Mathematics Books

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

Steven D. Levitt, Stephen J. Dubner

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Subjects -> Business & Investing -> Popular Economics -> General AAS

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Total reviews: 1581 Average rating: 4.0 of 5

Editorial Review:

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

The Drunkard's Walk: How Randomness Rules Our Lives

Leonard Mlodinow

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Total reviews: 50 Average rating: 4.5 of 5

Editorial Review:

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

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Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

Nassim Nicholas Taleb

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Total reviews: 387 Average rating: 4.0 of 5

Editorial Review:

If the prescriptions for getting rich that are outlined in books such as The Millionaire Next Door and Rich Dad Poor Dad are successful enough to make the books bestsellers, then one must ask, Why aren't there more millionaires? In Fooled by Randomness, Nassim Nicholas Taleb, a professional trader and mathematics professor, examines what randomness means in business and in life and why human beings are so prone to mistake dumb luck for consummate skill. This eccentric and highly personal exploration of the nature of randomness meanders from the court of Croesus and trading rooms in New York and London to Russian roulette, Monte Carlo engines, and the philosophy of Karl Popper. Part of what makes this book so good is Taleb's ability to make seemingly arcane mathematical concepts (at least to this reviewer) entirely relevant in evaluating and understanding everything from the stock market to the success of those millionaires cited in the aforementioned bestsellers. Here's an articulate, wise, and humorous meditation on the nature of success and failure that anyone who wants a little more of the former would do well to consider. Highly recommended. --Harry C. Edwards

The Visual Display of Quantitative Information, 2nd edition

Edward R. Tufte

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Total reviews: 96 Average rating: 4.5 of 5

The Ups and Downs of Tufte's Book 3 out of 5 stars.
0 of 0 people found this review helpful.

It definitely was interesting and educational to read and see Tufte's presentation on Visual Dispaly of Quantitative Information. He illustrates the good, the bad, and the ugly of graphic displays over the centuries. However, I was hoping to see more examples of current computer graphics that should be emulated in this edition instead of terse comments and skeletal constructs in this area.

Easy and fun to read 4 out of 5 stars.
0 of 0 people found this review helpful.

I was able to read this fairly quickly. (stealing a few hours here and there at work).

Although I did not find any direct solutions to my current problems - it definitely opened my imagination to consider new possibilities.

Editorial Review:

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.

Godel, Escher, Bach: An Eternal Golden Braid

Douglas R. Hofstadter

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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.

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

Arthur Benjamin, Michael Shermer

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Total reviews: 18 Average rating: 5.0 of 5

Editorial Review:

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.



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The Art of Strategy: A Game Theorist's Guide to Success in Business and Life

Avinash K. Dixit, Barry J. Nalebuff

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Total reviews: 2 Average rating: 5.0 of 5

A Great Success 5 out of 5 stars.
5 of 23 people found this review helpful.

"What do I do when I reach the top of the mountain?" the young man asked the master.
"Keep on climbing," replied the master.

Dixit and Nalebuff got to the top of the mountain with the first edition of this book in 1991. They have continued to climb the last 17 years.

I know of no higher praise.

Editorial Review:

The authors who brought you the bestseller in game theory, Thinking Strategically, now provide the long-awaited sequel.

Game theory means rigorous strategic thinking. It's the art of anticipating your opponent's next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies—from pop culture, TV, movies, sports, politics, and history—the authors show how nearly every business and personal interaction has a game-theory component to it. Are the winners of reality-TV contests instinctive game theorists? Do big-time investors see things that most people miss? What do great poker players know that you don't? Mastering game theory will make you more successful in business and life, and this lively book is the key to that mastery.

The Fractal Geometry of Nature

Benoit B. Mandelbrot

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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.

A Student's Guide to Maxwell's Equations

Daniel Fleisch

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Total reviews: 17 Average rating: 5.0 of 5

A Student's Guide to Maxwell's Equations 4 out of 5 stars.
2 of 2 people found this review helpful.

For me this book is a great review. I took advantage of both the pod casts and problem solutions. I prefer this authors notations to many of the other EM texts I have read.

Editorial Review:

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Against the Gods: The Remarkable Story of Risk

Peter L. Bernstein

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Total reviews: 155 Average rating: 4.0 of 5

Today's hero is often tomorrow's blockhead. 4 out of 5 stars.
2 of 2 people found this review helpful.

There are two things that I really liked about this book, and one thing that I didn't. The good things:

1) The author's vast knowledge of the financial markets, from most of a century of experience.
2) His extensive and entertaining history of risk analysis.

The bad thing:

His attempts to explain math concepts that he apparently doesn't understand very well.

His history of risk analysis was a pleasure to read -- from Fibonacci and Cardano, to Markowitz and Sharpe. My favorite, was his coverage of Francis Galton, the man who measured everything.

Above all, the greatest value in this book is that it's packed with the author's knowledge of finance, from 63 years of experience. He's 89 years old now, and appears to still be going strong.

This book is well worth reading.

My favorite quote from the book:
Today's hero is often tomorrow's blockhead.(pg 297)

Editorial Review:

With the stock market breaking records almost daily, leaving longtime market analysts shaking their heads and revising their forecasts, a study of the concept of risk seems quite timely. Peter Bernstein has written a comprehensive history of man's efforts to understand risk and probability, beginning with early gamblers in ancient Greece, continuing through the 17th-century French mathematicians Pascal and Fermat and up to modern chaos theory. Along the way he demonstrates that understanding risk underlies everything from game theory to bridge-building to winemaking.