Imagine a highly reliable cancer test. It detects 95% of a certain type of cancer, and has a "false positive" rate of only 1%. This test is used on a population in which this type of cancer occurs in 0.5%. One day your doctor tells you that you have tested positive. What is the chance that you are actually sick? Surprisingly, it is only about 32 percent!
Having just returned from the Gordon Research Conference on Chemical Education Research and Practice, I can attest to the central role that statistics plays in chemical education.
This beautiful book could certainly enhance your coffee table, but don't buy it just for its looks. Be prepared to spend some time with it, and join the wonder that mathematicians are expressing at the brilliance of this new way of describing and inventing symmetries.
I am an enthusiastic fan of Brian Hayes' "Computing Science" column in the Sigma Xi publication, American Scientist, which is the source of most of the essays in this book. Before that, I read his articles in The Sciences, a now-defunct but beautiful little magazine once published by the New York Academy of Sciences.
George Gamow introduced me to Monte Carlo methods in a chapter of "One Two Three Infinity" (Hal's Pick of April, 2001) that I first read when I was about twelve. His vivid description and witty illustration of the path of a staggering drunk comes clearly to mind even these many decades later, and it surely inspired my research on a number of projects.
I have noticed a significant decline over the years in the ability of my students to estimate quantities, and have attributed it to an increased reliance on calculators and computers, but it may be a consequence of more subtle differences in brain development.
Like Malcolm Gladwell s Tipping Point , Nassim Taleb s Black Swan threatens to become a permanent part of the lexicon. In this best-selling book, he makes the argument that evolution has prepared us to over-emphasize continuous, Gaussian relationships because they occur much more frequently than do rare but momentous, unpredictable events.
1.618033989... is a magic number.
Back in the 1960's, I was captivated by "Percentage Baseball" by Earnshaw Cook. Now long out of print and a collector's item, this book was a forerunner of the "science" of SABRmetrics (after the Society for American Baseball Research) that refers to the scientific (statistical) evaluation of the game.
In 1900, David Hilbert gave an address to the International Congress of Mathematicians that outlined the twenty three most important unsolved problems of mathematics, as he saw them. In "The Honors Class", Benjamin Yandell describes the problems and the very remarkable people who worked on them.
