Mathematics

The Drunkard's Walk: How Randomness Rules Our Lives

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.

Freakonomics [Revised and Expanded]: A Rogue Economist Explores the Hidden Side of Everything

Economics is not widely considered to be one of the sexier sciences. The annual Nobel Prize winner in that field never receives as much publicity as his or her compatriots in peace, literature, or physics. But if such slights are based on the notion that economics is dull, or that economists are concerned only with finance itself, Steven D. Levitt will change some minds. In Freakonomics (written with Stephen J. Dubner), Levitt argues that many apparent mysteries of everyday life don't need to be so mysterious: they could be illuminated and made even more fascinating by asking the right questions and drawing connections. For example, Levitt traces the drop in violent crime rates to a drop in violent criminals and, digging further, to the Roe v. Wade decision that preempted the existence of some people who would be born to poverty and hardship. Elsewhere, by analyzing data gathered from inner-city Chicago drug-dealing gangs, Levitt outlines a corporate structure much like McDonald's, where the top bosses make great money while scores of underlings make something below minimum wage. And in a section that may alarm or relieve worried parents, Levitt argues that parenting methods don't really matter much and that a backyard swimming pool is much more dangerous than a gun. These enlightening chapters are separated by effusive passages from Dubner's 2003 profile of Levitt in The New York Times Magazine, which led to the book being written. In a book filled with bold logic, such back-patting veers Freakonomics, however briefly, away from what Levitt actually has to say. Although maybe there's a good economic reason for that too, and we're just not getting it yet. --John Moe

Which is more dangerous, a gun or a swimming pool? What do schoolteachers and sumo wrestlers have in common? Why do drug dealers still live with their moms? How much do parents really matter? How did the legalization of abortion affect the rate of violent crime?

These may not sound like typical questions for an econo-mist to ask. But Steven D. Levitt is not a typical economist. He is a much-heralded scholar who studies the riddles of everyday life—from cheating and crime to sports and child-rearing—and whose conclusions turn conventional wisdom on its head.

Freakonomics is a groundbreaking collaboration between Levitt and Stephen J. Dubner, an award-winning author and journalist. They usually begin with a mountain of data and a simple question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics.

Through forceful storytelling and wry insight, Levitt and Dubner show that economics is, at root, the study of incentives—how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they explore the hidden side of . . . well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Klu Klux Klan.

What unites all these stories is a belief that the modern world, despite a great deal of complexity and downright deceit, is not impenetrable, is not unknowable, and—if the right questions are asked—is even more intriguing than we think. All it takes is a new way of looking.

Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.

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Which is more dangerous, a gun or a swimming pool? What do schoolteachers and sumo wrestlers have in common? Why do drug dealers still live with their moms? How much do parents really matter? What kind of impact did Roe v. Wade have on violent crime?

These may not sound like typical questions for an economist to ask. But Steven D. Levitt is not a typical economist. He is a much heralded scholar who studies the stuff and riddles of everyday life -- from cheating and crime to sports and child rearing -- and whose conclusions regularly turn the conventional wisdom on its head. He usually begins with a mountain of data and a simple, unasked question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics.

Through forceful storytelling and wry insight, Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives -- how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they set out to explore the hidden side of ... well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Ku Klux Klan.

What unites all these stories is a belief that the modern world, despite a surfeit of obfuscation, complication, and downright deceit, is not impenetrable, is not unknowable, and -- if the right questions are asked -- is even more intriguing than we think. All it takes is a new way of looking. Steven Levitt, through devilishly clever and clear-eyed thinking, shows how to see through all the clutter.

Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.

One to Nine: The Inner Life of Numbers

What Lynne Truss did for grammar in Eats, Shoots & Leaves, Andrew Hodges now does for mathematics.

Andrew Hodges, one of Britain's leading biographers and mathematical writers, brings numbers to three-dimensional life in this delightful and illuminating volume, filled with illustrations, which makes even the most challenging math problems accessible to the layperson. Inspired by millennia of human attempts to figure things out, this pithy book, which tackles mathematical conundrums from the ancient Greeks to superstring theory, finds a new twist to everything from musical harmony to code breaking, from the chemistry of sunflowers to the mystery of magic squares. Starting with the puzzle of defining unity, and ending with the recurring nines of infinite decimals, Hodges tells a story that takes in quantum physics, cosmology, climate change, and the origin of the computer. Hodges has written a classic work, at once playful but satisfyingly instructional, which will be ideal for the math aficionado and the Sudoku addict as well as for the life of the party. 40 illustrations.

Kaplan GRE Math Workbook, Sixth Edition

* 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

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

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

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

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.

Calculus for Dummies

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

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.