Books -- Math<ul>

Math

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The Drunkard's Walk: How Randomness Rules Our Lives

Release Date: 2008-05-13

Sales rank: 64

Amazon Guest Review: Stephen Hawking
Published in 1988, Stephen Hawking's A Brief History of Time became perhaps one of the unlikeliest bestsellers in history: a not-so-dumbed-down exploration of physics and the universe that occupied the London Sunday Times bestseller list for 237 weeks. Later successes include 1995's A Briefer History of Time, The Universe in a Nutshell, and God Created the Integers: The Mathematical Breakthroughs that Changed History. Stephen Hawking is Lucasian Professor of Mathematics at the University of Cambridge.

In The Drunkard's Walk Leonard Mlodinow provides readers with a wonderfully readable guide to how the mathematical laws of randomness affect our lives. With insight he shows how the hallmarks of chance are apparent in the course of events all around us. The understanding of randomness has brought about profound changes in the way we view our surroundings, and our universe. I am pleased that Leonard has skillfully explained this important branch of mathematics. --Stephen Hawking

In this irreverent and illuminating book, acclaimed writer and scientist Leonard Mlodinow shows us how randomness, change, and probability reveal a tremendous amount about our daily lives, and how we misunderstand the significance of everything from a casual conversation to a major financial setback. As a result, successes and failures in life are often attributed to clear and obvious cases, when in actuality they are more profoundly influenced by chance.

The rise and fall of your favorite movie star of the most reviled CEO--in fact, of all our destinies--reflects as much as planning and innate abilities. Even the legendary Roger Maris, who beat Babe Ruth's single-season home run record, was in all likelihood not great but just lucky. And it might be shocking to realize that you are twice as likely to be killed in a car accident on your way to buying a lottery ticket than you are to win the lottery.

How could it have happened that a wine was given five out of five stars, the highest rating, in one journal and in another it was called the worst wine of the decade? Mlodinow vividly demonstrates how wine ratings, school grades, political polls, and many other things in daily life are less reliable than we believe. By showing us the true nature of change and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives fresh insight into what is really meaningful and how we can make decisions based on a deeper truth. From the classroom to the courtroom, from financial markets to supermarkets, from the doctor's office to the Oval Office, Mlodinow's insights will intrigue, awe, and inspire.

Offering readers not only a tour of randomness, chance, and probability but also a new way of looking at the world, this original, unexpected journey reminds us that much in our lives is about as predictable as the steps of a stumbling man fresh from a night at the bar.

Kaplan GRE Math Workbook, Sixth Edition

Sales rank: 1668

* Hundreds of test-like practice questions

* Detailed answer explanations

* Proven score-raising strategies

* Tactics for solving all question types

* Review of core math concepts

* Details on the linear computer-based testing format and on-screen calculator

The Visual Display of Quantitative Information, 2nd edition

Sales rank: 1447

A timeless classic in how complex information should be presented graphically. The Strunk & White of visual design. Should occupy a place of honor--within arm's reach--of everyone attempting to understand or depict numerical data graphically. The design of the book is an exemplar of the principles it espouses: elegant typography and layout, and seamless integration of lucid text and perfectly chosen graphical examples. Very Highly Recommended.

Math Workbook for the New SAT (Barron's Math Workbook for the Sat I)3rd Edition

Sales rank: 1906

Revised to reflect the newly structured math section on the SAT, the new edition of this workbook offers students intensive preparation for the test’s all-important math questions. The author suggests special math strategies to help students approach unfamiliar types of questions and come up with correct answers. Exercises include hundreds of multiple-choice questions and “grid-in” questions with worked-out solutions, plus a new focus on third-year college preparatory math topics.

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

Release Date: 2006-08-08

Sales rank: 2314

These simple math secrets and tricks will forever change how you look at the world of numbers.

Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.

Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

Also available as an eBook

Godel, Escher, Bach: An Eternal Golden Braid

Sales rank: 1626

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.

Douglas Hofstadter’s book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel Escher and Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

Calculus for Dummies

Sales rank: 1580

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.

Algebra Workbook For Dummies

Sales rank: 2613

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.

Cracking the SAT Math 1 and 2 Subject Tests, 2007-2008 Edition (College Test Prep)

Release Date: 2007-03-06

Sales rank: 1963

The Princeton Review realizes that acing the SAT Math Subject Tests is very different from earning straight A’s in school. We don’t try to teach you everything there is to know about math–only the techniques and information you’ll need to maximize your score. In Cracking the SAT Math 1 and 2 Subject Tests, we’ll teach you how to think like the test writers and

·Learn what subject matter will be tested so you can study more effectively
·Review key math vocabulary, basic functions, and equations
·Use proven techniques to solve complicated questions

The 2007-2008 edition of Cracking the SAT Math 1 and 2 Subject Tests is revised and updated to include the most current information possible.

How to Lie With Statistics

Sales rank: 3493

"There is terror in numbers," writes Darrell Huff in How to Lie with Statistics. And nowhere does this terror translate to blind acceptance of authority more than in the slippery world of averages, correlations, graphs, and trends. Huff sought to break through "the daze that follows the collision of statistics with the human mind" with this slim volume, first published in 1954. The book remains relevant as a wake-up call for people unaccustomed to examining the endless flow of numbers pouring from Wall Street, Madison Avenue, and everywhere else someone has an axe to grind, a point to prove, or a product to sell. "The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify," warns Huff.

Although many of the examples used in the book are charmingly dated, the cautions are timeless. Statistics are rife with opportunities for misuse, from "gee-whiz graphs" that add nonexistent drama to trends, to "results" detached from their method and meaning, to statistics' ultimate bugaboo--faulty cause-and-effect reasoning. Huff's tone is tolerant and amused, but no-nonsense. Like a lecturing father, he expects you to learn something useful from the book, and start applying it every day. Never be a sucker again, he cries!

Even if you can't find a source of demonstrable bias, allow yourself some degree of skepticism about the results as long as there is a possibility of bias somewhere. There always is.

Read How to Lie with Statistics. Whether you encounter statistics at work, at school, or in advertising, you'll remember its simple lessons. Don't be terrorized by numbers, Huff implores. "The fact is that, despite its mathematical base, statistics is as much an art as it is a science." --Therese Littleton

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