This text is the book I recommend for graduate students and clinicians who wish to learn the basics of statistical genetics, but who do not have a strThis text is the book I recommend for graduate students and clinicians who wish to learn the basics of statistical genetics, but who do not have a strong grounding in statistics. It covers the basics without getting too mired in derivations. On the other hand, it leaves a few gaps that must be filled elsewhere in a comprehensive survey of genetic epidemiology. ...more

**spoiler alert** Pak Sham's book is, in my opinion, the strongest of the graduate-level textbooks in genetic epidemiology. Although no text in statis**spoiler alert** Pak Sham's book is, in my opinion, the strongest of the graduate-level textbooks in genetic epidemiology. Although no text in statistical genetics covers everything I would like to cover in an introductory course, Statistics in Human Genetics covers most of the middle- to upper-level material in depth. If I need to look something up about heritability or genetic variance, I'll reach for this book first....more

**spoiler alert** An invaluable resource for statistical consultants. Includes and explains many of those formulae for back-of-the-envelope sample-siz**spoiler alert** An invaluable resource for statistical consultants. Includes and explains many of those formulae for back-of-the-envelope sample-size calculations learned in a consulting class and then promptly forgotten. The guidelines for presenting data for publication are also useful, although I disagree with Dr. vanBelle on the appropriateness of bar graphs (I prefer them when the x axis is categorical)....more

Asimov on Numbers is a non-traditional compilation of Isaac Asimov's essays for The Magazine of Fantasy and Science Fiction, collected by subject rathAsimov on Numbers is a non-traditional compilation of Isaac Asimov's essays for The Magazine of Fantasy and Science Fiction, collected by subject rather than by date of appearance. Of course, the articles focus on numbers, but not entirely on mathematics: "Forget it!", for instance, explains why some knowledge is better off no longer being taught in grade school, even if it had been vital at some point. This group of essays includes two of my all-time favorites, "The Days of Our Years" and "Begin at the Beginning," both concerned with the history of calendrical systems. However, "Skewered"--an attempt to appreciate the sheer magnitude of the largest number ever contained in a mathematical proof (at the time of writing)--was somehow overlooked, and that alone deducts a star from my rating....more

A variety of puzzles and riddles with simple, but not easily divined, solutions from Martin Gardner, former "Mathematical Games" columnist for ScientiA variety of puzzles and riddles with simple, but not easily divined, solutions from Martin Gardner, former "Mathematical Games" columnist for Scientific American (back when it was still very intellectual). Each puzzle is accompanied by both a short, direct explanation and more in-depth discussion generalizing the particular insight to other relevant problems and, in some cases, offering more challenging questions of the same form. Topics range from straight-up mathematics—arithmetic, geometry and number theory—to logic and even word games. These conundrums—and just as much, the abstract, seemingly childish yet sophisticated illustrations—delighted me as a child, though I was a bit young to appreciate their beauty and usefulness....more

I did learn, from reading this book, about some Lewis Carroll works I'd like to read in full, but overall Martin Gardner—for the first time ever—let mI did learn, from reading this book, about some Lewis Carroll works I'd like to read in full, but overall Martin Gardner—for the first time ever—let me down. Or perhaps it was Carroll himself, by means of a 120-year language gap. The instructions for many of the games and puzzles described here are incomprehensible to the modern reader unschooled in Victorian English. This book has, however, piqued my interest in late-19th-century British society. Some of the wildly popular parlor games that Carroll devised sound difficult even for the MENSA crowd of today....more

An excellent, if non-transparent, introduction to fractals, with emphasis on computer graphics. Includes detailed algorithms in "pseudo-code" (approxiAn excellent, if non-transparent, introduction to fractals, with emphasis on computer graphics. Includes detailed algorithms in "pseudo-code" (approximately Pascal) for drawing Julia sets and the Mandelbrot set, as well as simpler fractal shapes such as the Koch snowflake. The book is studded with high-resolution images that are impressive even in the present day, and astonishing for 1988 (the date of publication). A note of warning: most of the material is written for students with a strong background in mathematics. ...more

[Warning: This review may contain an unexpected tiger. You won't know where the tiger will be until you encounter it. Now you know the tiger can't be[Warning: This review may contain an unexpected tiger. You won't know where the tiger will be until you encounter it. Now you know the tiger can't be the last word, because then it wouldn't be unexpected; having read all the words but one without finding the tiger, you would know the tiger was next before you actually saw it. By the same logic, the tiger couldn't be the penultimate word, either, because if you read up to the third-to-last word, you'd know the tiger would come next, and you'd expect it. You can extend this line of reasoning to prove that the tiger can't be anywhere within the review.]

Martin Gardner, mathematician and former Scientific American "Mathematical Games" columnist, compiled this treasury of curious and entertaining paradoxes in logic, mathematics and probability. The collection includes some famous conundrums, such as Zeno's Paradox, Pascal's Wager, Simpson's Paradox (in the form of a search for swingers at a singles' club) and the Gambler's Fallacy. Examples are illustrated TIGER with crude but hilarious drawings (some of which originally appeared in a series of filmstrips (anyone remember filmstrips? the soundtrack beeping to tell you to advance the frame? the projector's light bulb, hotter than the sun's surface, always just about to explode?) about paradoxes). This book is lots of fun for accomplished and aspiring nerds, but is also a good first introduction to infinite sets and (very) basic probability theory....more

Quick summary: Navigating Wallace's tortuous prose is like eating a glass jawbreaker with a wisdom center: if you can tough it out through the pain, nQuick summary: Navigating Wallace's tortuous prose is like eating a glass jawbreaker with a wisdom center: if you can tough it out through the pain, not to mention considerable loss of blood, you will discover something beautiful and profound. If you enjoy beauty and profundity in mathematics, at least. If you aren’t, but are still curious about Georg Cantor’s work showing that not all infinities are created equal, the essentials of Everything and More are summarized far more succinctly and accessibly in Aha! Gotcha by Martin Gardner (see “Hotel Infinity,” “The Ladder of Alephs” and “Zeno’s Paradoxes,” pp. 50-53, 143-144 of the 1982 paperback edition).

Full review:

§1a.Everything and More traces Western thought on the infinite from Pythagoras to the 20th century. The classical Greeks viewed infinity as a philosophical conundrum: like irrational numbers (numbers that can’t be expressed as a ratio of integers, like the square root of 2), transfinite (i.e., infinite) numbers had no place in their orderly universe. Infinity really got its start in the paradoxes of Zeno of Elea (ca. 490-430 BCE). Take his famous story of Achilles and the Tortoise, for example. Imagine the great warrior Achilles in a race against a tortoise. Achilles, a sporting fellow, gives the tortoise a hundred-meter head start. Now suppose that in the time Achilles runs the hundred meters to the tortoise’s starting line, the tortoise manages to walk ten meters. (It’s an uncommonly fast tortoise.) Achilles now has to catch up ten meters, but while he does, his opponent pulls ahead another meter. We can continue forever this way: each time Achilles closes the gap between where he is and where the tortoise was, the tortoise gains a little more ground, and so on, ad infinitum. The important point is that although we can easily identify the flaw in Zeno’s thinking; namely, that an infinite series can have a finite sum (here, the infinite series is the ever-decreasing lengths the tortoise gains on Achilles as the latter is catching up), a conceptual solution is not the same as a mathematical proof. Amazingly, Zeno’s paradoxes weren’t resolved with what we today consider mathematical rigor until the 19th century—nearly two and a half millennia later.

The first four-fifths of Everything and More is a long crescendo building toward the central figure of the story, 19th-century mathematician Georg Cantor, whose ideas on infinite sets revolutionized set theory and shook the very foundations of mathematics. Within that last fifty pages we finally get the lowdown on the different classes of infinity*, and consequently, the great undecidable proposition rumored to have driven Cantor insane.

(*IYI It wasn’t until p. 248 that I encountered the word “countable.” I’d been expecting it since p. 1.)

§1b. Wallace appears to be motivated by veneration of his high-school AP math teacher, E. Robert Goris, about whom nothing is available on the Web. Dr. Goris clearly made the subject fun and exciting, and did so largely by relating fascinating tidbits about the history of mathematics. Wallace attempts to do the same for the reader, but with limited success.

§2a. Wallace briefly reviews the mathematics necessary to understand Cantor's work on transfinite numbers, but be warned: unless you've had at least integral calculus, and preferably analysis—a subject usually reserved for hard-science majors—you’re going to have a rough time of it. The technical level isn’t even remotely similar to what I’ve seen in other (alleged) popular science books.

§2b. That’s the first challenge of this book that might narrow the audience a bit. The second is that the style of writing is, to put it kindly, informal, and the organization, t.p.i.k, haphazard. While the narrative generally follows a historical timeline, Wallace takes so many diversions and delegates so much crucial information to footnotes (and not necessarily where it’s most needed) that much of the time it’s hard to distinguish the main avenue from all the side streets. The text is imperceptibly divided into seven major sections, each with several subsections. If, through superhuman effort, you succeed in noticing any section heading (see the beginning of this paragraph for an example), you’d better mark it with a Post-It Note, because you’ll be flipping back to it a dozen or more times later on. Most of the footnotes, and a fair amount of the main text, is marked “If You’re Interested,” or IYI for short. In principle, this material is expendable—but as it contains the bulk of the most informative and enjoyable reading, I would disagree.

(IYI With these section signs, Wallace may be imitating the style of certain famous books on math such as The Principles of Mathematics by Bertrand Russell. If so, he has succeeded too well.)

Also important, but nearly impossible to find later on, are the three Emergency Glossaries plunked down seemingly at random, containing mathematical terms that are either about to become crucial, or not. Fortunately, my math major served me well and I didn’t need to refer back to them; but the non-mathematician reader had better mark these, as well.

§2c. Don’t get me wrong; I like informal writing. And sentence fragments, with which this volume abounds. Wallace’s tongue-in-cheek writing style reminds me of my own, which is simultaneously flattering and embarrassing. Yet some of the more eccentric passages and phrases fall less into the “informal” category and more into the “help, I need an editor” category. Foremost in the latter is the author’s frequent, and inconsistent, use of abbreviations for words that really don’t call for abbreviating.

At one point, a bit of parenthetical material was concluded with, “This may be important later.” With comments like this, it is difficult to believe that any editor even glanced at the manuscript—but Wallace clearly refers elsewhere that a particular footnote was inserted “at the insistence of the editor.” Which creates a paradox all of its own.

§3a. I shouldn’t lead you on that everything I thought about this book was negative. With patience, I gained an entirely new, historical perspective on the mathematics of the infinite—a story whose end I already knew from the classroom, but in the absence of any meaningful context. As a side benefit, I also understood, for the first time, the proof showing that the square root of 2 is irrational, and why the harmonic series—{1/2, 1/3, 1/4, …}—has an infinite sum. If these are the kinds of things that pique your interest, by all means give this book a try. Otherwise, if you wish to know a little about transfinite numbers, look elsewhere for a more accessible introduction without all the brain ouchies....more

Many of the conundrums in this collection also appear in Dr. Gardner's Aha. Of the puzzles I hadn't seen, I was able to solve a few in my head, and aMany of the conundrums in this collection also appear in Dr. Gardner's Aha. Of the puzzles I hadn't seen, I was able to solve a few in my head, and a fair number were straightforward with pencil and paper. Many, however, require a profound insight of the "wouldn't get that in a million years" variety—one that I didn't feel at all ashamed for not finding. (Disclaimer: I have a BA in math and am a statistician by trade.)

Regardless of the difficulty, the puzzles in this book are fair tests of intellect for anyone with a good grasp of algebra and geometry. There are no cheap shots that require an unreasonable, universe-spanning leap of logic like you find in some "mindbender" puzzle collections. You know, the kind that expect you to postulate the existence of a hedgehog wearing a leather skirt at the side of the road, or something even less likely, and then make you feel stupid when you give up in disgust. Those aren't puzzles—they're mind-reading exercises. I hate that shit....more

A cute math book for precocious children, You Can Count on Monsters illustrates the concept of prime factorization by combining "monsters," representiA cute math book for precocious children, You Can Count on Monsters illustrates the concept of prime factorization by combining "monsters," representing the prime numbers, in strange and silly ways to form composite numbers. Also includes an carefully explained version of Euclid's proof that the prime numbers are unbounded (i.e., that there is no largest prime number)....more

If there existed such a thing as an "epidemiological thriller," this book would be the archetype. Dr. John Snow's efforts to track down the source ofIf there existed such a thing as an "epidemiological thriller," this book would be the archetype. Dr. John Snow's efforts to track down the source of a deadly outbreak of cholera in Victorian London is often cited (not quite correctly) as the birth of modern epidemiology. Not as well know is the pivotal role in the investigation played by Reverend Henry Whitehead, a local minister who contributed key information linking the outbreak with a particular well that provided residents with fresh water....more

Very straightforward explanations; perfect for someone who's heard of game theory but knows nothing about it. I would have appreciated more mathematicVery straightforward explanations; perfect for someone who's heard of game theory but knows nothing about it. I would have appreciated more mathematics, but I'm weird that way....more