problem, identify the key physical principles at work, and devise a plan for obtaining the solution. Contains a unique 2-column format. Appropriate for readers interested in Algebra-based Physics | 677.169 | 1 |
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Math Computer Lab Policies
The Mathematics Computer Lab is a place for students to meet and work on mathematics assignments.
Please Do
Refrain from eating food or drinking beverages in the Mathematics Computer Lab Sign MATH COMPUTER LAB visitors book when you come in and leave Login as username: math password: lab Bring a USB flash drive of a CD-R Take your media and belongings with you when you leave Limit your printing to materials for math courses Enjoy our computers and use as many as math applications you like
Please Do Not
Alter any settings on our computers Install any sort of software or hardware View or transmit any offensive materials Transmit any sort of SPAMS Make illegal copies of software Spread worms or computer virus Move computer, monitor, mouse, and any other computer parts Plug or unplug any cables from any computers Leave your materials and belonging at a seat while not using the computers Use computer tables if you are not using the computer Reserve computer(s) for others
Priority for Math Lab Computers:
1) Math classes 2) Students enrolled in our math courses using math software 3) Other students using math software 4) Math majors 5) General students
Lab staff will assist users in the same priority scale.
In addition to the above guidelines, the lab staff reserves the right to resolve conflicts, dispute, or resolve other matters on the basis of rules not explicitly stated herein.
Thank you for your cooperation and enjoy what our math computer lab has to offer. | 677.169 | 1 |
lesson from Illuminations asks students to look at different classes of polynomial functions by exploring the graphs of the functions. Students should already have a grasp of linear functions, quadratic functions,...
Created by Lang Moore and David Smith for the Connected Curriculum Project, this is a module using differentiation to find coefficients of polynomial approximations to functions that are not polynomials. This is one of...
Using this Real World Learning Object, students will use data collected from the Global Sun ? Temperature Telecollaborative project to learn how ?linear functions, quadratic functions and other high-order pol...
Understanding Algebra is a textbook written by James Brennan of Boise State University. The entire contents of the textbook are located on this site, and a PDF version is also available through the author?s Website. B... | 677.169 | 1 |
Eighth grade class studying algebra at middle school
By Michael Jacobson
Starting this fall, eighth graders are solving linear equations like never before at Paynesville Area Middle School. This year, for the first time, one class of eighth graders at PAMS is taking algebra, a subject that traditionally has only been taught at the high school.
Todd Spanier, who is in his third year of teaching at PAMS, taught algebra to eighth graders during his five previous years of teaching in Buffalo. Upon coming to PAMS, the Paynesville native noticed that our math curriculum was not as advanced as that used in Buffalo. He immediately wanted to advance the curriculum and add algebra to eighth grade, but the timing wasn't right until this year.
With all the rearranging in the schedule at the middle school due to the effects of the budget cuts, Spanier decided he might as well suggest adding an algebra class in the eighth grade. "As long as there's so much change, let's throw something else in there," he thought.
The inquisitive algebra class is a teacher's dream, according to Todd Spanier. and has helped other classes.
In conferring with administration and the other math teachers, he found support for adding an algebra class in eighth grade. "I'm glad we're finally doing it," said Deb Gillman, the district's curriculum coordinator. "It's something we've wanted to do for several years."
Spanier has 26 students in the algebra class this year. Students were identified for the class by standardized test scores, by class performance, and by recommendations from math teachers and aides. Letters were sent to students and their parents, who could opt out of the class. None did, though one student left the district.
"My mom thought it'd be good for me," said eighth grader Kristi Louis.
Erica Geurts, another eighth grader in the class, wanted to take algebra this year "because everything else would be a big review," she said.
Brad Hemmesch, another eighth grader, thinks it's fun to be challenged in algebra. The other math classes are too easy, he said.
In seventh grade, the introduction to algebra includes only basic concepts and elementary equations such as a + 2 = 5. Students can solve these equations in their heads (by saying three plus two equals five, so a must be three) without really learning the process of solving an algebraic equation, said Spanier.
"They call it an introduction to algebra, but the numbers are so easy (the students) can just use guess and check," he explained.
So far in algebra, the students have encountered lots of new concepts, including solving equations with negatives, with fractions, and with variables on both sides. A few weeks ago, Spanier surveyed the students in his algebra class to get their input on how the class was going, whether they were going too fast, etc., and was pleased to find that they were satisfied with the pacing.
Spanier loves teaching the class. "It's the ideal class," he said. "It's heaven for a math teacher to have a class like this."
"These guys," said Spanier of the algebra class, "they see it once and they get it."
The kids have taken to the challenge of learning algebra, asking questions of Spanier in class and during study times. Spanier thinks it's much better to challenge them with new material rather than bore these students with the regular eighth grade math curriculum, which includes a lot of review that they don't need. "They've learned it once and they got it. They don't need another chapter of it, another year of it," he said.
And the other eighth grade classes have benefitted, too, Spanier thinks. "When you take 26 kids off the top, you're taking six of the top math kids out of each class. The others have to step it up," he said.
The other classes, though they struggled at first, have developed new leaders and have had students who have gained confidence and started to participate in class more. "It's as beneficial for the other classes as it is for the algebra students," Spanier added. "I think both have benefited. I don't see any losers in it."
They hoped to find used textbooks for the new algebra class, but could not, so they had to buy another set of new textbooks...the same algebra books as used in the high school.
Having algebra in eighth grade should allow students to have more math in high school. In addition to algebra, the high school offers geometry, trigonometry, and analysis. Ultimately, teaching algrebra to eighth graders could pave the way to offering a college-credit math class to seniors, said Spanier.
Or it should at least encourage students to take geometry, trigonometry, and analysis in high school, since they now will have four years to take these three classes, rather than having to take a math class every year. For example, if students are in band and choir, noted Spanier, the only way they can take all three math courses is if they don't have a study hall their senior year.
This means that next year the eighth graders should be mixed with the current ninth graders in geometry, the next step in the progression of the math curriculum. "I'm hoping these eighth graders will be in there and you won't be able to tell the difference," said Spanier.
Geurts, Hemmesch, Louis, and Cary Schlick, another eighth grader, were unanimous in planning to take geometry next year as ninth graders.
Spanier sees adding algebra in eighth grade as the first step in improving the math curriculum. He thinks some years two classes of algebra could be added. And if some concepts were added to sixth and seventh grade math, maybe eventually all eighth graders could take algebra.
Changing the math curriculum that drastically will have to wait at least until it's the math department's turn in the curriculum cycle again, said Deb Gillman, the district's curriculum coordinator. While the review of the curriculum is coming in the next couple years, the math department's turn to purchase materials - new books, etc. - is three years away. | 677.169 | 1 |
Peer Review
Ratings
Overall Rating:
This site is a sub collection of a larger set Manipula Math containing a variety of learning material, both textual and visual. It is a self-contained collection of Java Applets that can be used in the teaching and learning of geometry.
Please see the related reviews of the main href=" Math with Java site, as well as the following sub-sites:
The Manipula Math-Geometry 2 applets are designed to help the user explore the elementary geometry concepts.
Target Student Population:
Students in a geometry course.
Prerequisite Knowledge or Skills:
The applets are self-explanatory. Any geometry student can work with these applets.
Type of Material:
Simulation, animation, and exploration
Recommended Uses:
These applets could be used as classroom demonstration tools or as aids to students problem solving on homework assignments.
Technical Requirements:
A "Java-enabled" browser is required.
Evaluation and Observation
Content Quality
Rating:
Strengths:
Manipula Math-Geometry 2 contains two groups of applets: Circles and Pythagorean Theorem. The groups have 20 and 16 modules, respectively. The applets illustrate the geometry concepts very well, demonstrating the theorems and properties in a simple style. The user will have a more hands on visual knowledge of geometry concepts after exploring with the applets.
The applets vary in their approaches. Most involve the moving of a point or rotation of a figure to demonstrate the principle. A few involve watching as the computer demonstrates a proof one step at a time. Many are activities that could be assigned in a laboratory setting or as homework. For many of the applets, the student can decide whether or not to get a hint. The computer will then sketch the key angle, line, or triangle involved in the solution. The diagrams are well structured in that they contain all the necessary information without being cluttered. In particular, there are eight demonstrations of the proof of the Pythagorean Theorem. The Peaucellier Apparatus applet provides a historical perspective as well as activities for the student. This is an excellent and very useful package.
Concerns:
Occasional grammatical and spelling errors exist.
The Pythagorean Theorem applets all include various misspellings: Pythagoriean, Pytharoras, Pythagrean.
Shortest Distance has errors in terminology, referring to line BC as side BC. The directions should be restated to, ?The points A to G are vertices?.?
Problem of Two Circles (3) does not make the entire conclusion visible when pressing the Next button.
Quoits is a good idea but it only shows purple beads on one side. A bead counter would assist this applet.
Eye Ball Theorem is a dead link.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This site provides a truly excellent teaching tool. The modules are easy to use, have a standard interface, and most come with an explanation section. The activities are exploration based and most can be used without the aid of the instructor. Students can play with the applets to get an intuitive understanding of the geometry concepts and follow-up with a traditional proof. Many of the applets require the student to develop their own conclusion after having manipulated the geometrical objects and are therefore suitable as assignments. These applets will be particularly instructive for the kinesthetic learner. An instructor has the option of selecting from a large variety of visual approaches to the proof of the Pythagorean Theorem.
Concerns:
Feedback is not provided for some of the applets and the student could develop an incorrect conclusion. Instructor intervention to provide the correct answers and require development of proofs for the conclusions generated is necessary to guarantee that the concepts are correctly mastered.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applets have controls that are easy to use, clearly labeled, and self-explanatory in function. Hence, the operation of the applets is fairly intuitive. A short explanation section is always found at the beginning of the more complex applets. Available options give the user good control over the appearance of the graphical output of the modules.
A single user license is available for use offline. Network/site licenses are available for schools, teachers, and researchers. These licenses allow the purchaser to place the applets on home pages and to make changes to the applets by editing the HTML files. The license may be purchased for the Geometry 2 applets only, or for the Manipula Math Applet Collections, which includes additional applets in Geometry,
Trigonometry, Vectors and Calculus.
Concerns:
No concerns | 677.169 | 1 |
Search Results
This course, presented by MIT and taught by professor Sanjoy Mahajan, teaches guessing results and solving problems without having to do a proof or an exact calculation. The material is useful for students who have a...
This algebra lesson helps students connect how logarithms work to the real world example of financing a car. Students will use a formula to calculate the number of months it will take them to pay off a car loan based on...
This intermediate algebra lesson has students use data from the U.S. Census Bureau's website to explore population growth and exponential functions. The learning object demonstrates how these mathematical functions can...
This word document introduces a lesson that helps students work out how much they would actually pay for a house with a 30-year fixed-rate mortgage, with interest included, after 30 years. The material involves working...
This algebra lesson from Illuminations involves slope as a rate of change. Distance-time graphs for three bicyclists climbing a mountain are compared and contrasted. The material will help students understand how to... | 677.169 | 1 |
Like the guys above said, you can think of Linear Algebra is a sort of "sophisticated, ideal form" of an algebraic structure. The study of L.A. focuses on vector spaces. In algebra, you can relax certain axioms of vector spaces and generalize groups, rings, and fields (among other things...). Conversely, you can start with basic group/ring theory and build up by adding axioms to form an algebraic vector space.
–
JeffAug 23 '12 at 9:08
Adding to other comments: Linear models and multivariate analysis in statistics can be seen as a sort of "advanced linear algebra". I have learnt a lot of linear algebra stuff from appendices to such books!
–
kjetil b halvorsenSep 22 '12 at 18:52
4 Answers
4
At my [undergraduate] university [which was University of Cincinnati, at the time of this post], the first linear algebra sequence is taught to sophomores. It is mostly computational. Everything takes place in the reals and complex numbers. The class begins with row reducing and culminates with finding determinants and eigenvalues. I don't remember which book we use for this but it's terrible and the class is very easy.
Later, students are encouraged to take "abstract" linear algebra, which focuses on abstract vector spaces (though they are all assumed to be over fields of characteristic $0$), inner product spaces, quadratic forms, proving the spectral theorem, and culminates with Jordan canonical form and the theory of convex sets. For this we use Lang's linear algebra. More emphasis is placed on the spectral theorem than anything, with Jordan form and convex sets only if the class moves fast enough so there's time.
Finally, after a student has taken the senior level abstract algebra sequence (featuring the basics of groups, rings, and fields), he may elect to take the graduate algebraic structures class, in which module theory, more advanced ring theory, and some representation theory are covered. For this class we use Dummit and Foote (and whichever other books we feel like). [At my incumbent university, University of Florida, basic ring and module theory is done in the first year graduate course, also using Dummit and Foote. Multilinear algebra (tensors) and more advanced ring theory are covered during spring semester of second year graduate algebra, which concurrently uses Lang, Hungerford, and Matsumura.]
I have heard that other universities offer graduate courses strictly in advanced linear algebra. An example of a book they may use is Roman, which I have used as a reference many times and I must say I like very much.
Different universities will teach different things under the heading "advanced linear algebra", and at different levels. I would suggest you go to a few university websites and see what they have on offer and what the contents are.
First of all, it's not clear what an advanced course in linear algebra at either the undergraduate or graduate level consists of. It really depends on what the first course consists of and this varies enormously from university to university depending not only on the background and career paths of the students, but the aims of the instructor. It can be a largely applied course where rigorous theorems about linear transformations and abstract vector spaces are either largely avoided or downplayed, such as those based on Gilbert Strang's textbooks. It can also be a highly abstract course where applications are barely mentioned at all and the fine theoretical structure of finite dimensional vector spaces is developed in full detail, such as Axler's, Halmos' or Hoffman/Kunze's textbooks. And there are textbooks which try to steer a middle course between the 2 extremes, developing both theory and application in more or less equal measure. The classic example of this kind of course is Charles Curtis' textbook.
I'm quite sympathetic to the last kind of textbook - finding both the theoretical and applied sides of linear algebra to be of equal importance in developing the subject in it's fullest utility for both mathematicians and scientists.
Then again, it's not that cut and dried often, either - often actual courses in linear algebra resist such simple classification - therefore, advanced courses to follow such classes up will be even more difficult to construct. Gilbert Strang's justly famous course at MIT, for example, is a course built around the applications of linear algebra to real world problems. But it's hardly a plug-and-chug, mindless algorithm course: Strang analyzes each application and algorithm, as well as the theory behind it, thoroughly. But at the same time, it's not really an abstract mathematics course the way we describe it-the deep theorems and proofs of linear algebra, while not ignored, are not really the core concerns of the class. For Strang, the abstract theory of linear algebra is really the domain of an abstract algebra course. (Indeed, Strang's course is partially designed to provide a mastery of the computational aspects of linear algebra needed for MIT students to go on to effectively study modern algebra in Micheal Artin's equally famous course!). However, this is MIT we're talking about-hardly your average program with average mathematics majors.
In my experience, what most people mean when they say "advanced linear algebra", they mean the abstract theory of linear operators in the context of modern algebra. At most universities, this material is covered in serious abstract algebra courses at either honors undergraduate or first-year graduate level. This means the study of R-modules over commutative rings in the special case where R is a commutative division ring i.e. a field. This means modules, algebras over R, submodules, R-module maps, product spaces, the Jordan-Holder theorem, tensor products, dual spaces, free modules and perhaps some elementary homological algebra. As I've said, this is usually covered in the student's first substantial year-long algebra course, at either the undergraduate or graduate levels.
Also in my experience, there usually isn't a separate "advanced linear algebra" class for students at the advanced undergraduate or graduate level. But there are exceptions. For example, Peter Lax's linear algebra book is based on a graduate course on the subject that he's taught there for many years designed to bring incoming graduate students at NYU who are weak in linear algebra up to speed for a second year functional analysis course. Lax became frustrated with the anemic skills in basic linear algebra most graduate students at NYU had and designed this course to rectify this very damaging lacuna in thier training.
If you're looking for a text that focuses purely on the abstract theory of linear operators, the best book is probably Module Theory: An Approach To Linear Algebra by T.S. Blythe. THE book on the subject and sadly, out of print and hard to find. Here's to Dover republishing it.
+1 for comments on Gilbert Strang's book, I don't know about other books, but I find Insel is good book to start learning Linear Algebra.
–
RamJan 6 '13 at 3:40
@Ram I like Friedberg,Insel and Spence a great deal-it's extremely well written,careful,comprehensive and has a wealth of applications in addition to careful theory. The problem with this book is that it's TOO comprehensive-unless you assign huge chunks of the book to the students for independent reading,you'll never get through most of the book in a year,let alone one semester! Curtis is a similar book of a much more manageable size. Also, the section on diagonalizable matrices and the Jordan form in Friedberg,et.al is a mess,frankly.The presentation in Curtis is much clearer.
–
Mathemagician1234Oct 28 '14 at 5:35
To answer your question succinctly, a first course on linear algebra should cover the basic computational tools: row reduction, determinants, and eigenvalues. A more advanced course should force the students to come to terms with more abstract language (vector spaces over an arbitrary field), and it should contain a sophisticated treatment of the spectral theorem. In an ideal world it would also introduce multilinear algebra and/or the canonical forms, but these topics are often reserved for graduate courses (often in the context of rings and modules).
In practice there is quite a large gap between advanced undergraduate and graduate algebra. This can lead to strange circumstances wherein students first learn about tensor products in a differential geometry course or the Jordan canonical form in a number theory course. I recommend that undergraduates take as much linear algebra as possible since good graduate programs will often assume that students know more linear algebra than they do in practice. | 677.169 | 1 |
books.google.com - This book includes over 1500 exercises, many with multiple parts, ranging in scope from routine to fairly sophisticated, and ranging in purpose from basic application of text material to exploration of important theoretical or computational techniques. The structure of the book permits instructors and... Algebra
Abstract Algebra
This book includes over 1500 exercises, many with multiple parts, ranging in scope from routine to fairly sophisticated, and ranging in purpose from basic application of text material to exploration of important theoretical or computational techniques. The structure of the book permits instructors and students to pursue certain areas from their beginnings to an in-depth treatment, or to survey a wider range of areas, seeing how various themes recur and how different structures are related. The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible. Contains many topics not usually found in introductory texts. Students are able to see how these fit naturally into the main themes of algebra.
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Review: Abstract Algebra
User Review - Justin - Goodreads
Wow. Another page turner. This is a wonderful text for anyone looking to learn abstract algebra. No wonder it's called the algebra bible! David S. Dummit weaves in tons of juicy examples for basically ...Read full review
Review: Abstract Algebra
User Review - Angm81 - Goodreads
I certainly wouldn't say I liked this book, but I wouldn't say I liked any advanced math textbook. It did help me survive a 600-level Abstract Algebra class, though. The book itself was frustrating in ...Read full review | 677.169 | 1 |
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Tom Adams made this video for the Algebra for All Project social network Part of this project involved the use of technology in the classroom, a document camera and projector. Videos can be uploaded to schools websites to be viewed on the internet. Tom uses his videos for the kids to review at home while doing their homework, or for students to make-up lectures after absences. Document cameras are widely used in education now, and many teachers can benefit from video. Topic: algebra, polynomials, add, subtract, multiply, adams, thomas, slope, intercept, system, inequality,...
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Search Results
This website from David M. Harrison of the University of Toronto's physics department provides an animation of the addition of two vectors. Instructors may use this animation in explaining the concept of adding vectors...
This page is interactive resource allowing the teacher to choose among topics related to vector operations. The subjects are organized in flow charts that make it easy to move from one topic to a related item. Vector...
This applet demonstrates a method to find two vectors that sum to a given vector. The component vectors can be in any directions relative to the given vector and each other. This is a generalization of finding...
Linked essay covering the beginning of the vector concept and the move away from coordinate methods through the beginning of the 20th century with Peano, Hilbert, Schmidt and Banach, with 13 references (books/articles).
An idiosyncratic and personal selection of particularly important or particularly intriguing mathematical equations, not all of them complicated. Mathematical Constants; The definition of Pi; The definition of e; A... | 677.169 | 1 |
Provides information to develop primary and secondary school mathematics materials and textbook series (OER or paper)....
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Provides information to develop primary and secondary school mathematics materials and textbook series (OER or paper). Content (uses 1000 of the most commonly historically used terms), content distribution (used within many textbook and OER series from 1972 to the present), standards (within the United States and other countries), curriculum parameters and sources of information to develop examples and excercises are provided. Spreadsheets are used to help understanding. Information is displayed in English, Spanish-12math.info to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material k-12math.info
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This first grade textbook provides an orderly development of historically grade level appropriate content that contributes to...
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This first grade textbook provides an orderly development of historically grade level appropriate content that contributes to the proper evolution of elementary school mathematics. It was created from some of the 24,377 modules in the CONNEXIONS collection, housed at Rice University, Houston, Texas. This textbook has from its creation in 2009 been the pioneering Open Educational Resource (OER) textbook for this Grade 1 to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Mathematics Grade 1
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This completely self-contained text proceeds from the fact that mathematics derives from the real world. For instance,...
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This completely self-contained text proceeds from the fact that mathematics derives from the real world. For instance, logical consequence is nothing but a reflection of real-world causality and statements are true or false, not because some author says so, but because the real world makes them necessarily so. Particular attention is given to the language needed to discuss and understand matters. The text is part of a package including homeworks, reviews, exams that is suitable for teaching a course in Developmental Math. The package is itself a standalone version of part of a much larger package, in progress, that should provide people with a realistic chance of going from Arithmetic to Differential Calculus in three semestersasonable Basic Algebra With Homework, Reviews and Exams to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Reasonable Basic Algebra With Homework, Reviews and Exams
Select this link to open drop down to add material Reasonable Basic Algebra With Homework, Reviews and Exams to your Bookmark Collection or Course ePortfolio | 677.169 | 1 |
This book examines the development of mathematics from the late 16th Century to the end of the 19th Century. Each chapter will focus on a particular topic and outline its history with the provision of facsimiles of primary source material along with explanatory notes and modern interpretations. - ;Aimed at students and researchers in Mathematics, History... more...
Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices... more...
This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key point to understanding their structure and classifying them lies in the hyperbolic geometry of the unit disk. The book develops a number of important problems whose... more...
A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered... more...
Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics. - ;This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights... more...
This book presents the first five Abel Prize in Mathematics winners, from 2003 to 2007. Leading experts in the field detail the work of each Abel Prize winner. The book also includes a brief history of the Abel Prize. more...
Writings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills... more... | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Basic Business Math
A basic understanding of decimals and percentages is key to any businessperson, whether tallying costs for warehouse supplies or estimating resource allocation.
Therefore learn to use decimals, addition, subtraction, multiplication, and division; and to solve problems involving percentages.
Also, knowledge of ratios and averages is indispensable in the business world. Using real-world scenarios, this course explains the concepts of ratio, proportion, and how to compare different kinds of numbers; and discusses simple, weighted, and moving averages. | 677.169 | 1 |
Developing Mathematics: Probability Through Algebra: Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in secondary level, and is related to the mathematical theme of the Institute. Careful work on this topic allows teachers (and students) to understand exactly how elementary and more advanced procedures in the specific content area are derived and generalize. The course is structured so that each participant can work at his/her own level. Those who are more mathematically advanced may be asked to help those with less preparation. The course is conducted by teacher leaders from the PROMYS program at Boston University. The focus of this strand is entirely on mathematics, although opportunity is provided within the course for reflection on the approach used by the instructors and to consider the implications of such an approach for teaching in secondary classrooms. The topic for the summer is described below:
You're at deuce in a tennis game and are 60% likely to win each point. How likely are you to win the game? What is the probability that you roll a sum of 13 when 5 dice are thrown? What is the most likely sum when 5 dice are thrown? Take an expression like x^6+x^5+x^4+x^3+x^2+x and raise it to the fifth power.
What do you get? If you raise it to higher and higher powers, what is the distribution of the coefficients "in the long run?" How does the "random" button on your calculator work? What's the probability that two positive integers, chosen at random, have no common factor? And most importantly, what do all these questions have to do with each other?
In this three-week course, we'll investigate questions like these (and more). No background in probability or polynomial algebra is assumed, but by the end of three weeks, we promise beautiful mathematical ideas that will make your head spin.
July 2 - July 20, 2007
Download Days 1 - 14 [PDF file]
[PCMI generic login required to access original file] in press for publication in 2015, American Mathematical Society
NOTE: As you select any of the links listed above, they will download as PDF files. To open PDF files use Adobe Acrobat Reader, available free from Adobe: | 677.169 | 1 |
Title Card: Now the class is aware of the principles for real numbers which correspond with those for number of arithmetic. However, the students find that
there are additional principles for real numbers.
Title Card: From Lesson 29 . . .
Title Card: Lesson 30 The Next Day
Title Card: Lesson 48
Title Card: Lesson 49
Title Card: Lesson 50
Title Card: This Film is Background for:
Basic Principles for Real Numbers Part IV e_mb_0017
Numerical Variables: Developing the Concept e_mb_0020
Bound Variables: Developing the Concept e_mb_0021
Prelude to Deduction e_mb_0023
Substitution and the Linking Rule e_mb_0024
Prelude to Proof-Making e_mb_0025
Proving Generalizations e_mb_0026, e_mb_0027
Principles and Discovery in Algebraic Manipulation
Credits [Title cards]
Instructor: Max Beberman
Produced by the University of Illinois Committee on School Mathematics
with grants from the National Science Foundation and the US Office of Education
Metadata
Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part III: Principles of Arithmetic for Real Numbers
Identifier:
e_mb_0016
Related:
e_mb_0046
e_mb_0001
e_mb_0007
e_mb_0008
e_mb_0017
e_mb_0020
e_mb_0021
e_mb_0023
e_mb_0024
e_mb_0015
Description:
Max Beberman leads students on an investigation to find and prove various mathematical principles, including the Communitive
Principle for Multiplication of Real Numbers, the Associative Property for Addition of Real Numbers, the Communitive Principles for Addition of Real Numbers, and the Principle for Adding the
Real Number Zero. The students learn to check their findings and develop a working acquaintance with all of the principles. They also begin to use letters as variables to indicate patterns and
to generate terms and sentences. In addition, Beberman introduces the pupils to using letters as indices to modify a sentence to indicate generalizations, which is discussed in future films.
Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965. | 677.169 | 1 |
Developmental Mathematics: Basic Mathematics and Algebra
9780321599209
ISBN:
0321599209
Edition: 2 Publisher: Addison Wesley
Summary: Lial, Margaret L. is the author of Developmental Mathematics: Basic Mathematics and Algebra, published under ISBN 9780321599209 and 0321599209. One hundred twenty two Developmental Mathematics: Basic Mathematics and Algebra textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $34.98, or buy new starting at $133.75.the primary subject of this book is math. Its basic math, such as addition, subtraction, multiplication and division but not only that. It contains many more mathematical equations that are useful and good to go over and study. It was effective in my math class I was taking because it helped me not only review what I already knew but also to go over fractions which I really do not like. | 677.169 | 1 |
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Making Math Is a User Interface for Computer-Based Math™
Scott Gray
In this talk from the Wolfram Technology Conference, Scott Gray, director of Making Math at O'Reilly Media, shares his views on Computer-Based Math™ and gives an overview of the Mathematica-based online course platform he's developing as a user interface to mathematics | 677.169 | 1 |
...It is a foundation course for both higher math and science education. It is also very useful in several quantitative business and economics courses. As a math major in college and a management science PhD, I can attest to the importance of mastering basic Algebra | 677.169 | 1 |
Mathematicians After 1700 - MAT-913 stories behind mathematical discoveries are fascinating but rarely told. When students learn how persons like themselves have discovered and shaped mathematics, their interest and motivation grows. This course examines the lives and work of great mathematicians who lived after 1700. It is designed to help teachers of grades 3-12 show the human dimension of mathematics.
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"The course was clear, concise and allowed me to work at my own pace and to travel with it. For example, while at lunch I was able to spend a few minutes working on it versus being too complicated to take out in short stretches of time to work on it." | 677.169 | 1 |
Textbooks in Mathematics
The authors of this classroom-tested, student-friendly text illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems such as congruences in the ISBN system…
Theory,Technique and Practice with Boundary Value Problems
This version of the primary text (published in 2014) adds a chapter of Sturm Liouville theory and problems to the current manuscript. This coverage creates a Boundary Value Problems version to add this coverage for instructors who look to offer it in the Ordinary Differential Equations course.
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Designed for a one-semester undergraduate introduction to numerical methods, this text covers both the theory and practice of numerical methods for mathematics and engineering. With a wealth of exercises, it emphasizes the practical aspects of numerical methods and addresses their advantages and…
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern…
Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need…
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Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.
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Using Maple and MATLAB, Third Edition
Mathematical Modelling with Case Studies: Using Maple™ and MATLAB®, Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting…
The Essentials of a First Linear Algebra Course and More
Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the…
Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.
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An Introduction to Probability
The Mathematics of Games: An Introduction to Probability takes an inquiry-based approach to teaching the standard material for an introductory probability course. It also discusses different games and ideas that relate to the law of large numbers, as well as some more mathematical topics not…
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon–delta methods.…
Labs and Projects with Mathematica ®
Exploring Linear Algebra: Labs and Projects with Mathematica® is a hands-on lab manual for daily use in the classroom. Each lab includes exercises, theorems, and problems that guide your students on an exploration of linear algebra.
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Theory, Technique and Practice, Second Edition
"Krantz is a very prolific writer. He … creates excellent examples and problem sets."—Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA
Designed for a one- or two-semester undergraduate course, Differential Equations:…
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and…
From Elementary Calculus to the Beginnings of Analysis
This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to…
Exploration, Applications, and Theory
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential…
Unlike other books on algebraic geometry, this text includes applications from various areas of mathematics, biology, and physics. Designed for advanced undergraduate and graduate students with an applied mathematics background, the book develops most of the necessary commutative algebra. It…
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich…
An Inquiry Based Approach
To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how…
Theory and Practice
Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical…
A Readable yet Rigorous Approach to an Essential Part of Mathematical ThinkingBack by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along…
A Unified Development
Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and…
Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to…
Applications, Models, and Computing
In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a…
Updated to conform to Mathematica® 7.0, Introduction to Probability with Mathematica®, Second Edition continues to show students how to easily create simulations from templates and solve problems using Mathematica. It provides a real understanding of probabilistic modeling and the analysis of data…
An Interactive Approach
By integrating the use of GAP and Mathematica®, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several…
Brings Readers Up to Speed in This Important and Rapidly Growing Area
Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology.…
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With an emphasis on mathematical thinking and problem solving, Mathematics in Games, Sports, and Gambling — The Games People Play shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples,…
A Transition
Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics Courses
Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize…
Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering.…
A First Course with Applications
Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to GoogleOne of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to…
A Physical Approach with Applications and MATLAB
From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with…
Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these…
Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray's famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and…
Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come.The…
Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors…
With a growing range of applications in fields from computer science to chemistry and communications networks, graph theory has enjoyed a rapid increase of interest and widespread recognition as an important area of mathematics. Through more than 20 years of publication, Graphs & Digraphs has…
Models, Methods, and Analysis with MATLAB and MPI
Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses…
A Differential Equations Approach using Maple and MATLAB, Second Edition
Certain basic modeling skills can be applied to a wide variety of problems. It focuses on those mathematical techniques which are applicable to models involving differential equations. Models in three different areas are considered: growth and decay process, interacting populations and heating/…
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward…
Newcomers to the world of probability face several potential stumbling blocks. They often struggle with key concepts-sample space, random variable, distribution, and expectation; they must regularly confront integration, infrequently mastered in calculus classes; and they must labor over lengthy,… | 677.169 | 1 |
Introduction
We here introduce vectors and matrices and the notion of
dot product and matrix multiplication.. We notice that the
dot product is invariant under coordinate rotations, define
linear dependence, and describe polar coordinates and their
generalizations to three dimensions. | 677.169 | 1 |
Abstract and Linear Algebra to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Elements of Abstract and Linear Algebra
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This section of a broader work, gives students a series of tutorial exercises in matrix multiplication. Topics include...
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This section of a broader work, gives students a series of tutorial exercises in matrix multiplication. Topics include matrix multiplication, vector multiplication, and the identity matrix. This page presents students with question that the enter answers to. Students are given feedback based on there:Matrix Multiplication to your Bookmark Collection or Course ePortfolio
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'Learn solving two equations system by example, by plugging the equation Coefficients. You will be able to build your...
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'Learn solving two equations system by example, by plugging the equation Coefficients. You will be able to build your examples, which is the best way to learn Algebra. This application provide step by step solution to the two equation system in additions to providing the value of x and y. Enter the equation Coefficients and see the full solution which can be sent as an email message.״Solve and email solutions with steps of the two equations two variables system.״Do you want to solve the "two equations, two variables" instantly?Ax + By = C [1]Dx + Ey = F [2]All you need to do is enter the values for A, B, C, D, E, and F and select Solve to get the values of X and Y. For Example, one can enter the following values3x + -2y = -4-3 + 5y = 8 Why go through the hassle of performing complex steps of solving the equations, when this program will not only solve your equations reliably, but also will always get you the correct results guaranteed. This program will help you focus on solving the bigger problems in physics, calculus, complex financial and Engineering problems. Why spend money and time programming your programmable calculator when you can use this program already on your iPhone or iPod Touch.Current features -(1) Show step by step solution(2) Able to email the equation, with the detailed solutionAlgebra Helper will help you in your Math problems, and this is the first application focusing on Linear Algebra, two equations, two variables problem Helper 1 App for iOS to your Bookmark Collection or Course ePortfolio
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Select this link to open drop down to add material Matrix multiplication: an interactive micro-course for beginners Solving Equations by Combining Like Terms to your Bookmark Collection or Course ePortfolio
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Summary:The purpose of this module is to gain a better understanding for boolean functions and truth tables for these functions, by both looking at a general case and a specific example of a boolean function.
Subject:
Mathematics and Statistics,
Science and Technology
Language:
English
Popularity:
35.80%
Revised:
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Closer and Closer: Introducing Real Analysis
Publisher:
Jones and Bartlett
Number of Pages:
438
Price:
134.95
ISBN:
9780763735937
Closer and Closer is a new textbook for undergraduate real analysis. There is near-universal agreement on what an undergraduate class in real analysis should cover, and the table of contents of this book corresponds to that consensus. Closer and Closer stands out not for its choice of topics but for how those topics are presented.
Closer and Closer is divided into two parts: "central ideas" and "excursions." The central ideas are the main theory of the real analysis, while the excursions are common examples and applications. A glance at the table of contents would suggest that the two parts are to be covered sequentially. That is not the intention. The excursions are meant to be covered thoughout the course of the main development. The chapters include pointers directing students to specific excursions once they have sufficient background.
Why separate the applications from the main development? This doesn't seem necessary, but there are perhaps a few advantages. First, it may help students distinguish the basic theory from specific examples. Second, it could help instructors decide what material to cut if a course is running out of time. On the other hand, most the material in the excursions is essential. Labeling these topics as "excursions" might imply that they are less important than they actually are.
The strength of Closer and Closer is its exposition. Schumacher does a fine job of proving theorems rigorously, but also provides intuitive explanations and motivation. While such exposition is appreciated in any mathematics book, it is especially important in real analysis. A course in real analysis is of course supposed to present the basic results of real analysis. But it also does much more. It teaches students to take intuitive ideas and express them as rigorous mathematical statements. Other courses do the same, but in general it is more difficult to formalize continuous mathematics than discrete mathematics.
The history of mathematics bears this out. The material in a rigorous real analysis course represents the conclusion of decades of research and heated debate on the foundations of continuous mathematics. It is especially important in real analysis to explain the correspondence between formal mathematics and intuitive notions.
Closer and Closer contains in written form much of the dialog given in lecture by a good instructor but not often committed to paper. Having such good explanations in the textbook may allow an instructor to devote a little more class time to discussion and problem solving.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour. | 677.169 | 1 |
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About the book:
Mathematics majors learn the underlying concepts and how to apply them to problem solving and proofs in this introduction to the fundamentals in mathematical reasoning and the basic properties of the real numbers and set theory. Proof techniques are covered in detail so that students gain the background they need for courses in abstract algebra and real analysisDaniel Borlean via United States
Softcover, ISBN 0030928001 Publisher: Brooks Cole, 1993 Usually ships in 1-2 business days
Softcover, ISBN 0030928001 Publisher: Harcourt College Pub, 1993 Softcover. Used - Good Good . Minimal damage to cover and binding. Pages show light use. With pride from Motor City. All books guaranteed. Best Service, Best Prices.
Softcover, ISBN 0030928001 Publisher: Brooks/Cole, 1993 Used - Acceptable, Usually dispatched within 1-2 business days, Ships from the USA. Please allow up to 21 business days for delivery. Book selection as BIG as Texas.
Softcover, ISBN 0030928001 Publisher: Brooks/Cole, 1993 Used - Acceptable, Usually dispatched within 1-2 business days, Ships from the USA; Allow 2 to 3 weeks for delivery. Book selection as BIG as Texas.
Softcover, ISBN 0030928001 Publisher: Brooks/Cole, 1993 Used - Good, Usually dispatched within 1-2 business days, Ships from the USA; Allow 2 to 3 weeks for delivery. With pride from the Motor City. Minimal damage to cover and binding. Pages show light use. | 677.169 | 1 |
Mathematics is a creative and highly inter-connected problem solving discipline developed over centuries. Through history, mathematics has been essential for solving some of the most intriguing problems and today it is just as necessary for everyday life. Although we now have technological advances to solve many difficult calculations, these are a direct result of mathematical knowledge and the needs for mathematical thinking in science, technology and engineering, demonstrating its power and importance.
The mathematics curriculum provides a foundation for understanding and develops reasoning, ability whilst also developing enjoyment and curiosity about the subject.
Aims
We aim to develop pupils' understanding of key mathematical concepts and processes in order to enable pupils to solve problems using a variety of techniques and skills. This requires pupils to be fluent in the fundamentals of mathematics and to reason mathematically. This is turn happens through repeated practise to increase fluency and mastery, application of skills to familiar and unfamiliar contexts, learning of formulae, application to calculations, analysis and interpretation of mathematical information, as well as contextualising and applying appropriate elements to situations within which pupils are familiar.
Areas of study/Subject content
Number
Algebra
Ratio, proportion and rates of change
Geometry and measures: learn and apply formulae in order to calculate problems.
Probability
Statistics
Year 7 – All year 7 pupils start secondary mathematics with strong links to STEM (Science Technology Engineering and Mathematics). This enables Pupils to develop a depth of understanding for core operations + - × ÷ with strong links to physical application to support their understanding of core concepts.
Key Stage 3 - Throughout Key Stage 3, all pupils study mathematics covering the full spectrum of: Number, Calculating, Algebra, Geometry and Statistics. These sit alongside Mathematical Processes and Applications and Functional mathematics in order to develop independent mathematicians with skills which are transferable to other subject areas.
Key Stage 4 - All pupils are studying a Linear GCSE mathematics course set by Edexcel. This is a two year course with two examination papers sat in the summer of Year 11, one of which is a calculator paper and the other a non-calculator paper. These will test the core skills of Number, Algebra, Geometry, Statistics, Probability and Ratio.
Courses
offered
Key
stage/year:
Qualification:
Main topics students study &
Main skills students develop:
Compulsory
Collins Mathematics
KS3
National Curriculum
Main topics students study:
Number
Algebra
Shape
Data
Main skills students develop:
Our 2 year KS3 course is designed to ensure our pupils have the full tool kit in Mathematics that they need to tackle GCSE.
It builds on their numeracy and starts to develop their ability to use and manipulate algebra.
It also continues to develop their skills in data handling and shape, space and measure.
Functional Mathematics is built into the course and is also the focus of a dedicated lesson every half term.
We teach the Edexcel linear course with pupils either following the foundation or higher specification.
The foundation course covers a range of topics in Number, Algebra, Shape and Data handling up to C grade. It emphasises pupils ability to use these skills and also be able to apply them to real life problems.
The higher course takes these topics further so pupils can tackle more complex problems, as well as giving them the basis they need to use Mathematics beyond GCSE. | 677.169 | 1 |
Mathematica is a tool for quantitative methods from simple calculator operations to large-scale programming and interactive-document preparation in scientific research, engineering analysis and modeling.
With Mathematica use growing on campus, we've been asked by several Mathematica users how they can access documentation and training. Here are a few resources that new and experienced users will find useful in building their Mathematica skills.
The Wolfram Mathematica Tutorial Collection is an invaluable aid to students and faculty who use Mathematica in their work. This 23-title collection documents the features and capabilities of Mathematica 7--from graphics to data analysis to programming--and can be viewed online, dowloaded as a PDF, or ordered in print:
Users who wish to explore additional resources for learning Mathematica are also invited to check out the Wolfram Mathematica Learning Center. From screencasts to seminars to "How-tos", the Learning Center offers a variety of ways for users to learn the skills they need to make the most of their use of Mathematica:
If users are interested in more comprehensive training, Wolfram also offers a variety of courses through the Wolfram Education Group, many of which can be held on campus and adapted to specific needs. Onsite training offers a fast and inexpensive way to make a whole group productive with Mathematica, often for less than $250 per person. For more information please contact the Helpdesk to forward to the UT Arlington Wolfram Representative. | 677.169 | 1 |
,...
Show More, and meaningful ways. Features abundant, step-by-step, annotated Examplesthat provide a problem-solving approach to reach the solution; annotations are conversational in tone, explaining key steps and ideas as the problem is solved. Begins each section with a compelling vignette highlighting an everyday scenario, posing a question about it, and exploring how the chapter section subject can be applied to answer the question. A highly readable reference for anyone who needs to brush up their mathematics | 677.169 | 1 |
Open Educational Resource
Description The purpose of this course is to support your personal growth in knowledge, skills, abilities, and motivation as you pursue your educational goals and embark on life-long learning. This self-paced course has been developed in order to get you "prepared" for college-level math, reading, and English. Our goal is to help you:
• Strengthen your reading, writing, and math skills
• Provide you with opportunities to practice your skills
• Provide you with a solid foundation – so that you can more successfully adapt to college-level work. Please note each of the three skill areas -- reading, writing and mathematics -- are independent of one another. So if you only need assistance in one or more of these subject areas please feel free to focus on that section. This self-paced course has been developed in order to get you "prepared" for these important subject areas. | 677.169 | 1 |
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Recently changed in this version
Description
The universe is fully dependent on mathematics. Here in "Mathematical Formulae" you can learn the basic formulas in mathematics.
It is an offline app which acts as a portable library of significant mathematical formulas.
The app covers the following:-
ALGEBRA
CALCULUS
GEOMETRY
TRIGONOMETRY
The further sub-section contains basic properties and methods to solve.
You don't need to carry a formula book in your hand.
Our commitments are respecting user privacy and delivering cool experience. Please help us by rating this app and recommending to the others. | 677.169 | 1 |
Search Results
This learning object from Wisc-Online covers the sphere, examining the properties and components of the shape. The lesson uses the geometric formulas for finding the volume and surface area of the shape. Practice...
This learning object from Wisc-Online covers solving systems of linear equations using the addition or subtraction method. The unit looks at the common solution to simultaneous linear equations (also referred to as...
This learning object from Wisc-Online covers solving systems of linear equations using the substitution method. The unit looks at the common solution to two or more linear equations in two variables. Practice questions...
This learning object from Wisc-Online covers trade discount word problems. The lesson teaches a method of solving these problems which requires students to memorize only one equation. Example problems are included.
This learning object from Wisc-Online covers the properties of equality as related to algebraic equations. The unit's activities include defining the terminology and properties of equality associated with algebraic... | 677.169 | 1 |
Rick Hansen Secondary School 2011-2012
DEPARTMENT: Mathematics CODE: MCR 3U0
COURSE: Functions, Grade 11, University Preparation CREDIT: 1
PREREQUISITE: Principles of Mathematics, Grade 10, Academic
TEACHER: Ms. Johal PHONE: (905) 567-4260 x 533 (voicemail)
STRONGLY RECOMMENDED PREPARATION: 75% or higher in MPM 2D0
COURSE DESCRIPTION:
This course introduces the mathematical concept of the function by extending students' experiences with
linear and quadratic relations. Students will investigate properties of discrete and continuous functions,
including trigonometric and exponential functions; represent functions numerically, algebraically, and
graphically; solve problems involving applications of functions; investigate inverse functions; and develop
facility in determining equivalent algebraic expressions. Students will reason mathematically and
communicate their thinking as they solve multi-step problems.
Throughout this course, students will:
• Develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve
problems and conduct investigations, to help deepen their mathematical understanding;
• Develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-
examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify
conclusions, and plan and construct organized mathematical arguments;
• Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding
as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and
processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying
solutions);
• Select and use a variety of concrete, visual, and electronic learning tools and appropriate computational
strategies to investigate mathematical ideas and to solve problems;
• Make connections among mathematical concepts and procedures, and relate mathematical ideas to
situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events,
art and culture, sports);
• Create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical,
pictorial representations; onscreen dynamic representations), connect and compare them, and select and
apply the appropriate representations to solve problems;
• Communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary
and a variety of appropriate representations, and observing mathematical conventions.
OVERALL EXPECTATIONS:
By the end of this course, students will be able to:
Demonstrate an understanding of a variety of functions (including quadratic, exponential, trigonometric,
and discrete functions), identify and represent these functions and their inverses, describe properties
of these functions, and make connections between the numerical, algebraic, and graphical
representations of these functions using transformations;
Demonstrate an understanding of: expressions containing rational exponents and radicals; recursive
sequences and their connection to Pascal's Triangle; trigonometric ratios for angles less than 360 ;
0
periodic relationships and sinusoidal functions;
Solve problems involving functions, including those arising from real-world applications ;
Demonstrate an understanding of arithmetic and geometric sequences and series, make connections to
financial applications, and solve related problems (including those involving compound interest and
annuities).
TECHNOLOGICAL EXPECTATIONS:
Information and communication technologies provide a range of tools that can significantly extend, enrich,
and support student learning in Mathematics. Technology will be used, where appropriate, to reduce the
time spent on routine mathematical tasks, to allow students to devote more of their efforts to thinking and
concept understanding and development. For example:
1. Throughout the term, students will be required to access and print material from the course website:
myclass.peelschools.org, select Rick Hansen Secondary School from the second drop down menu;
find the course code. MCR 3U0 Attia.
2. Students will be provided with instructions to download Virtual TI and Geometers' Sketchpad. This will
provide them the opportunity to have access to graphing calculator and dynamic geometry software
outside of the classroom. Students' access to these resources is a course expectation, and assignments
may require that the student use this software. Students will also be given the opportunity to use this
and other software in the classroom.
ASSESSMENT & EVALUATION:
Assessment and evaluation will be based on provincial curriculum expectations and will incorporate the four
categories of the Provincial Achievement Chart with approximately the following weightings:
Knowledge & Application Communication Thinking
Understanding
23% 30% 17% 30%
tests problem solving appropriate use of mathematical investigations
quizzes problem posing language & symbols construction of
assignments applying individual or group presentations mathematical models
mathematical journals problem solving
models portfolios
NOTE: On some assessment tasks, students will be graded using a rating scale called a rubric. Based on
any of the categories of the Provincial Achievement Chart for Mathematics, a student's work may be rated
at a particular level. At some point, these "levels" will be converted to percentage grades using the
following conversion table:
LEVEL CONVERSIONS:
LEVEL % Grade LEVEL % Grade LEVEL % Grade LEVEL % Grade
4++ 95 – 100 3+ 78 2 65 1- 52
4+ 93 3 75 2- 62 R+ 45
4 88 3- 72 1+ 58 R 40
4- 82 2+ 68 1 55 R- 0 - 35
FORMAT OF EVALUATION:
During the term, students will have many opportunities to practice the various skills they are learning and
may receive feedback in the form of a written comment, a level, or a score. These practice opportunities
(called FORMATIVE ASSESSMENTS) are not necessarily counted as part of their final grade. They are
intended to provide feedback with respect to how well the student is grasping the concepts being taught.
70% of the students final grade will be based on work that is done throughout the term in class. The work
that students complete throughout the term for grading purposes is called SUMMATIVE EVALUATION.
In any given unit, overall and specific expectations will be assessed to measure student achievement in the
areas of knowledge/understanding, application, communication, and problem solving. The categories assessed
will vary with each assessment task, and will carry different weightings depending on the complexity of the
task. Students will receive feedback in the form of levels or marks.
At the end of the course, students are expected to complete a FINAL SUMMATIVE, worth 30% of
their final mark. This summative could take the form of a performance task, an exam, a formal writing
piece, or a combination of these.
FINAL GRADE: Term Work (70%) + Final Summative Assessment (30%)
DEADLINES:
1. Deadlines are set to encourage students to manage their workload and time. Some task deadlines are
negotiable; some are absolute.
2. There will be "key assessment tasks" that must be completed by students in order for their teachers to
properly determine how well students have grasped the concepts or skills that have been taught in a
unit/course. A student who fails to submit one of these tasks may receive a mark of 'zero' if any of the
following conditions apply:
a) s/he was provided with sufficient or reasonable time to complete the task
b) s/he had the opportunity to negotiate an extension with the teacher prior to the deadline
c) the assessment has already been marked and returned to the whole class
d) the assessment was plagiarized from another person's work
Since students must provide sufficient evidence of their learning, incomplete tasks could result in the
loss of their credit. It is therefore imperative that all students submit all assigned assessments in
order to demonstrate a thorough understanding of course expectations and concepts.
3. It is never acceptable to submit work late without negotiating alternate deadlines. This responsibility
will be reflected in the learning skills on the mid-term and final report card.
LEARNING SKILLS EXPECTATIONS:
It is an expectation that each student is assessed not only on their academic achievement but also on their
Learning Skills. These skills include: Responsibility, Organization, Independent Work, Collaboration,
Initiative, Self-regulation. Students will have the opportunity to assess themselves and their classmates
in these categories in addition to the teacher providing feedback. Students will be provided a rubric,
checklist or some other form of feedback sheet when this type of feedback occurs.
Note to Student and Parents/Guardians: Please sign below to show that you are aware of the
expectations of this course and that you have the name and contact number for your son/daughter's
teacher.
PARENT SIGNATURE: _______________________________ DATE: ________________
STUDENT SIGNATURE: _____________________________ DATE: ________________ | 677.169 | 1 |
...The math sections measure a student's ability to reason quantitatively, solve mathematical problems, and interpret data presented in graphical form. These sections focus on four areas of mathematics that are typically covered in the first three years of American high school education: Arithmetic... | 677.169 | 1 |
Numerical Methods Algorithms and Applications
9780130314000
ISBN:
0130314005
Pub Date: 2002 Publisher: Prentice Hall
Summary: The purpose of this text is to present the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a manner that is both interesting and understandable to undergraduate and beginning graduate students in those fields. The organization of the chapters, and of the material within each chapter, is designed with student learning as the primary obj...ective. A detailed algorithm is given for each method presented, so that students can write simple programs implementing the technique in the computer language of their choice. Numerous examples of the use of the methods are also included. The first chapter sets the stage for the material in the rest of the text, giving a brief introduction to the long history of numerical techniques and a "preview of coming attractions" for some of the recurring themes in the remainder of the text. It also presents a summary of the key components of a computer program for solving problems involving numerical techniques such as those given in the text. The trapezoid rule for numerical integration is used to illustrate the relationship between a numerical algorithm and a computer program implementing the algorithm. Sample programs are given in several different languages. Each of the subsequent chapters begins with a one page overview of the subject matter, together with an indication as to how the topics presented in the chapter are related to those in previous and subsequent chapters. Introductory examples are presented to suggest a few of the types of problems for which the topics of the chapter may be used. Following the sections in which the methods are presented, each chapter concludes with a summary of the most important formulas, of suggestions for further reading, and an extensive set of exercises. The first group of problems provides fairly routine practice of the techniques; the second group includes applications adapted from a variety of fields, and the final group of problems encourages students to extend their understanding of either the theoretical or the computational aspects of the methods. The presentation of each numerical technique is based on the successful teaching methodology of providing examples and geometric motivation for a method, and a concise statement of the steps to carry out the computation, before giving a mathematical derivation of the process or a discussion of the more theoretical issues that are relevant to the use and understanding of the topic. Each topic is illustrated by examples that range in complexity from very simple to moderate. Geometrical or graphical illustrations are included whenever they are appropriate. The last section of each chapter gives a brief discussion of more advanced methods for solving the kinds of problems covered in the chapter, including methods used in MATLAB, Mathcad,Mathematica,and various software libraries. The chapters are arranged according to the following general areas: Chapter 2 deals with solving nonlinear equations of a single variable. Chapters 3-6 treat topics from numerical linear algebra. Chapter 7 considers nonlinear functions of several variables Chapters 8-10 cover numerical methods for data interpolation and approximation. Chapter 11 presents numerical differentiation and integration. Chapters 12-15 introduce numerical techniques for solving differential equations. For much of the material, a calculus sequence that includes an introduction to differential equations and linear algebra provides adequate background. For more in-depth coverage of the topics from linear algebra (especially the OR method for eigenvalues), a linear algebra course would be an appropriate prerequisite. The coverage of Fourier approximation and FFT (Chapter 10) and partial differential equations (Chapter 15) assumes that the students have somewhat more mathematical maturity sin
Fausett, Laurene V. is the author of Numerical Methods Algorithms and Applications, published 2002 under ISBN 9780130314000 and 0130314005. One hundred nine Numerical Methods Algorithms and Applications textbooks are available for sale on ValoreBooks.com, fifty eight used from the cheapest price of $20.55, or buy new starting at $82.98.[read more | 677.169 | 1 |
Mathematics: General Statistics with: Dr. Ji Son, Ph.D.
In Educator's General Statistics course, Dr. Ji Son covers information applicable for both high school and college statistics courses. She teaches through a combination of equations, diagrams, and relevant examples. Dr. Son also uses Excel to breakdown the difficult concepts of statistics into understandable and memorable ideas. Topics include everything from Central Tendency and Normal Distribution to Correlation, Probability, and Hypothesis Testing. Dr. Son has a Ph.D. in Psychology and Cognitive Science and is a published researcher on how people learn and apply abstract concepts. Excel files and data used in lessons are downloadable so students can follow along. | 677.169 | 1 |
The book is virtually unique in providing, in a single volume, a comprehensive analysis of The General Prologue. It places the work in the context of the social change in late fourteenth century England and analyzes each pilgrim's description in socio-historical terms. The poem is supported by the author's own modernization of the text to enable the reader to understand Chaucer's Middle English.
This eBook introduces the trigonometric ratios, the trigonometric ratios of standard triangles, the sine rule, the cosine rule, the formula to calculate the area of a triangle as well as generic trigonometric equations equation of a circle, the graphs of cos x, sin x and tan x, transformed trigonometric graphs as well as the graph and CAST methods of solving trigonometric equations in a given ...
This eBook reviews simultaneous equations and inequalities. We introduce simultaneous equations as systems of equations, and consider some relatively simple pairs of simultaneous equations, one pair involving a pair of linear equations, and another pair involving one linear equation and one quadratic equation. We go on to introduce the two methods of solving simultaneous equations, elimim. ...
This eBook introduces the subjects of sequences and series, and introduces sequences in general, as well as arithmetic and geometric progressions, series within arithmetic and geometric progressions, the concepts of convergence and divergence as well as the binomial expansion. Suitable questions are asked throughout the discourse to test and develop the students comprehension of the subject.
This eBook reviews quadratics, cubics and other polynomials, in ways from sketching and understanding their graphs, to factorising quadratics, understanding the quadratic formula, solving quadratic 'like' equations, completing the square, factorising cubics, algebraic division and understanding the remainder and factor theorems. Further, we include an extensive selection of questions for the ...
This eBook introduces the subject of logarithms and exponentials, from the basic definition of logarithm, through the laws of logarithms, undertaking an assessment and an appreciation of exponential graphs, looking at the linear form of exponentials interspersed with a series of questions and worked examples.
This eBook introduces the subject of integration, starting by introducing integration as the inverse of differentiation, with a twist or two. We then introduce the indefinite integral and its constant of integration, and go on to introduce the definite integral. As well as this, we provide ample examples and illustrations to illuminate the prose. We go on to introduce trapeziums linear ...
This eBook introduces the subjects of indices and surds, ranging from introducing both indices and the laws of indices, surds and the laws of surds, to developing the students skills in manipulation such numbers through setting a wide range of questions..
This eBook introduces the subject of differentiation, across this wide-ranging subject, starting with definitions and first principles to developing an understanding and appreciation of the first and second order differentials of the equation y = xn through a development of the equations of the gradient and normal to a curve at a particular point as well as a thorough review of maximum, minimum ..
This eBook introduces co-ordinate geometry and graphs, ranging from finding the equations of the straight-line joining two points for which the co-ordinates are known, to calculating both the mid-point and length of a line between two known co-ordinates to plotting equations of the form y = kx^n where n is even or odd for various values of k, as well as y = k√(x) where x is positive.
This eBook introduces the subject of circle and circle geometry, introduces the equation of a circle, explores circle geometry, examines tangential lines to circles and their properties and equations, as well as exploring arc-length and sector area of circles where angles are represented in radians. Further, we include some elementary questions for the student to enjoy.
This eBook reviews some advanced topics in algebra, including exploring the nature of polynomials, functions, equations and identity's, examining the mathematical nomenclature used in multiplication and division. We consider multiplying out brackets, taking out common factors, manipulating algebraic fractions and simplifying expressions. We include an extensive selection of questions.
In 1995 Anna Nandi fails to sit her final technical exams due to financial problems. After painfully giving up all the privileges of College life for a second attempt to go to University,
She finds herself back in secondary school.The buildings are converted former chicken houses;when it rains her bed gets clogged with mud. Her teachers think she will fail again, but she vows to prove them wrong.
A simple, step-by-step approach to learning the piano.
Beginner's Piano is designed to make learning the basics of piano playing and music theory as simple as possible for students and teachers alike. A no-nonsense approach with ideas clearly introduced using jargon-free text, the course is dedicated to developing fluency in reading and a thorough foundation in music.
BOOK 4 provides useful, high frequency language and examples heard everyday on the streets of China. Part 1 gives the reader a solid basis for understanding Chinese in additional day-to-day situations, such as traveling, renting apartments, sports, dating, and many more.
Chinese facts and cultural information are also touched upon in Part 2 to give a better understanding of the Chinese people.
BOOK 3 provides useful, high frequency language and examples heard everyday on the streets of China. This book is designed to give the reader a solid basis for understanding Chinese in different day-to-day situations, such as eating as a restaurant, shopping, social situations, dealing with emergencies, and many more. You can study these daily life topics in any order.
In BOOK 2, Part 1 provides more grammar points which continue from BOOK 1. There are useful examples to help you grasp each of the grammar points. Part 1 is arranged in such a way that any topic in this part can be studied independently.
Upon completion of this book, you will attain not only mastery of Chinese grammar and vocabulary, but also an expanded knowledge of Chinese writing. | 677.169 | 1 |
Maths calculus Covering all syllabus Ebook PDF download
Here is the ebook for calculus:
The right way to begin a calculus book is with calculus. This chapter will jump directly into the two problems that the subject was invented to solve. You will see what the questions are, and you will see an important part of the answer. There are
plenty of good things left for the other chapters, so why not get started? The book begins with an example that is familiar to everybody who drives a car. It is calculus in action-the driver sees it happening. The example is the relation
between the speedometer and the odometer. One measures the speed (or velocity); the other measures the distance traveled. We will write v for the velocity, and f for how far the car has gone. The two instruments sit together on the dashboard:
Notice that the units of measurement are different for v and f.The distance f is measured in kilometers or miles (it is easier to say miles). The velocity v is measured in km/hr or miles per hour. A unit of time enters the velocity but not the distance.
Every formula to compute v from f will have f divided by time. | 677.169 | 1 |
books.google.com - This book is written for students at bachelor and master programs and has four different purposes, which split the book into four parts: 1. To teach first or early year undergraduate engineering students basic knowledge in technical computations and programming using MATLAB. The first part starts from... for Engineers Explained | 677.169 | 1 |
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MAT-221 Mathematics for Elementary Teachers I4
credits
Prerequisites: MAT-102 or placment according to the Math Placement Guide.
Topics include number systems, problem solving, sets, logic and properties of whole numbers and rational numbers. The emphasis is on mathematics taught in the elementary school classroom, using a variety of teaching techniques, methods, and hands-on materials including manipulatives and technology. | 677.169 | 1 |
Intermediate Algebra: Connecting Concepts through Applications
9780534496364
ISBN:
0534496369
Edition: 1 Pub Date: 2011 Publisher: Brooks Cole
Summary: INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate so...lutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skills.
Clark, Mark is the author of Intermediate Algebra: Connecting Concepts through Applications, published 2011 under ISBN 9780534496364 and 0534496369. Four hundred forty seven Intermediate Algebra: Connecting Concepts through Applications textbooks are available for sale on ValoreBooks.com, seventy eight used from the cheapest price of $44.98, or buy new starting at $168 A brand new never used instructor edition,just like the student version but will have prestamped teacher labels,these will be covered with blackbook tape,no answers included,f [more]
ALTERNATE EDITION: A brand new never used instructor edition,just like the student version but will have prestamped teacher labels,these will be covered with blackbook tape,no answers included,from smoke free environment![less] | 677.169 | 1 |
Introduction to Computational Science
Introduction to scientific computing, emphasizing basic numerical algorithms
and the informed use of mathematical software.
Matrix computation, systems of linear equations, differential equations.
Students will learn and use the Matlab language.
Textbook:
The textbook is:
Numerical Computing with Matlab,
by Cleve Moler.
The book has a
web site.
Besides the bookstore,
you can download the book from its web site,
or you can order it
from SIAM,
the Society for Industrial and Applied Mathematics.
You can get a discount on the book if you are a
member
of SIAM, which is free for UCSB students (talk to me).
Course software and computer resources:
You'll use Matlab for all your programming in the course.
It works on the Linux computers in CSIL and on the Windows
computers in the ECI labs.
To run Matlab from your personal machine, you can
log in
to CSIL remotely and forward the graphics,
or else buy a copy of the "student version" at the bookstore.
The course will also use the "NCM" software,
which you can put on your Matlab path at CSIL in any of several ways:
Homework policy:
There will be a homework assignment every week.
You may talk to each other about the assignment, but what you submit
must be your own work.
Most weeks there will be two sets of problems:
one to be turned in for a grade,
and one for self-study to test your
own understanding of the course material.
All homework must be submitted in hard copy, on paper.
We strongly encourage you to write up your homework using
LaTeX,
which is the standard markup language for mathematical documents.
To get you started,
here is the LaTeX
for the
review quiz.
When a homework exercise requires a Matlab program, turn in four things:
the Matlab program listing (m-files; use "verbatim" mode in LaTeX)
the relevant lines from the diary of your Matlab session running the program ("verbatim" in LaTeX)
copies of any output figures or plots (save figures as pdf's and include in LaTeX)
a description in English of what you did and how
Homework is due every Monday at the beginning of class, or in the CS111
homework box in the Computer Science mailroom, 2108 HFH, by 9:00 am Monday.
No late homework will be accepted under
any circumstances,
but I will drop your two lowest homework grades.
If you have questions about grading of homework, talk to the grader
or the t.a. first.
If you are unable to reach an agreement, make an appointment to talk
to me.
The statute of limitations for regrades is one
week -- that is,
any requests for regrades must be made no later than one week after the
homework (or exam) was returned in class.
Due Mon, Nov 22: Exercises 7.4, 7.16, 7.18.
(Turn these in for a grade.)
Self study for Mon, Nov 22: Run all the examples in Section 7.7 in Matlab.
Also, do Exercise 7.2 (Don't turn these in.)
Due Wed, Dec 1 (extension due to CSIL closure): Exercise 7.21.
(This is a longer but moderately realistic problem about
modeling global warming.
Among other things you'll use an interpolation routine, "pchiptx",
from Chapter 3.
Turn this in for a grade.) | 677.169 | 1 |
This file describes an experimental setup (using a motion detector) in which a ball's distance from start is recorded as the ball rolls up then down an inclined plane. It includes a simulation applet... More: lessons, discussions, ratings, reviews,...
Students investigate the models by which fractal patterns aggregate. Several questions are posed and different activities are suggested to go along with the Diffusion-Limited Aggregation applet. More: lessons, discussions, ratings, reviews,...
An interactive applet that allows the user to graphically explore the properties of a cubic function. Specifically,
it is designed to foster an intuitive understanding of the effects of changin... More: lessons, discussions, ratings, reviews,...
An application problem that asks students to help an excavation company prepare a bid for one of their clients by calculating what they should charge to dig a hole. To solve the problem students must ... More: lessons, discussions, ratings, reviews,...
Guided activities with the Graph Explorer applet, designed to let students learning about quadratic functions explore: the parabolic shape of the graphs of quadratic functions; how coefficients affect... More: lessons, discussions, ratings, reviews,...
When the sun moves around in the sky, the shadow cast by a vertical stick moves on the ground. The tip of the shadow traces some kind of curve. The curve depends on the observation point, and it also ... More: lessons, discussions, ratings, reviews,...
This is a 10 question multiple choice quiz on parabolas. Includes both vertical and horizontal parabolas as well as questions involving the directrix, all with optional hints. Self Checking with imm... More: lessons, discussions, ratings, reviews,...
A pair of congruent triangles holds the key to this unusual Sketchpad ellipse construction. The link to the activity itself is to a zip file that contains both the activity in pdf format and the co... More: lessons, discussions, ratings, reviews,...
Students will explore the richness of conic sections by building their own physical models and then constructing more flexible models with Sketchpad. Students retain a solid connection with th... More: lessons, discussions, ratings, reviews,...
This activity is an introduction to geometric constructions of parabolas. We will investigate their properties and characteristics. This activity has been adapted from the following article: Olmstead,... More: lessons, discussions, ratings, reviews,...
The 56 activities in this collection give students the opportunity to directly experience, through dynamic visualization and manipulation, the topics covered in precalculus. It finishes with a dynami... More: lessons, discussions, ratings, reviews,...
With just a blank sheet of paper and a single point, students can fold a genuine parabola. Students model the technique with Sketchpad to reveal the underlying mathematics. The link to the activit... More: lessons, discussions, ratings, reviews,...
Students create both geometric and algebraic translations of a function, match the two translations, and use the components of the geometric vector to write an equation for translated image. The li... More: lessons, discussions, ratings, reviews,...
How does a scale change in an equation effect the points on the graph? Given an equation, students often confuse what happens to an equation in function form with what happens to the points in a list... More: lessons, discussions, ratings, reviews,...
TI InterActive! is a new product that enables high school and college teachers and students to easily investigate ideas in mathematics and science. The purpose of this workbook is to introduce algebra... More: lessons, discussions, ratings, reviews,...
This workbook provides high school students with activities from algebra to calculus that use Texas Instruments software TI InterActive! TI InterActive! is software for the PC that combines a word pro... More: lessons, discussions, ratings, reviews,...
This collection of activities is intended to provide middle and high school Algebra I students with a set of data collection investigations that integrate mathematics and science and promote mathemati... More: lessons, discussions, ratings, reviews,...
Step-by-step directions on how to use the Conic Graphing App to help students learn about circles, ellipses, hyperbolas, and parabolas, and solve for the conic's characteristics. Equations are present | 677.169 | 1 |
Math Course Takes 'Real Life' Approach to Algebra
Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life."
Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts.
The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback | 677.169 | 1 |
Product Details
Methods for Euclidean Geometry is a college geometry textbook with a unique mission. Instead of treating the subject as a distinct unit in the math curriculum, the authors integrate a variety of mathematical disciplines to engage and enlighten the reader...
--MAA Reviews
Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses. | 677.169 | 1 |
GeoGebra 5.0.134.0
GeoGebra is a very useful mathematics tool for education in secondary schools, which brings together geometry, algebra and calculus.
GeoGebra is also a dynamic geometry system, meaning you can do constructions with points, segments, vectors, lines, conic sections as well as functions and change them dynamically afterwards.
On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.
These two views are characteristic of GeoGebra: an expression in the algebra window corresponds to an object in the geometry window and vice versa.
Related Programs | 677.169 | 1 |
Teaching High School Mathematics; First Course; Verbalizing Generalizations in the Classroom
Description:
Mathematician Max Beberman teaches students name principles and provides instances to justify shortcuts in arithmetic computations. Beberman emphasizes that a student can use a generalization without having heard it spoken or seen it in print, and he can apply the generalization to solve problems. But, he cannot test his intuitive insight by a deductive proof without first supplementing the insight with a precise linguistic formulation. Also, until he achieves this formulation, the student cannot use an insight as an assumption from which to derive new generalizations. Black and white picture with sound. Kodak edge code reads "square triangle," which correlates to 1965. | 677.169 | 1 |
2.0 EVALUATING ARITHMETIC AND FORMULA EXPRESSIONS:
2.1 Use the basic operations of addition, subtraction, multiplication, division, opposites, roots, and exponents.
2.2 Differentiate between subtraction and negative buttons.
2.3 Understand that the calculator evaluates expressions according to the order of operations (e.g. complex fractions and radicals).
2.4 Be able to use the parentheses as grouping symbols.
2.5 Be able to read, input, and interpret numbers in scientific notation.
2.6 (Casio specific) Be able to use 2D tab.
3.0 EDITING ARITHMETIC OR FORMULA EXPRESSIONS:
3.1 Reuse previous inputs and outputs.
3.1.1 (TI specific) Be able to use both 2nd Enter feature and arrow keys.
3.1.2 (Casio specific) Be familiar with drag-and-drop feature.
3.2 Use the arrow pad to move cursor throughout an expression that requires editing.
3.2.1 Use the cut/copy/paste features.
3.2.2 Know how to delete, clear, and insert.
3.2.3 Understand the tool bar options.
3.3 (Casio specific) Know the difference between Action and Interactive menu items.
6.0 SOLVE EQUATIONS:
6.1 Use SOLVE feature to solve equations.
6.2 Use the graphing option to display the graphs and the solutions.
6.3 Use SOLVE feature to solve inequalities. Include calculator limitations such as absolute value inequalities.
ADDITIONAL TOPICS
(1 to 2 of these topics should be covered, instructor's choice)
The goal is to provide additional topics relevant to the students' areas of study. The instructor should supplement the core-required topics (items 1 - 6) with one or two of the following topics.
7.0 PLOTTING DATA:
7.1 Input, edit and delete a set of ordered pairs. Be able to delete entire column by putting cursor on top of the file name.
7.2 Draw a scatter plot, a box plot, and a histogram.
7.3 Change the icon used to plot points.
7.4 Plot different sets of ordered pairs simultaneously.
7.5 Find a graph of various regression functions.
8.0 PROGRAMMING:
8.1 Write, input and run a simple program.
8.2 Transfer programs from one calculator to another.
8.3 Download, install, and run programs from the TI web site.
8.4 Upgrade the operating system.
9.0 USING LISTS:
9.1 Know how to input a list and store it to a variable.
9.2 Use a list of parameters to study the changes that occur to an equation (e.g. y=0.3x + b, where b = {2, 4, 5, 10})
9.3 Explore the operations that can be performed to a list.
10.0 APPLICATIONS AND DOWNLOADS:
10.1 (TI-89 specific) Use the Apps' Polynomial Root Finder application.
10.2 (TI-89 specific) Use the Apps' Simultaneous Equations Solver.
10.3 (TI-89 specific) Use the Unit Conversion feature.
10.3.1 Explore the different conversion units available.
10.3.2 Understand the different symbols used on the edit line for conversion between units.
10.3.3 Use the temp( ) function.
10.4 Download additional resources from Texas Instrument or Casio website | 677.169 | 1 |
Each Tier of the "Students' Book" has parallel chapters with similar contents, but with questions and explanations at appropriate levels for each tier. Ma 1 activities are integrated throughout. It encourages mathematical discussion, mental methods and prepares you for the non-calculator examination paper. Coursework ideas and IT opportunities add variety to your course. End of chapter tests check students' understanding and numerous exercises develop and consolidate learning. Structured Revision sections in year 11 Books provide invaluable exam preparation. Discussion points introduce new ideas in an interactive and motivating way.
The "Task Maths for Key Stage 4" provides complete coverage of all 5 Attainment Targets in the form of theme-based tasks with optional coursework extensions. The importance of Attainment Target 1 - "Using and applying mathematics" - is recognized throughout. The tasks are relevant to all students, providing a sense of purpose. Throughout these open-ended tasks, students learn mathematical skills, and gain knowledge and understanding in contexts where they can be used. Each task is introduced by an activity and then developed by means of a series of questions of increasing difficulty to cater for students working at different levels of Key Stage 4. Tasks are suitable for both individual and group work. Each chapter ends with a number of coursework tasks, some of which are intended to enable all students to explore the theme of the chapter in more depth. In addition to the chapters, there are review exercises organized into syllabus topics which provide consolidation and revision. The exercises include GCSE examination questions, giving students examination practice. Resources for the series are: two students' books; each students'book is accompanied by a teacher's resource book which outlines compliance with the National Curriculum, and provides support for the coursework tasks, giving guidance on such aspects as time and the use of equipment, for example, computers. Detailed help is given with the assessment of coursework by way of example responses and guidelines for assessment. The coursework tasks are open-ended, challenging students to approach each activity in their own way. However, support is offered by providing ideas about how coursework tasks might be tackled; one pack of copymasters to accompany students' books 4 and 5; and "Task Maths" software disks for books 4 and 5, available for Archmides, RM Nimbus and BBC formats. | 677.169 | 1 |
Math 142 Trigonometry
Did you ever want to build a skateboard ramp whose incline was exactly 12 degrees? Well Trigonometry can help you determine the measurements you need to cut the wood to build your perfect ramp!
Maybe you want to know which direction to point your airplane as it flies through the skies, to compensate for the wind so that you end up at your dream destination. Trigonometry comes to the rescue and teaches you how to plan your next flight!
Course Description
Trigonometry helps us understand how the world works in a very physical way through analyzing angles, triangles and vectors. You will learn to solve equations and application problems, create and analyze intricate graphs of all the Trigonometric Functions, and work with complex numbers, polar coordinates and parametric equations. It is also where you will learn techniques of trigonometric proof, and get prepared for taking more advanced classes such as Calculus I and Physics.
Pre-Requisite
Math 141 College Algebra, with grade C or better. Equivalent courses: Pre-Calculus, or high school Math Analysis.
Course Requirements
Textbook: Trigonometry, tenth edition, by Lial, Hornsby, Schneider. Hardcopy textbook is optional as the eBook is included with your MyMathLab access. | 677.169 | 1 |
07506038Introduction to the Mathematics of Finance: Published in association with the Institute of Actuaries and Faculty of Actuaries Author(s): J J McCutcheon, W F Scott
ISBN: 0750603887
ISBN-13: 9780750603881
Book Description
Introduction to the Mathematics of Finance: Published in association with the Institute of Actuaries and Faculty of Actuaries
In today's money markets interest rates are all-important. This book, which is intended as a successor to D.W.A Donald's Compound Interest and Annuities-certain, develops the classical theory of compound interest (in which the force of interest is constant) as a special case of a more general model.
There is a concise but thorough treatment of the basic compound interest functions, nominal rate of interest, and the yield (or internal rate of return) and there are many examples on discounted cash flow. Also discussed are applications of the theory to capital redemption policies (with allowance for income tax, capital gains tax and index-linking), and consumer credit calculations. The final chapter provides a simple introduction to stochastic interest rate models.
Concise and thorough Extensive use of examples Endorsed by the Institute of Actuaries and the Faculty of Actuaries | 677.169 | 1 |
Quick Review Math Handbook Hot Words, Hot Topics book 3
9780078607554
ISBN:
0078607558
Pub Date: 2005 Publisher: Glencoe/McGraw-Hill
Summary: Quick Review Math Handbook: Hot Words, Hot Topics (available in English and Spanish) provides students and parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. This handbook also includes short-instruction and practice of key standards for Middle School and High School success.
Glencoe McGraw-Hill Staff is the author of Quick Revie...w Math Handbook Hot Words, Hot Topics book 3, published 2005 under ISBN 9780078607554 and 0078607558. One hundred twelve Quick Review Math Handbook Hot Words, Hot Topics book 3 textbooks are available for sale on ValoreBooks.com, sixty one used from the cheapest price of $0.01, or buy new starting at $39.41.[read more] | 677.169 | 1 |
Pine Hill, NJ Precalculus manipulation of equations is expanded to include simultaneous equations and systems of equations. Exponents, logarithms, roots, and radicals are introduced, along with the new concepts of infinite sequences and series. Equations and inequalities with absolute value-terms, imaginary numbers,...Killian M.
...I am a math and physics major and understand the concepts very thoroughly and can explain them well. I | 677.169 | 1 |
We Offer Four Types of Student Programs
Overview
Catchup Math is for students in grades 7 and above, but our Programs will "drill down"
to review material taught in elementary school as necessary. We offer Subject Proficiency Programs,
Graduation Test Prep Programs, Chapter-based Programs and Custom (Teacher-Created) Programs.
Subject Proficiency (K12 and College)
Each Subject Proficiency Program reviews a full subject in six sections. Students advance from section to
section by taking diagnostic quizzes and reviewing prescribed lessons (with practice) until a passing quiz
score is attained. Our K12 Subject Proficiency Programs are
Foundations (arithmetic review),
Essentials (covering grades 6-7 Math),
Pre-Algebra, Algebra 1,
Geometry, and Algebra 2.
For colleges, we offer College Basic Math
and Elementary Algebra.
Teachers may enroll students in specific Proficiency Programs or have them auto-enroll via an online diagnostic placement test.
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Students may prepare for their high school exit exam with one of our Graduation Test Prep Programs.
These programs typically cover the material for a specific state, in eight sections. Students advance
from section to section as they demonstrate mastery of the material.
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Teachers can assign material based on typical textbook chapter topics.
Each of the ten or more chapters within our Chapter-based Programs consists of two sections. Our five
Chapter-based subjects are Pre-Algebra, Algebra 1, Geometry, Algebra 2, and Elementary Algebra (for colleges).
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Faculty may quickly and easily create their own Programs without quizzes by selecting among all the lessons
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convenience. Also, teachers may create their own custom pre-tests, post-tests, quizzes, and exams by selecting
from our complete online question bank. Teachers may also create their own problems for use in assignments
using our Custom Problems facility. | 677.169 | 1 |
APStatistics 2007 Free-Response Questions The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association ...
22s:152 Linear Regression Exam1 Fall 2007 Friday, September 28,9:30-10:20am 100 possiblepoints Student Name Instructions: 1) Make sure you have the correct number of pages.
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The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college ...
Prepared by Lynn Ibarra APStatistics Syllabus Overview The usual sequence of courses leading to APStatistics is: Algebra I Geometry Algebra II Some students ...
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APStatistics class rules and grading policy. Mr. Eleuterio 2007-08 1) Co-operate with others and treat them with respect. 2) Be on time and prepared for class every day.
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The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college ... | 677.169 | 1 |
Additional Skill and Drill Manual for Beginning and Intermediate Algebra
Beginning & Intermediate Algebra
Beginning and Intermediate Algebra Video Lectures With Solution Clips
Beginning and Intermediate Algebra Mathxl Tutorials
Beginning and Intermediate Algebra, Pass the Test
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Worksheets for Classroom or Lab Practice offer extra practice exercises for every section of the text, with ample space for students to show their work. These lab- and classroom-friendly workbooksalso list the learning objectives and key vocabulary terms for every text section,along with vocabulary practice problems. | 677.169 | 1 |
Transcript of "Linear algebra with aplications - Steven J. Leon"
2.
PREFACE
This solutions manual is designed to accompany the seventh edition of Linear
Algebra with Applications by Steven J. Leon. The answers in this manual supplement those given in the answer key of the textbook. In addition this manual contains
the complete solutions to all of the nonroutine exercises in the book.
At the end of each chapter of the textbook there are two chapter tests (A and
B) and a section of computer exercises to be solved using MATLAB. The questions
in each Chapter Test A are to be answered as either true or false. Although the truefalse answers are given in the Answer Section of the textbook, students are required
to explain or prove their answers. This manual includes explanations, proofs, and
counterexamples for all Chapter Test A questions. The chapter tests labelled B
contain workout problems. The answers to these problems are not given in the
Answers to Selected Exercises Section of the textbook, however, they are provided
in this manual. Complete solutions are given for all of the nonroutine Chapter Test
B exercises.
In the MATLAB exercises most of the computations are straightforward. Consequently they have not been included in this solutions manual. On the other hand,
the text also includes questions related to the computations. The purpose of the
questions is to emphasize the significance of the computations. The solutions manual does provide the answers to most of these questions. There are some questions
for which it is not possible to provide a single answer. For example, aome exercises
involve randomly generated matrices. In these cases the answers may depend on
the particular random matrices that were generated.
Steven J. Leon
sleon@umassd.edu
5.
2
CHAPTER 1
(a) If m1 = m2 , then one can solve the second equation for x1
x1 =
b2 − b1
m1 − m2
One can then plug this value of x1 into the first equation and solve for
x2 . Thus, if m1 = m2 , there will be a unique ordered pair (x1, x2) that
satisfies the two equations.
(b) If m1 = m2 , then the x1 term drops out in the second equation
0 = b2 − b1
This is possible if and only if b1 = b2.
(c) If m1 = m2 , then the two equations represent lines in the plane with
different slopes. Two nonparallel lines intersect in a point. That point
will be the unique solution to the system. If m1 = m2 and b1 = b2 , then
both equations represent the same line and consequently every point on
that line will satisfy both equations. If m1 = m2 and b1 = b2 , then the
equations represent parallel lines. Since parallel lines do not intersect,
there is no point on both lines and hence no solution to the system.
10. The system must be consistent since (0, 0) is a solution.
11. A linear equation in 3 unknowns represents a plane in three space. The
solution set to a 3 × 3 linear system would be the set of all points that lie
on all three planes. If the planes are parallel or one plane is parallel to the
line of intersection of the other two, then the solution set will be empty. The
three equations could represent the same plane or the three planes could
all intersect in a line. In either case the solution set will contain infinitely
many points. If the three planes intersect in a point then the solution set
will contain only that point.
SECTION 2
2. (b) The system is consistent with a unique solution (4, −1).
4. (b) x1 and x3 are lead variables and x2 is a free variable.
(d) x1 and x3 are lead variables and x2 and x4 are free variables.
(f) x2 and x3 are lead variables and x1 is a free variable.
5. (l) The solution is (0, −1.5, −3.5).
6. (c) The solution set consists of all ordered triples of the form (0, −α, α).
7. A homogeneous linear equation in 3 unknowns corresponds to a plane that
passes through the origin in 3-space. Two such equations would correspond
to two planes through the origin. If one equation is a multiple of the other,
then both represent the same plane through the origin and every point on
that plane will be a solution to the system. If one equation is not a multiple of
the other, then we have two distinct planes that intersect in a line through the
origin. Every point on the line of intersection will be a solution to the linear
system. So in either case the system must have infinitely many solutions.
6.
Section 3
3
In the case of a nonhomogeneous 2 × 3 linear system, the equations correspond to planes that do not both pass through the origin. If one equation
is a multiple of the other, then both represent the same plane and there are
infinitely many solutions. If the equations represent planes that are parallel,
then they do not intersect and hence the system will not have any solutions.
If the equations represent distinct planes that are not parallel, then they
must intersect in a line and hence there will be infinitely many solutions.
So the only possibilities for a nonhomogeneous 2 × 3 linear system are 0 or
infinitely many solutions.
9. (a) Since the system is homogeneous it must be consistent.
14. At each intersection the number of vehicles entering must equal the number
of vehicles leaving in order for the traffic to flow. This condition leads to the
following system of equations
x1 + a1 = x2 + b1
x2 + a2 = x3 + b2
x3 + a3 = x4 + b3
x4 + a4 = x1 + b4
If we add all four equations we get
x1 + x2 + x3 + x4 + a1 + a2 + a3 + a4 = x1 + x2 + x3 + x4 + b1 + b2 + b3 + b4
and hence
a1 + a2 + a3 + a4 = b1 + b2 + b3 + b4
15. If (c1 , c2) is a solution, then
a11c1 + a12c2 = 0
a21c1 + a22c2 = 0
Multiplying both equations through by α, one obtains
a11(αc1) + a12(αc2 ) = α · 0 = 0
a21(αc1) + a22(αc2 ) = α · 0 = 0
Thus (αc1, αc2) is also a solution.
16. (a) If x4 = 0 then x1 , x2 , and x3 will all be 0. Thus if no glucose is produced
then there is no reaction. (0, 0, 0, 0) is the trivial solution in the sense that
if there are no molecules of carbon dioxide and water, then there will be no
reaction.
(b) If we choose another value of x4, say x4 = 2, then we end up with
solution x1 = 12, x2 = 12, x3 = 12, x4 = 2. Note the ratios are still 6:6:6:1.
SECTION 3
1. (e)
8
0
−1
−15
−4
−6
11
−3
6
15.
12
CHAPTER 1
Therefore
tjj = ujj rjj
j = 1, . . . , n
T
15. If we set x = (2, 1 − 4) , then
Ax = 2a1 + 1a2 − 4a3 = 0
Thus x is a nonzero solution to the system Ax = 0. But if a homogeneous
system has a nonzero solution, then it must have infinitely many solutions.
In particular, if c is any scalar, then cx is also a solution to the system since
A(cx) = cAx = c0 = 0
Since Ax = 0 and x = 0 it follows that the matrix A must be singular. (See
Theorem 1.4.2)
16. If a1 = 3a2 − 2a3, then
a1 − 3a2 + 2a3 = 0
Therefore x = (1, −3, 2)T is a nontrivial solution to Ax = 0. It follows form
Theorem 1.4.2 that A must be singular.
17. If x0 = 0 and Ax0 = Bx0 , then Cx0 = 0 and it follows from Theorem 1.4.2
that C must be singular.
18. If B is singular, then it follows from Theorem 1.4.2 that there exists a nonzero
vector x such that Bx = 0. If C = AB, then
Cx = ABx = A0 = 0
Thus, by Theorem 1.4.2, C must also be singular.
19. (a) If U is upper triangular with nonzero diagonal entries, then using row
operation II, U can be transformed into an upper triangular matrix with
1's on the diagonal. Row operation III can then be used to eliminate
all of the entries above the diagonal. Thus U is row equivalent to I and
hence is nonsingular.
(b) The same row operations that were used to reduce U to the identity
matrix will transform I into U −1. Row operation II applied to I will
just change the values of the diagonal entries. When the row operation
III steps referred to in part (a) are applied to a diagonal matrix, the
entries above the diagonal are filled in. The resulting matrix, U −1, will
be upper triangular.
20. Since A is nonsingular it is row equivalent to I. Hence there exist elementary
matrices E1, E2, . . . , Ek such that
Ek · · · E1 A = I
It follows that
A−1 = Ek · · · E1
and
Ek · · · E1 B = A−1B = C
The same row operations that reduce A to I, will transform B to C. Therefore the reduced row echelon form of (A | B) will be (I | C).
16.
Section 4
13
21. (a) If the diagonal entries of D1 are α1 , α2, . . . , αn and the diagonal entries
of D2 are β1 , β2, . . . , βn , then D1 D2 will be a diagonal matrix with diagonal entries α1β1 , α2β2 , . . . , αnβn and D2 D1 will be a diagonal matrix
with diagonal entries β1 α1, β2α2 , . . ., βn αn. Since the two have the same
diagonal entries it follows that D1 D2 = D2 D1 .
(b)
AB = A(a0 I + a1A + · · · + ak Ak )
= a0A + a1 A2 + · · · + ak Ak+1
= (a0I + a1A + · · · + ak Ak )A
= BA
22. If A is symmetric and nonsingular, then
(A−1)T = (A−1 )T (AA−1 ) = ((A−1 )TAT )A−1 = A−1
23. If A is row equivalent to B then there exist elementary matrices E1, E2, . . . , Ek
such that
A = Ek Ek−1 · · · E1B
−1
Each of the Ei 's is invertible and Ei is also an elementary matrix (Theorem
1.4.1). Thus
−1 −1
−1
B = E1 E2 · · · Ek A
and hence B is row equivalent to A.
24. (a) If A is row equivalent to B, then there exist elementary matrices E1 , E2, . . . , Ek
such that
A = Ek Ek−1 · · · E1B
Since B is row equivalent to C, there exist elementary matrices H1, H2, . . ., Hj
such that
B = Hj Hj−1 · · · H1C
Thus
A = Ek Ek−1 · · · E1Hj Hj−1 · · · H1C
and hence A is row equivalent to C.
(b) If A and B are nonsingular n × n matrices then A and B are row
equivalent to I. Since A is row equivalent to I and I is row equivalent
to B it follows from part (a) that A is row equivalent to B.
25. If U is any row echelon form of A then A can be reduced to U using row
operations, so A is row equivalent to U . If B is row equivalent to A then it
follows from the result in Exercise 24(a) that B is row equivalent to U .
26. If B is row equivalent to A, then there exist elementary matrices E1, E2, . . ., Ek
such that
B = Ek Ek−1 · · · E1A
Let M = Ek Ek−1 · · · E1 . The matrix M is nonsingular since each of the Ei's
is nonsingular.
22.
MATLAB Exercises
19
(c) If D = B + C, then
AD = AB + AC = O + AC = AC
4. By construction B is upper triangular whose diagonal entries are all equal to
1. Thus B is row equivalent to I and hence B is nonsingular. If one changes
B by setting b10,1 = −1/256 and computes Bx, the result is the zero vector.
Since x = 0, the matrix B must be singular.
5. (a) Since A is nonsingular its reduced row echelon form is I. If E1, . . . , Ek
are elementary matrices such that Ek · · · E1 A = I, then these same
matrices can be used to transform (A b) to its reduced row echelon
form U . It follows then that
U = Ek · · · E1 (A b) = A−1 (A b) = (I A−1 b)
Thus, the last column of U should be equal to the solution x of the
system Ax = b.
(b) After the third column of A is changed, the new matrix A is now singular. Examining the last row of the reduced row echelon form of the
augmented matrix (A b), we see that the system is inconsistent.
(c) The system Ax = c is consistent since y is a solution. There is a free
variable x3, so the system will have infinitely many solutions.
(f) The vector v is a solution since
Av = A(w + 3z) = Aw + 3Az = c
6.
8.
9.
10.
For this solution the free variable x3 = v3 = 3. To determine the general
solution just set x = w + tz. This will give the solution corresponding
to x3 = t for any real number t.
(c) There will be no walks of even length from Vi to Vj whenever i + j is
odd.
(d) There will be no walks of length k from Vi to Vj whenever i + j + k is
odd.
(e) The conjecture is still valid for the graph containing the additional
edges.
(f) If the edge {V6 , V8} is included, then the conjecture is no longer valid.
There is now a walk of length 1 V6 to V8 and i + j + k = 6 + 8 + 1 is
odd.
The change in part (b) should not have a significant effect on the survival
potential for the turtles. The change in part (c) will effect the (2, 2) and (3, 2)
of the Leslie matrix. The new values for these entries will be l22 = 0.9540 and
l32 = 0.0101. With these values the Leslie population model should predict
that the survival period will double but the turtles will still eventually die
out.
(b) x1 = c − V x2.
(b)
kB
I
A2k =
kB
I
25.
22
Chapter 1
7. The statement is false in general. If A is nonsingular and AB = AC, then we
can multiply both sides of the equation by A−1 and conclude that B = C.
However, if A is singular, then it is possible to have AB = AC and B = C.
For example, if
1 1
, B = 1 1, C = 2 2
A=
1 1
4 4
3 3
then
1
AB =
1
1
AC =
1
11
1
4
12
1
3
1 5
=
4
5
2 5
=
3
5
5
5
5
5
8. The statement is false. An elementary matrix is a matrix that is constructed
by performing exactly one elementary row operation on the identity matrix.
The product of two elementary matrices will be a matrix formed by performing two elementary row operations on the identity matrix. For example,
1 0 0
1 0 0
E1 = 2 1 0
and
E2 = 0 1 0
0 0 1
3 0 1
are elementary matrices, however,
1 0 0
E1E2 = 2 1 0
3 0 1
is not an elementary matrix.
9. The statement is true. The row vectors of A are x1yT , x2yT , . . . , xnyT . Note,
all of the row vectors are multiples of yT . Since x and y are nonzero vectors,
at least one of these row vectors must be nonzero. However, if any nonzero
row is picked as a pivot row, then since all of the other rows are multiples
of the pivot row, they will all be eliminated in the first step of the reduction
process. The resulting row echelon form will have exactly one nonzero row.
10. The statement is true. If b = a1 + a2 + a3 , then x = (1, 1, 1)T is a solution
to Ax = b, since
Ax = x1 a1 + x2a2 + x3a3 = a1 + a2 + a3 = b
If a2 = a3, then we can also express b as a linear combination
b = a1 + 0a2 + 2a3
Thus y = (1, 0, 2)T is also a solution to the system. However, if there is more
than one solution, then the echelon form of A must involve a free variable. A
consistent system with a free variable must have infinitely many solutions.
26.
Chapter Test B
23
CHAPTER TEST B
1.
1 −1 3 2 1
1 −1
−1 1 −2 1 −2 → 0
0
2 −2 7 7 1
0
0
1 −1
→ 0
0
0
0
1
3 2
1 3 −1
1 3 −1
0 −7
4
1
3 −1
0
0
0
The free variables are x2 and x4. If we set x2 = a and x4 = b, then
x1 = 4 + a + 7b
and
x3 = −1 − 3b
and hence the solution set consists of all vectors of the form
4 + a + 7b
a
x=
−1 − 3b
b
2. (a) A linear equation in 3 unknowns corresponds to a plane in 3-space.
(b) Given 2 equations in 3 unknowns, each equation corresponds to a plane.
If one equation is a multiple of the other then the equations represent
the same plane and any point on the that plane will be a solution to
the system. If the two planes are distinct then they are either parallel
or they intersect in a line. If they are parallel they do not intersect, so
the system will have no solutions. If they intersect in a line then there
will be infinitely many solutions.
(c) A homogeneous linear system is always consistent since it has the trivial
solution x = 0. It follows from part (b) then that a homogeneous system of 2 equations in 3 unknowns must have infinitely many solutions.
Geometrically the 2 equations represent planes that both pass through
the origin, so if the planes are distinct they must intersect in a line.
3. (a) If the system is consistent and there are two distinct solutions there must
be a free variable and hence there must be infinitely many solutions. In
fact all vectors of the form x = x1 + c(x1 − x2) will be solutions since
Ax = Ax1 + c(Ax1 − Ax2 ) = b + c(b − b) = b
(b) If we set z = x1 − x2 then z = 0 and Az = 0. Therefore it follows from
Theorem 1.4.2 that A must be singular.
4. (a) The system will be consistent if and only if the vector b = (3, 1)T can
be written as a linear combination of the column vectors of A. Linear
combinations of the column vectors of A are vectors of the form
α
+ c2 β = (c1 α + c2β) 1
c1
2α
2β
2
Since b is not a multiple of (1, 2)T the system must be inconsistent.
27.
24
Chapter 1
(b) To obtain a consistent system choose b to be a multiple of (1, 2)T . If
this is done the second row of the augmented matrix will zero out in
the elimination process and you will end up with one equation in 2
unknowns. The reduced system will have infinitely many solutions.
5. (a) To transform A to B you need to interchange the second and third rows
of A. The elementary matrix that does this is
1 0 0
E = 0 0 1
0 1 0
(b) To transform A to C using a column operation you need to subtract
twice the second column of A from the first column. The elementary
matrix that does this is
1 0 0
F = −2 1 0
0 0 1
6. If b = 3a1 + a2 + 4a3 then b is a linear combination of the column vectors
of A and it follows from the consistency theorem that the system Ax = b is
consistent. In fact x = (3, 1, 4)T is a solution to the system.
7. If a1 − 3a2 + 2a3 = 0 then x = (1, −3, 2)T is a solution to Ax = 0. It follows
from Theorem 1.4.2 that A must be singular.
8. If
1 4
2 3
A=
and
B=
1 4
2 3
then
1 41 5 2
= =
Ax =
1 4
1
5
2
3 1
= Bx
3
1
9. In general the product of two symmetric matrices is not necessarily symmetric. For example if
1 2
, B = 1 1
A=
1 4
2 2
then A and B are both symmetric but their product
1 21 1 3 9
=
AB =
1 4
4 10
2 2
is not symmetric.
10. If E and F are elementary matrices then they are both nonsingular and their
inverses are elementary matrices of the same type. If C = EF then C is a
product of nonsingular matrices, so C is nonsingular and C −1 = F −1E −1 .
11.
O O
I
−1
O
I
O
A =
O −B
I
28.
Chapter Test B
25
12. (a) The column partition of A and the row partition of B must match up,
so k must be equal to 5. There is really no restriction on r, it can be
any integer in the range 1 ≤ r ≤ 9. In fact r = 10 will work when B has
block structure
B11
B21
(b) The (2,2) block of the product is given by A21B12 + A22 B22
29.
Chapter
2
SECTION 1
1. (c) det(A) = −3
7. Given that a11 = 0 and a21 = 0, let us interchange the first two rows of
A and also multiply the third row through by −a21. We end up with the
matrix
a22
a23
a21
0
a12
a13
−a21 a31
−a21 a32
−a21a33
Now if we add a31 times the first row to the third, we obtain the matrix
a22
a23
a21
0
a12
a13
0
a31a22 − a21a32
a31a23 − a21a33
This matrix will be row equivalent to I if and only if
a12
a31a22 − a21a32
a13
a31a23 − a21a33
=0
Thus the original matrix A will be row equivalent to I if and only if
a12a31a23 − a12a21a33 − a13a31a22 + a13a21a32 = 0
8. Theorem 2.1.3. If A is an n × n triangular matrix then the determinant
of A equals the product of the diagonal elements of A.
Proof: The proof is by induction on n. In the case n = 1, A = (a11) and
det(A) = a11. Assume the result holds for all k × k triangular matrices and
26
32.
Section 2
29
SECTION 2
5. To transform the matrix A into the matrix αA one must perform row operation II n times. Each time row operation II is performed the value of the
determinant is changed by a factor of α. Thus
det(αA) = αn det(A)
Alternatively, one can show this result holds by noting that det(αI) is equal
to the product of its diagonal entries. Thus, det(αI) = αn and it follows
that
det(αA) = det(αIA) = det(αI) det(A) = αn det(A)
6. Since
det(A−1 ) det(A) = det(A−1 A) = det(I) = 1
it follows that
det(A−1 ) =
1
det(A)
8. If E is an elementary matrix of type I or II then E is symmetric, so E T = E.
If E is an elementary matrix of type III formed from the identity matrix by
adding c times its ith row to its jth row, then E T will be the elementary
matrix of type III formed from the identity matrix by adding c times its jth
row to its ith row
9. (b) 18;
(d) −6;
(f) −3
10. Row operation III has no effect on the value of the determinant. Thus if B
can be obtained from A using only row operation III, then det(B) = det(A).
Row operation I has the effect of changing the sign of the determinant. If
B is obtained from A using only row operations I and III, then det(B) =
det(A) if row operation I has been applied an even number of times and
det(B) = − det(A) if row operation I has been applied an odd number of
times.
11. Since det(A2 ) = det(A)2 it follows that det(A2 ) must be a nonnegative
real number. (We are assuming the entries of A are all real numbers.) If
A2 + I = O then A2 = −I and hence det(A2 ) = det(−I). This is not
possible if n is odd, since for n odd, det(−I) = −1. On the other hand it is
possible for A2 + I = O when n is even. For example when n = 2, if we take
0 1
A=
−1 0
then it is easily verified that A2 + I = O.
12. (a) Row operation III has no effect on the value of the determinant. Thus
1
det(V ) =
x1
x2
1
1
x2
x2
2
1
x3
x2
3
1
=
x1
x2
1
0
x2 − x1
x2 − x2
2
1
0
x3 − x1
x2 − x2
3
1
36.
MATLAB Exercises
33
Also
adj A−1 = det(A−1 )(A−1 )−1 = det(A−1 )A
11. If A = O then adj A is also the zero matrix and hence is singular. If A is
singular and A = O then
A adj A = det(A)I = 0I = O
If aT is any nonzero row vector of A then
aT adj A = 0T
or
(adj A)T a = 0
By Theorem 1.4.2, (adj A)T is singular. Since
det(adj A) = det[(adj A)T ] = 0
it follows that adj A is singular.
12. If det(A) = 1 then
adj A = det(A)A−1 = A−1
and hence
adj(adj A) = adj(A−1 )
It follows from Exercise 10 that
adj(adj A) = det(A−1 )A =
1
A=A
det(A)
13. The (j, i) entry of QT is qij . Since
Q−1 =
1
adj Q
det(Q)
its (j, i) entry is Qij / det(Q). If Q−1 = QT , then
qij =
Qij
det(Q)
MATLAB EXERCISES
2. The magic squares generated by MATLAB have the property that they are
nonsingular when n is odd and singular when n is even.
3. (a) The matrix B is formed by interchanging the first two rows of A.
det(B) = − det(A).
(b) The matrix C is formed by multiplying the third row of A by 4.
det(C) = 4 det(A).
(c) The matrix D is formed from A by adding 4 times the fourth row of A
to the fifth row.
det(D) = det(A).
37.
34
Chapter 2
5. The matrix U is very ill-conditioned. In fact it is singular with respect to the
machine precision used by MATLAB. So in general one could not expect to
get even a single digit of accuracy in the computed values of det(U T ) and
det(U U T ). On the other hand, since U is upper triangular, the computed
value of det(U ) is the product of its diagonal entries. This value should be
accurate to the machine precision.
6. (a) Since Ax = 0 and x = 0, the matrix must be singular. However,
there may be no indication of this if the computations are done in
floating point arithmetic. To compute the determinant MATLAB does
Gaussian elimination to reduce the matrix to upper triangular form U
and then multiplies the diagonal entries of U . In this case the product
u11u22u33u44u55 has magnitude on the order of 1014. If the computed
value of u66 has magnitude of the order 10−k and k ≤ 14, then MATLAB will round the result to a nonzero integer. (MATLAB knows that
if you started with an integer matrix, you should end up with an integer
value for the determinant.) In general if the determinant is computed
in floating point arithmetic, then you cannot expect it to be a reliable
indicator of whether or not a matrix is nonsingular.
(c) Since A is singular, B = AAT should also be singular. Hence the exact
value of det(B) should be 0.
CHAPTER TEST A
1. The statement is true since
det(AB) = det(A) det(B) = det(B) det(A) = det(BA)
2. The statement is false in general. For example, if
1 0
0
A=
and
B=
0 0
0
0
1
then det(A + B) = det(I) = 1 while det(A) + det(B) = 0 + 0 = 0.
3. The statement is false in general. For example, if A = I, (the 2 × 2 identity
matrix), then det(2A) = 4 while 2 det(A) = 2.
4. The statement is true. For any matrix C, det(C T ) = det(C), so in particular
for C = AB we have
det((AB)T ) = det(AB) = det(A) det(B)
5. The statement is false in general. For example if
2 3
1
A=
and
B=
0 4
0
0
8
then det(A) = det(B) = 8, however, A = B.
6. The statement is true. For a product of two matrices we know that
det(AB) = det(A) det(B)
54.
Section 6
51
is a basis for the row space. Since the reduced row echelon form of the
matrix involves one free variable the nullspace will have dimension 1.
Setting the free variable x4 = 1 we get
x1 = 10/7,
x2 = 2/7,
x3 = 0
Thus {(10/7, 2/7, 0, 1)T } is a basis for the nullspace. The dimension
of the column space equals the rank of the matrix which is 3. Thus the
column space must be R3 and we can take as our basis the standard
basis {e1 , e2, e3}.
(c) The reduced row echelon form of the matrix is
0
0
−0.65
1
0
1
0
1.05
0
0
1
0.75
The set {(1, 0, 0, −0.65), (0, 1, 0, 1.05), (0, 0, 1, 0, 0.75)} is a basis
for the row space. The set {(0.65, −1.05, −0.75, 1)T } is a basis for
the nullspace. As in part (b) the column space is R3 and we can take
{e1 , e2 , e3 } as our basis.
3 (b) The reduced row echelon form of A is given by
2
0
5
−3
0
1
0
1
−1
2
0
U = 0
0
0
0
0
0
1
The lead variables correspond to columns 1, 3, and 6. Thus a1 , a3 , a6 form
a basis for the column space of A. The remaining column vectors satisfy the
following dependency relationships.
a2 = 2a1
a4 = 5a1 − a3
a5 = −3a1 + 2a3
4. (c) consistent, (d) inconsistent, (f) consistent
6. There will be exactly one solution. The condition that b is in the column
space of A guarantees that the system is consistent. If the column vectors
are linearly independent, then there is at most one solution. Thus the two
conditions together imply exactly one solution.
7. (a) Since N (A) = {0}
Ax = x1a1 + · · · + xnan = 0
has only the trivial solution x = 0, and hence a1 , . . . , an are linearly
independent. The column vectors cannot span Rm since there are only
n vectors and n < m.
(b) If b is not in the column space of A, then the system must be inconsistent
and hence there will be no solutions. If b is in the column space of A,
then the system will be consistent, so there will be at least one solution.
By part (a), the column vectors are linearly independent, so there cannot
56.
Section 6
53
then
c1Ax1 + c2 Ax2 + c3 Ax3 = 0
A(c1 x1 + c2 x2 + c3 x3 ) = 0
and it follows that c1 x1 + c2x2 + c3 x3 is in N (A). However, we know
from part (a) that N (A) = {0}. Therefore
c1x1 + c2 x2 + c3 x3 = 0
Since x1 , x2 , x3 are linearly independent it follows that c1 = c2 = c3 = 0
and hence y1, y2, y3 are linearly independent.
(c) Since dim R5 = 5 it takes 5 linearly independent vectors to span the
vector space. The vectors y1 , y2, y3 do not span R5 and hence cannot
form a basis for R5.
14. Given A is m × n with rank n and y = Ax where x = 0. If y = 0 then
x 1 a1 + x 2 a2 + · · · + x n an = 0
But this would imply that the columns vectors of A are linearly dependent.
Since A has rank n we know that its column vectors must be linearly independent. Therefore y cannot be equal to 0.
15. If the system Ax = b is consistent, then b is in the column space of A.
Therefore the column space of (A | b) will equal the column space of A.
Since the rank of a matrix is equal to the dimension of the column space it
follows that the rank of (A | b) equals the rank of A.
Conversely if (A | b) and A have the same rank, then b must be in the
column space of A. If b were not in the column space of A, then the rank of
(A | b) would equal rank(A) + 1.
16. (a) If x ∈ N (A), then
BAx = B0 = 0
and hence x ∈ N (BA). Thus N (A) is a subspace of N (BA). On the
other hand, if x ∈ N (BA), then
B(Ax) = BAx = 0
and hence Ax ∈ N (B). But N (B) = {0} since B is nonsingular. Therefore Ax = 0 and hence x ∈ N (A). Thus BA and A have the same
nullspace. It follows from the Rank-Nullity Theorem that
rank(A) = n − dim N (A)
= n − dim N (BA)
= rank(BA)
(b) By part (a), left multiplication by a nonsingular matrix does not alter
the rank. Thus
rank(A) = rank(AT ) = rank(C T AT )
= rank((AC)T )
= rank(AC)
57.
54
Chapter 3
17. Corollary 3.6.4. An n×n matrix A is nonsingular if and only if the column
vectors of A form a basis for Rn .
Proof: It follows from Theorem 3.6.3 that the column vectors of A form a
basis for Rn if and only if for each b ∈ Rn the system Ax = b has a unique
solution. We claim Ax = b has a unique solution for each b ∈ Rn if and
only if A is nonsingular. If A is nonsingular then x = A−1b is the unique
solution to Ax = b. Conversely, if for each b ∈ Rn , Ax = b has a unique
solution, then x = 0 is the only solution to Ax = 0. Thus it follows from
Theorem 1.4.2 that A is nonsingular.
18. If N (A − B) = Rn then the nullity of A − B is n and consequently the rank
of A − B must be 0. Therefore
A−B = O
A = B
19. (a) The column space of B will be a subspace of N (A) if and only if
Abj = 0
for j = 1, . . ., n
However, the jth column of AB is
ABej = Abj ,
j = 1, . . . , n
Thus the column space of B will be a subspace of N (A) if and only if
all the column vectors of AB are 0 or equivalently AB = O.
(b) Suppose that A has rank r and B has rank k and AB = O. By part (a)
the column space of B is a subspace of N (A). Since N (A) has dimension
n − r, it follows that the dimension of the column space of B must be
less than or equal to n − r. Therefore
rank(A) + rank(B) = r + k ≤ r + (n − r) = n
20. Let x0 be a particular solution to Ax = b. If y = x0 + z, where z ∈ N (A),
then
Ay = Ax0 + Az = b + 0 = b
and hence y is also a solution.
Conversely, if x0 and y are both solutions to Ax = b and z = y − x0 ,
then
Az = Ay − Ax0 = b − b = 0
and hence z ∈ N (A).
21. (a) Since
T
x1
x1 y
T
x
2
T x2 y
y =
T
A = xy = .
.
.
.
.
.
T
xm
xm y
the rows of A are all multiples of yT . Thus {yT } is a basis for the row
space of A. Since
A = xyT = x(y1 , y2, . . . , yn)
58.
Section 6
55
= (y1 x, y2x, . . . , yn x)
it follows that the columns of A are all multiples of x and hence {x} is
a basis for the column space of A.
(b) Since A has rank 1, the nullity of A is n − 1.
22. (a) If c is a vector in the column space of C, then
c = ABx
for some x ∈ Rr . Let y = Bx. Since c = Ay, it follows that c is in the
column space of A and hence the column space of C is a subspace of
the column space of A.
(b) If cT is a row vector of C, then c is in the column space of C T . But
C T = B TAT . Thus, by part (a), c must be in the column space of B T
and hence cT must be in the row space of B.
(c) It follows from part (a) that rank(C) ≤ rank(A) and it follows from
part (b) that rank(C) ≤ rank(B). Therefore
rank(C) ≤ min{rank(A), rank(B)}
23 (a) In general a matrix E will have linearly independent column vectors if
and only if Ex = 0 has only the trivial solution x = 0. To show that
C has linearly independent column vectors we will show that Cx = 0
for all x = 0 and hence that Cx = 0 has only the trivial solution. Let
x be any nonzero vector in Rr and let y = Bx. Since B has linearly
independent column vectors it follows that y = 0. Similarly since A has
linearly independent column vectors, Ay = 0. Thus
Cx = ABx = Ay = 0
(b) If A and B both have linearly independent row vectors, then B T and
AT both have linearly independent column vectors. Since C T = B TAT ,
it follows from part (a) that the column vectors of C T are linearly independent, and hence the row vectors of C must be linearly independent.
24. (a) If the column vectors of B are linearly dependent then Bx = 0 for some
nonzero vector x ∈ Rr . Thus
Cx = ABx = A0 = 0
and hence the column vectors of C must be linearly dependent.
(b) If the row vectors of A are linearly dependent then the column vectors
of AT must be linearly dependent. Since C T = B T AT , it follows from
part (a) that the column vectors of C T must be linearly dependent. If
the column vectors of C T are linearly dependent, then the row vectors
of C must be linearly dependent.
25. (a) Let C denote the right inverse of A and let b ∈ Rm . If we set x = Cb
then
Ax = ACb = Im b = b
Thus if A has a right inverse then Ax = b will be consistent for each
b ∈ Rm and consequently the column vectors of A will span Rm .
59.
56
Chapter 3
(b) No set of less than m vectors can span Rm . Thus if n < m, then the
column vectors of A cannot span Rm and consequently A cannot have
a right inverse. If n ≥ m then a right inverse is possible.
27. Let B be an n × m matrix. Since
DB = Im
if and only if
T
B TDT = Im = Im
it follows that D is a left inverse for B if and only if DT is a right inverse
for B T .
28. If the column vectors of B are linearly independent, then the row vectors
of B T are linearly independent. Thus B T has rank m and consequently the
column space of B T is Rm . By Exercise 26, B T has a right inverse and
consequently B must have a left inverse.
29. Let B be an n × m matrix. If B has a left inverse, then B T has a right
inverse. It follows from Exercise 25 that the column vectors of B T span Rm .
Thus the rank of B T is m. The rank of B must also be m and consequently
the column vectors of B must be linearly independent.
30. Let u(1, :), u(2, :), . . ., u(k, :) be the nonzero row vectors of U . If
c1 u(1, :) + c2 u(2, :) + · · · + ck u(k, :) = 0T
then we claim
c1 = c2 = · · · = ck = 0
This is true since the leading nonzero entry in u(i, :) is the only nonzero entry
in its column. Let us refer to the column containing the leading nonzero entry
of u(i, :) as j(i). Thus if
yT = c1u(1, :) + c2 u(2, :) + · · · + ck u(k, :) = 0T
then
0 = yj(i) = ci ,
i = 1, . . . , k
and it follows that the nonzero row vectors of U are linearly independent.
MATLAB EXERCISES
1. (a) The column vectors of U will be linearly independent if and only if the
rank of U is 4.
(d) The matrices S and T should be inverses.
2. (a) Since
r = dim of row space ≤ m
and
r = dim of column space ≤ n
60.
MATLAB Exercises
57
it follows that
r ≤ min(m, n)
(c) All the rows of A are multiples of yT and all of the columns of A are
multiples of x. Thus the rank of A is 1.
(d) Since X and Y T were generated randomly, both should have rank 2 and
consequently we would expect that their product should also have rank
2.
3. (a) The column space of C is a subspace of the column space of B. Thus
A and B must have the same column space and hence the same rank.
Therefore we would expect the rank of A to be 4.
(b) The first four columns of A should be linearly independent and hence
should form a basis for the column space of A. The first four columns
of the reduced row echelon form of A should be the same as the first
four columns of the 8 × 8 identity matrix. Since the rank is 4, the last
four rows should consist entirely of 0's.
(c) If U is the reduced row echelon form of B, then U = M B where M is
a product of elementary matrices. If B is an n × n matrix of rank n,
then U = I and M = B −1 . In this case it follows that the reduced row
echelon form of (B BX) will be
B −1 (B BX) = (I X)
If B is m × n of rank n and n < m, then its reduced row echelon form
is given by
I
U = MB =
O
It follows that the reduced row echelon form of (B BX) will be
X
I
I
M B(I X) = (I X) =
O
O
O
4. (d) The vectors Cy and b + cu are equal since
Cy = (A + uvT )y = Ay + cu = b + cu
The vectors Cz and (1 + d)u are equal since
Cz = (A + uvT )z = Az + du = u + du
It follows that
Cx = C(y − ez) = b + cu − e(1 + d)u = b
The rank one update method will fail if d = −1. In this case
Cz = (1 + d)u = 0
Since z is nonzero, the matrix C must be singular. | 677.169 | 1 |
Teach Yourself VISUALLY Algebra
Algebra may seem intimidating?but it doesn't have to be. With Teach Yourself VISUALLY Algebra, you can learn algebra in a fraction of the time and without ever losing your cool. This visual guide takes advantage of color and illustrations to factor out confusion and helps you easily master the subject. You'll review the various properties of numbers, as well as how to use powers and exponents, fractions, decimals and percentages, and square and cube roots. Each chapter concludes with exercises to reinforce your skills.
David Alan Herzog is the author of numerous mathematics books and more than 100 educational software programs. He taught math education at Fairleigh Dickinson University, was mathematics coordinator for New Jersey's Rockaway Township public schools, and taught in the New York City public school system | 677.169 | 1 |
qsQuest Contents: search engine, textbooks, tutorials, websites Access Level: Free, Open Access Descriptions:Click the specialized virtual keyboard with various symbol sets to type in various types of mathematical problems and search the web for results. Links to textbooks, forums, encyclopedic entries and lecture excerpts, as well as related search listings, help to illuminate problems in statistics, linear, quadratic and differential equations, etc.. A chemistry component is promised for the future.
Keywords: calculus, equations, mathematics, statistics, students
Provider: National Institute of Standards and Technology (NIST) Descriptions: The NIST website outlines the role of the National Institute of Standards and Technology in establishing standards that enhance many areas of American life, including the health care industry, for example: statistics, calibration and other measurement tools, screening and diagnostics, information science and optical physics. Drilling down to division level, one can read about the various research projects under way and some full-text articles on these are freely available. NIST is also the source for official, precise time in the United States. Keywords: calibration, federal agencies, information science, information technology, mathematics, measurement, medical devices, physics, products, science, statistical
Provider: math.com Descriptions: This site offers handy access to calculations, conversions, definitions, a glossary, games, formulas and tables, study and practice resources- and also links to other sources of math-related help and information. Keywords: general reference, kids, mathematics, measurement, student | 677.169 | 1 |
Search Results (16)
This is the final installment of my three part tutorial on the ...
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This is the final installment of my three part tutorial on the CNXML language. It is currently valid for the most recent release of the 0.3 language. The keywords contain a list of the tags described in this tutorial. Along with the example code in this module there is also an example module that has been growing throughout the tutorial.
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This book is designed for the transition course between calculus and differential ...
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It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.
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The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.
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This lesson lays some of the ground work for eventually writing two ...
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This lesson lays some of the ground work for eventually writing two column proofs. In the lesson students use known geometric facts to solve for missing angles. Students are asked to identify the key concepts required for the solution and to record the a path for finding the measure of a particular angle. Key concepts include the sum of the measures of the interior angles of a triangle and quadrilateral, parallel line relationships, and what can and cannot be assumed from a drawing.
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An interactive applet and associated web page that demonstrates a graphical proof ...
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An interactive applet and associated web page that demonstrates a graphical proof of Pythagoras' Theorem. The applet shows a right triangle that is replicated and then moved around to demonstrate the relationship between the sides. It can can be stepped through slowly to allow classroom discussion, or let to run as a movie. Useful for students who like to see things graphically as opposed to symbolically. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at
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This lesson teaches students about the history of the Pythagorean theorem, along ...
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This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.
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This task is intended to help model a concrete situation with geometry. ...
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This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
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The superhyperbolic doubt is the principle that "anything may be possible", for ...
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The superhyperbolic doubt is the principle that "anything may be possible", for that which could otherwise be believed to be absolutely (or 100%) certainly impossible at present could be possible as the intellectual capacities of the believer may be limited. That is, the proposition/s, for example, that are otherwise thought to be absolutely certainly true could be false. The superhyperbolic doubt is compared and attempted to shown to be superior to the hyperbolic Cartesian doubt and the idea/proposition that 'anything is possible'. Furthermore, its implications are stated and discussed, the implications like 'all axioms as 99.99% certainly true' and 'all mathematics as philosophy'. Since the superhyperbolic doubt is the first and the most basic principle of my superultramodern science and philosophy, it could also be referred to as the superultramodern doubt.
Less | 677.169 | 1 |
New in 8.0: Dynamic Interactivity
Mathematica 8 introduces interactive content delivered by Wolfram|Alpha directly into your documents. Additionally, Mathematica 8 extends the existing set of interface controls and introduces paradigms for running dynamic computations that are not linked directly to the output of those computations. | 677.169 | 1 |
IIT JEE Advanced Questions on Sequences and Series - [PLANCESS]
plancess.com - Learn Multiple Methods to solve a Tricky IIT JEE Advanced Questions on Sequences and Series from Shrikant Nagori ( IIT-JEE AIR - 30 ). Prepare for your Boards and New IIT-JEE Pattern-JEE Mains & JEE Advanced/ MH-CET/BITSAT/other Competitve Exams with Plancess
"Questions Covering on all Concepts ie Introduction to Sequences & Series, Arithemetic
Progression(A.P), Geometric Progression(G.P), Harmonic Progression(H.P),
Relation Between Different Means, Arithmetic Geometric Progression, Sum to n Terms of Special Series, Method of Difference"
Note - Please note that this is a sample video of lecture. Quality of the video is compressed due to best view in youtube. Also only Advance level is available for sample viewing. | 677.169 | 1 |
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About the book:
For junior/senior-level courses in Abstract Algebra and Cryptography in departments of mathematics, computer science, and engineering. Emphasizing the fact that solid mathematics leads to solid applications, this text builds a mathematical foundation that includes topics in number theory and the theory of infinite fields. - Hints for using Maple, MultiPAD, and Scientific Notebook. - Supplies students with explicit examples of how to use these technology products to perform calculations related to the course, and enables them to better understand the ideas developed in the text. - An entire chapter devoted to the Rijndael Algorithm - Featuresm the interesting mathematics upon which it is based. - Enables students to focus on and understand the recently adopted Advanced Encryption Standard (replacing the Data Encryption Standard) as the default for financial and web transactions. - Solutions to selected exercises. - Shows students how the solution was worked out - not just the correct answer. - A comprehensive presentation. - Provides students with numerous topics in cryptology, number theory, and error correcting codes - not found in other texts.
Hardcover, ISBN 0130674648 Publisher: Pearson, 2002 Usually dispatched within 1-2 business days, NEW Book, unused. Sent Airmail from New York. Please allow 7-15 Business days for delivery. Excellent Customer Service.
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Hardcover, ISBN 0130674648 Publisher: Prentice Hall 0130674648 Publisher: Prentice Hall Used - Very Good, Usually ships in 1-2 business days, -hardcover. -minimal use with little to no highlighting/writing. -ships within 24 business hours of purchase.
Hardcover, ISBN 0130674648 Publisher: Prentice Hall, 2002 Used - Acceptable, Usually ships in 1-2 business days, Textbook may contain underlining, highlighting or writing. Infotrac or untested CD may not be included. | 677.169 | 1 |
was one of the first books on the Theory of InventiveProblem Solving to appear in the U.S. It quickly became known as the best TRIZ primer available in English—a distinction that it maintains today, nine years after it was first published.Dr. Kaplan's straightforward explanation of the basic elements of TRIZ theory, and hisdescription of the tools that emerged from the first three decades of TRIZ development, arerelevant for experienced engineers and novices alike. His analogy between the search for aninventive solution and the process of solving a quadratic equation is both simple and profound,and makes the TRIZ problem-solving approach comprehensible to anyone with a knowledgeof basic algebra.Although TRIZ continues to evolve, its foundation remains intact—and is essential study for those pursuing a thorough understanding of this powerful methodology.Victoria RozaIdeation International Inc. | 677.169 | 1 |
Web Site Webmath.com This is a dynamic math website where students enter problems and where the site's math engine solves the problem. Students in most cases are given a step-by-... Curriculum: Mathematics Grades: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
8.
Web Site Prentice Hall Math Textbook Resources This site has middle school and high school lesson quizzes, vocabulary, chapter tests and projects for most chapters in each textbook. In some sections, ther... Curriculum: Mathematics Grades: 6, 7, 8, 9, 10, 11, 12
9.
Web Site Dave's Short Trig Course Check out the short trigonometry course and learn the new way of learning trig. This short course breaks into sections and allows user to learn at his/her o... Curriculum: Mathematics Grades: 9, 10, 11, 12
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Math Department
The Walsh Jesuit High School mathematics program is designed to provide each student with a concrete background for any progression of math courses that he/she may choose to embark upon in his/her college career. In order to achieve this objective, the mathematics department has developed a series of courses that, along with fulfilling each student's post-secondary needs, should also challenge each student's present abilities.
Because of the wide application of math to other areas of study, particularly the sciences, it is our goal to develop lifelong problem-solving skills. These skills should enable a student to be able to competently step into a world of ideas where the only tools are his/her mind and the ability to apply deductive mathematical reasoning to the solution of problems, mathematical and otherwise. | 677.169 | 1 |
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The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser,... more...
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Choose the Correct Solution Method for Your Optimization Problem
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Mathematics
Trained tutors and a variety of resources are available in the Learning Commons to assist with topics related to mathematics. Assistance is available to students on an individual or small group basis, and calculators, handouts and a variety of videos are available. Online homework can also be accessed in the LC.
Students should consult the tutoring schedule and bring the following items to all sessions:
Class notes and handouts
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Tutoring availability is subject to change depending upon day of the week and semester. Please check the tutoring schedule to see when writing help is available | 677.169 | 1 |
′s no doubt that algebra can be easy to some while extremely challenging to others. If you′re vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain–English, easy–to–follow guidance you need to get the right solution every time!
Now with 25% new and revised content, this easy–to–understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You′ll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations.
Other titles by Sterling: Algebra II For Dummies and Algebra Workbook For Dummies
Whether you′re currently enrolled in a high school or college algebra course or are just looking to brush–up your skills, Algebra I For Dummies, 2nd Edition gives you friendly and comprehensible guidance on this often difficult–to–grasp subject.
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Does the word polynomial make your hair stand on end? Let this friendly guide show you the easy way to tackle algebra. You′ll get plain–English explanations of the basics and the tougher stuff in terms you can understand. Whether you want to brush up on your math skills or help your children with their homework, this book gives you power to the nth degree.
It′s all about numbers get the lowdown on numbers rational and irrational, integers, and positive and negative
Factor in the fun discover the easy way to figure out working with prime numbers, factoring, and distributing
Don′t hate, equate! get a handle on the most common equations you′ll encounter in algebra, from basic linear problems to the quadratic formula and everything in between
Resolve to solve learn how to solve linear and quadratic equations, keep equations balanced, and check your work
Put it to use find out how to apply algebra to tackle measurements, formulas, story problems, and graphs
Open the book and find:
Plain–English explanations of "algebra speak"
How to figure out fractions and deal with decimals
Guidance on working with exponents and radicals
The rules of divisibility
The standard quadratic expression
When to use FOIL and unFOIL
Special cases for factoring
The ground rules for solving equations
How to put the Pythagorean theorem to work
Learn to:
Understand algebra
Solve complex problems
Find the solution every time
Increase your understanding of how algebra works
About the Author
Mary Jane Sterling has been teaching algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.
Most Helpful Customer Reviews
It took me six weeks in the evening to read every word, practice and take notes for the future from this book (an after work project and I never missed a day). This is not one of those do it in a weekend Dummies books unless your very up on math. My math at school stopped at GCSE level but I did well in it. However I did do A level physics and picked up some in my first degree. The last time I did math was 1998-2001 I am 31 now (yeah what a laugh worked for years and never needed it). I am getting ready to do another degree in science (we live longer now so I thought why not). I have found this book a good get ready/revision book. I would not advise it for kids it goes very quick and often into more depth than school will on a topic. Good for a parent though who wants to help pull their kid along and needs a refresher and find the curriculum the kids use just too slow and verbose.
I am just going on to Algebra 2 so I will drop a review when I finish it.
Algebra is the key to computer programming, physics, calculus etc the list is endless and it starts here. This book is time well spent as it will shortcut learning fields in which algebra is used or borrowed from. This book is a good investment in that regard.
Caveat this book will be really tough if you left school without any math qualifications you will need more rudimentary work first this does not cover general math at all...apart from a quick fire run at fractions, powers, roots, signs etc it just goes direct into algebra. Well it is an algebra book. :)
It really is a superb book for learning algebra. However I quickly realised that I didn't quite reach up to the "Dummie" level. Whilst it explains the basics, if you wish to learn algebra there are other important mathematical milestones need to be reached first. I have had to put this book away and start learning skills and levels I am too embarrassed to list here! great book, great service!!
Part of my uni computer course took in maths, serious maths, and this not being my best subject am prone to a struggle or two and actually think that I am number dyslectic consequently algebra frazzled my brain. This book starts with the basics - fractions - which are easy enough. Then we slowly progress through Factoring, Equations, Formulas, Graphs, and so it goes on. But the book is done so that an element of fun comes into the learning therefore making it easier to understand and retain in the old memory banks.
Mary Jane Sterling has done a sterling job of making this book easy to read and algebra to understand.
I have O level C grade and work in year 6 of a primary school as a TA. A basic knowledge of algebra seems to be necessary now to work in year 6 although I don't think it always was so I bought this book as I do not want to look stupid! I would say it assumes a knowledge of maths equating to about level 5 National Curriculum. I am finding it very helpful. I need to keep reading it as I need to know what 'simplify' means and also 'factorise'. I have forgotton now that I am getting on!
As far as service is concerned there is little to say. Everything functioned reasonably well and the book arrived in good condition in a reasonable time.
Regarding the book it seems to me a little more difficult to comment ... much depends on what people want. I bought the book to help my son review his Alegbra. The fact that he is not terribly motivated to read the book is certainly not the fault of the author. One impression we have had is that the book may not be the best approach for many teenagers: It seems to be structured more for °adults° that need a review of the basic concepts for one reason or another.
Certainly the book doesn't cost that much so it's worth trying it out. For those motivated to review quickly it is certainly worth .it
I love these books, i have purchased several for 2 of my daughters, they are so easy to understand and put everything in simple form that makes you think why do they just not teach the subject this way becaause it really does work, excellent product everytime.
I hadn't placed my nose in a maths book since 1976 and wanted to gain a basis to understanding the subject in greater detail. The author presents the subject in a structured fashion and injects this book with plenty of humour to help get the concept across with as little pain as possible. There are plenty of books which make algebra seem dull and dreary, but this is definitely not one of them! I did not read this book from cover to cover, but used it build up an idea of the subject over time. Not having a teacher to help me, I had to rely purely on the text and because of the way this is written did not find it too difficult. I liked the book so much I bought her book, Algebra ll as well. | 677.169 | 1 |
Knot Book: An Elementary Introduction to the Mathematical Theory of Knots…
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Knot Book: An Elementary Introduction to the Mathematical Theory of Knots available in
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Overview understood with only a background of high school algebra and can be solved by the curious amateur. All you need to begin is a piece of string, a little math, a little imagination, and Colin Adams's The Knot Book - the first book to make cutting-edge research in knot theory accessible to a nonspecialist audience. What are the different properties and classifications of knots? How do you determine whether a knot is actually knotted or can be untangled? What is the appropriate measure of the complexity of a knot? What does knot theory research offer to other sciences? In The Knot Book Colin Adams describes and illustrates the work being done to answer these questions. Starting with the simplest knot (the trivial knot or unknot), Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians now can solve, as well as those that remain open. He also looks at how knot theory is providing important insights in biology, chemistry, physics, and other fields. Included are hundreds of illustrations of knots (including a table at the end of the book displaying nearly 200 different knots) as well as worked examples, exercises open problems - even a few knot jokes and pastimes. Colin Adams explains knot theory with an enthusiasm and an informal style that makes this seemingly mysterious subject easy to approach. With The Knot Book and a mathematical background that includes no more than a familiarity with polynomials, you will be able to understand and work with some of the discipline's most modern and provocative ideas.
Editorial Reviews
Booknews
For the nonspecialist seeking the advanced merit badge, addresses such questions as the properties and types of knots, distinguishing between a true knot and a mere tangle, and measuring a knot's complexity. The emerging branch of mathematics dealing with knots is finding applications in DNA research and synthesizing new molecules, and is providing some interesting puzzles for statistical mechanics and quantum field theory. Does not cover knotholes. Illustrates nearly 200 knots. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
"Adams is an expert in knot theory, and this shows in the clarity and accuracy of his writing, and in the rich store of examples and problems . . . We are going to see much more of knot theory and its applications, and this book is an excellent place to start." —Nature | 677.169 | 1 |
0321069Built on AMATYC and NCTM standards, this book takes an active learning approach, focusing on collaborative for small groups. Independent learning is encouraged as problem-solving skills illustrate connections among mathematic ideas as readers discover and build on concepts explored as a group, as the book focuses on learning in a social context. Each section of a chapter opens with the investigation of a problem, in which readers gather data and collaborate on investigative activities. The book's discussion summarizes matheatic ideas gained from the investigations. At the end of each section concept maps enable readers to devise key ideas and draw connections between aspects of the concepts. For anyone interested concepts and processes or seeking an introduction to algebra | 677.169 | 1 |
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Visualization: Data Visualization Quick Start (German)
Harness the power of Mathematica to interactively visualize your data. This video features a series of examples that show how to create a rich interface for exploring data in depth. Includes German audio.
Channels: Virtual Events
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to learn to carry out certain types of operations, and to be
able to apply those operations to solve problems
to write coherently and correctly about calculus
methods. This includes being able to formulate and effectively
communicate a problem analysis and solution using methods of calculus
to recognize problem situations for which calculus methods are
applicable, and to be able to understand analyses of such problem
situations that make use of calculus methods
to understand the general characteristics of the mathematical
method.
Admittedly, parts of this list are vague. Paradoxically, in
order to understand a more specific set of objectives, you would
already need to know calculus. The objectives would naturally
mention new concepts and use terminology that you will learn in the
course, but which would not make any sense to you now (unless you have
already studied calculus).
To make an analogy, imagine that you have completed a study of the
arithmetic of whole numbers -- that is, addition, subtraction,
multiplication, and division of integers greater than or equal to
zero. Next you will take a course on the arithmetic of rational
numbers. The goals of instruction would mention concepts like
fractions, negative numbers, reciprocals. But until you have
studied rational numbers, these terms have no meaning, or what is more
confusing, a meaning in everyday usage that is quite different from the
intended meaning in the course.
In a sense, a math course is similar to a course in a foreign
language. A
fundamental goal is to master enough of the vocabulary and grammar and
idiom to carry on a conversation. You might say that every
mathematical subject corresponds to a different language, say
Algebraish for algebra, Trigish in trigonometry, and Calculish for
calculus. Of course, these aren't really separate
languages. Each mathematical language is actually a specialized
part of your normal language. That can give you a misleading
impression. You can listen to me conversing in Calculish and
think you are understanding it, because you understand the regular
English parts of it. However, true understanding only occurs when
we can communicate our ideas to each other, and that is impossible if
my ideas concern concepts you have not yet learned. From this
perspective, the point of studying calculus is to learn a new dialect
of English, namely Calculish, and to learn it well enough to understand
spoken and written conversation. In a word, your goal is fluency.
Many students are required to take calculus as they pursue majors in
other disciplines, like biology, or physics, or economics. If you
are one of these students, fluency in Calculish is probably the most
important goal of the course. That is because there are
important applications of calculus in your major. Your completion
of calculus 1 is not necessarily so that you can actively apply it in
your future work, or even so you can make direct use of results others
have obtained using calculus. Rather, it is so you can
participate meaningfully in the conversation.
This is a key observation about the objectives of the course.
Learning the methods and memorizing the definitions and being able to
solve homework problems accomplishes little or nothing if you do not
gain fluency in the process. That is why the first
objective listed above concerns conceptual understanding, and why
writing coherently and correctly are also included.
The last objective on the list is probably the vaguest of them
all. It reflects the fact that mathematical knowledge is
developed in a highly stylized form. Think of it as a combination
of grammatical structure and idiomatic usage that underlies all
mathematical language. True fluency demands an understanding of
the grammar and idiom of the language. And this is especially
true for mathematics, because its structure is so different from normal
conversational language. Over the course of the semester, you
will see how this structure appears in the specific context of
calculus. The better you understand the structure, the greater
your ability to converse fluently in Calculish. I refer to these
as general characteristics of the mathematical method because they
pervade all of mathematics. Developing an understanding of this
structure of mathematical knowledge is an important general education
goal, because it gives you access to a broad literature of mathematical
analyses and methods. | 677.169 | 1 |
college-level math classes, from remedial Calculus to Multivariate Calculus. | 677.169 | 1 |
This lesson received an honorable mention in the 2012 SoftChalk Lesson Challenge.'In this lesson we begin to examine what...
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This lesson received an honorable mention in the 2012 SoftChalk Lesson Challenge.'In this lesson we begin to examine what happens when we have a list of numbers, known as a sequence. We will determine when these lists of numbers, or sequences, have a pattern, when we can generalize that pattern to find any term and what it looks like if we sum up the numbers in the sequence. Let's start off with a few definitions and some terminology and from there we will see how we can determine their behaviorThis lesson was the second place winner in the 2012 SoftChalk Lesson Challenge.The lesson has the following objectives:...
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This lesson was the second place winner in the 2012 SoftChalk Lesson Challenge.The lesson has the following objectives: AState the integer that corresponds to a real-world situation.BGraph rational numbers on the number line.CConvert from fraction notation for a rational number to decimal notation.DDetermine which of two real numbers is greater and indicate which, using < or >.EFind the absolute value of a real number.FIdentify numbers that are members of the Real Number Numbers to your Bookmark Collection or Course ePortfolio
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Select this link to open drop down to add material The Real NumbersWe have deveoped and provide access to an extensive, interactive self-review library covering 26 lecture modules in general...
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We have deveoped and provide access to an extensive, interactive self-review library covering 26 lecture modules in general astronomy to give students instruction tailored to their rate of learning and mathematical abilities, with personal feedback, as they integrate new knowledge into their existing view of the universe. Students typically complete 1,600 problems over a semester, drawing from an archive of over 12,000 questions presenting both conceptual and mathematically-focused challenges.A companion instructor analysis tool for reviewing student work archives copies of each exercise completed by every student, including the details of incorrect answers, and reveals trends with topic and time for individuals and groups. Instructors are able to monitor individual and group progress, tracking every facet of student action and the global response to individual topics of study.Individual accounts are available by request to both students and to intructors and their classes Astronomy Online Tutor to your Bookmark Collection or Course ePortfolio
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