Pure Mathematics Books

Godel, Escher, Bach: An Eternal Golden Braid

Douglas R. Hofstadter

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Customer Reviews:
Total reviews: 244 Average rating: 4.5 of 5

Editorial Review:

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

The Fractal Geometry of Nature

Benoit B. Mandelbrot

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Customer Reviews:
Total reviews: 13 Average rating: 4.0 of 5

A seminal work 5 out of 5 stars.
19 of 21 people found this review helpful.

Very few books have so many quotes as this one. I am not sure if there is much left to be said, but I know this. For those professionals who still think that fractals are "spurious solutions coming from the discretization of differential equations", should take a closer look to this book. Not only won't harm, but also will show many interesting features about the nature of fractals and the "fractality" of nature, besides the fact that many of them come from *difference* equations, which are not necessarily related to the discretization of a differential equation. This book is based on serious work from many well-reputed mathematicians before Mandelbrot, e.g., Haussdorff, Lyapunov and some others. Although the book does talk about the mathematics behind fractals (wouldn't be so much a book of mathematics if it didn't, but also a philosophical one) and the necessity of coining some new mathematical terms, it also contains so much about history of mathematics, the path that leads towards fractals. As I said, the book is many times quoted, but (without trying to point a firing, accusing finger), there is a difference in quoting a book because it is famous, and another actually reading it, and having enlightenment for our own sake. Certainly I think is a "must-have-it" for most mathematicians, for many physicists, philosophers of science and engineers, but also it wouldn't be a bad guest in the library of any layman, provided the layman overcomes for some minutes the initial "classical" fear to mathematics. I would say this layman won't regret it at all. Mandelbrot does explain most of the concepts practically "ab initio", from the very scratch, including etymology and history as I previously said. One little thing against this book though: it doesn't have so many color plates as some other books on the subject, but it does have all the needed graphics to grasp the concepts.

Editorial Review:

Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.

Calculus for Dummies

Mark Ryan

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Total reviews: 67 Average rating: 4.5 of 5

Editorial Review:

The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein.

Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.

Calculus For Dummies is intended for three groups of readers:

• Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
• Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
• Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth.

This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:

• Real-world examples of calculus
• The two big ideas of calculus: differentiation and integration
• Why calculus works
• Pre-algebra and algebra review
• Common functions and their graphs
• Limits and continuity
• Integration and approximating area
• Sequences and series

Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression.

Cracking the AP Calculus AB & BC Exams, 2008 Edition (College Test Prep)

David S. Kahn

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Customer Reviews:
Total reviews: 8 Average rating: 5.0 of 5

My son got a 5 on the Test using this 5 out of 5 stars.
8 of 8 people found this review helpful.

My school does not offer AP Calculus, but by AP rules, you can take the test despite not having the class. So, my son decided to use this book to help him prepare. My son is very good at math, so he was able to learn from the way this presented the material. He ended up getting the highest possible score.

If you have the class-imagine what you can accomplish with this aid.

Editorial Review:

Scoring high on the AP Calculus AB & BC Exams is very different from earning straight A’s in school. We don’t try to teach you everything there is to know about calculus—only the strategies and information you’ll need to get your highest score. In Cracking the AP Calculus AB & BC Exams, we’ll teach you how to

·Use our preparation strategies and test-taking techniques to raise your score
·Focus on the topics most likely to appear on the test
·Test your knowledge with review questions for each calculus topic covered

This book includes 5 full-length practice AP Calculus AB & BC tests: 3 for AB and 2 for BC. All of our practice questions are just like those you’ll see on the actual exam, and we explain how to answer every question.

Cracking the AP Calculus AB & BC Exams has been fully updated for the 2008 tests.

The Misbehavior of Markets: A Fractal View of Risk, Ruin & Reward

Benoit Mandelbrot, Richard L. Hudson

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Customer Reviews:
Total reviews: 54 Average rating: 3.5 of 5

Editorial Review:

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change. In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again.

Algebra for Dummies

Mary Jane Sterling

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Total reviews: 32 Average rating: 3.5 of 5

Editorial Review:

One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you power" – the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on.

Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra For Dummies can provide the help you need.

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. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works.

In Algebra For Dummies, you'll discover the following topics and more:

• All about numbers – rational and irrational, variables, and positive and negative
• Figuring out fractions and decimals
• Explaining exponents and radicals
• Solving linear and quadratic equations
• Understanding formulas and solving story problems
• Having fun with graphs
• Top Ten lists on common algebraic errors, factoring tips, and divisibility rules.

No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra For Dummies can give you the tools you need to succeed.

Basic Math & Pre-Algebra For Dummies (For Dummies (Math & Science))

Mark Zegarelli

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Customer Reviews:
Total reviews: 6 Average rating: 4.0 of 5

Would not have passed without it!! 5 out of 5 stars.
5 of 5 people found this review helpful.

Amazing book! I HATED math in high school! When I found myself going to college at 35, the entrance exam with all the algebraic problems was all French to me...I took the Pre-Algebra prep course at the college but found the textbook to be overwhelmingly confusing. This book cured all that. The For Dummies series is one of the best inventions since the wheel and this volume helped me pass Pre-Algebra as well as showing me that math can actually be a better experience than going to the dentist.

Editorial Review:

Tips for simplifying tricky operations

Get the skills you need to solve problems and equations and be ready for algebra class

Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.


* Understand fractions, decimals, and percents
*

Unravel algebra word problems
*

Grasp prime numbers, factors, and multiples
*

Work with graphs and measures
*

Solve single and multiple variable equations

Algebra Workbook For Dummies

Mary Jane Sterling

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Total reviews: 15 Average rating: 4.5 of 5

Algebra for Dummies & Workbook for same 4 out of 5 stars.
2 of 3 people found this review helpful.

I recently ordered the Algebra for Dummies, as well as the workbook to go with it, for a friend who is trying to obtain a position with a company who is looking for someone with math skills in algebra.

He is working out of state, so I had the books shipped to his address. Upon asking him if he thought these books would help him, he said they definitely would. His comment was that they were easy to understand, and although it has been 20+ years since he was in school, he thought he had a good chance at getting the job.

Anything that I have ever ordered from Amazon has always come quickly, been the correct item, and I will certainly keep ordering things from them.

Algebra Workbook For Dummies 4 out of 5 stars.
1 of 1 people found this review helpful.

It was a good choice, to help my nephew with his algbra.
His in 8th grade and it makes algbra easier to understand
HECK i may even use it.

Editorial Review:

Problem topics can include improper numbers, grouping symbols, using proportions, rationalizing fractions, multiplying and factoring expressions, solving linear and quadratic equations, working with inequalities, and using formulas in story problems.

Practical Algebra: A Self-Teaching Guide, 2nd Edition

Peter H. Selby, Steve Slavin

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Total reviews: 63 Average rating: 4.5 of 5

Editorial Review:

Practical Algebra If you studied algebra years ago and now need a refresher course in order to use algebraic principles on the job, or if you're a student who needs an introduction to the subject, here's the perfect book for you. Practical Algebra is an easy and fun-to-use workout program that quickly puts you in command of all the basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you'll learn:
* The basic approach and application of algebra to problem solving
* The number system (in a much broader way than you have known it from arithmetic)
* Monomials and polynomials; factoring algebraic expressions; how to handle algebraic fractions; exponents, roots, and radicals; linear and fractional equations
* Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, and more
Authors Peter Selby and Steve Slavin emphasize practical algebra throughout by providing you with techniques for solving problems in a wide range of disciplines--from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology and business administration. Step by step, Practical Algebra shows you how to solve algebraic problems in each of these areas, then allows you to tackle similar problems on your own, at your own pace. Self-tests are provided at the end of each chapter so you can measure your mastery.

The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides)

Adrian Banner

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Total reviews: 15 Average rating: 5.0 of 5

Editorial Review:

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.

All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.

The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.

• Serves as a companion to any single-variable calculus textbook
• Informal, entertaining, and not intimidating
• Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--will be available through the book's Web site at www.calclifesaver.com
• More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
• Theorems and methods justified and connections made to actual practice
• Difficult topics such as improper integrals and infinite series covered in detail
• Tried and tested by students taking freshman calculus