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.

    Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the unreachable dream of time travel, this volume comprises a substantial and definitive monument to Gardner's influence on mathematics, science, and culture.In its twelve sections, The Colossal Book of Math explores a wide range of areas, each startlingly illuminated by Gardner's incisive expertise. Beginning with seemingly simple topics, Gardner expertly guides us through complicated and wondrous worlds: by way of basic algebra we contemplate the mesmerizing, often hilarious, linguistic and numerical possibilities of palindromes; using simple geometry, he dissects the principles of symmetry upon which the renowned mathematical artist M. C. Escher constructs his unique, dizzying universe. Gardner, like few thinkers today, melds a rigorous scientific skepticism with a profound artistic and imaginative impulse. His stunning exploration of "The Church of the Fourth Dimension," for example, bridges the disparate worlds of religion and science by brilliantly imagining the spatial possibility of God's presence in the world as a fourth dimension, at once "everywhere and nowhere."With boundless wisdom and his trademark wit, Gardner allows the reader to further engage challenging topics like probability and game theory which have plagued clever gamblers, and famous mathematicians, for centuries. Whether debunking Pascal's wager with basic probability, making visual music with fractals, or uncoiling a "knotted doughnut" with introductory topology, Gardner continuously displays his fierce intelligence and gentle humor. His articles confront both the comfortingly mundane—"Generalized Ticktacktoe" and "Sprouts and Brussel Sprouts"—and the quakingly abstract—"Hexaflexagons," "Nothing," and "Everything." He navigates these staggeringly obscure topics with a deft intelligence and, with addendums and suggested reading lists, he informs these classic articles with new insight.Admired by scientists and mathematicians, writers and readers alike, Gardner's vast knowledge and burning curiosity reveal themselves on every page. The culmination of a lifelong devotion to the wonders of mathematics, The Colossal Book of Mathematics is the largest and most comprehensive math book ever assembled by Gardner and remains an indispensable volume for the amateur and expert alike.

    Drawing heavily on the author's own real-world experiences, the book stresses design and analysis. Coverage is divided into two parts, the first being a general guide to techniques for the design and analysis of computer algorithms. The second is a reference section, which includes a catalog of the 75 most important algorithmic problems. By browsing this catalog, readers can quickly identify what the problem they have encountered is called, what is known about it, and how they should proceed if they need to solve it. This book is ideal for the working professional who uses algorithms on a daily basis and has need for a handy reference. This work can also readily be used in an upper-division course or as a student reference guide. THE ALGORITHM DESIGN MANUAL comes with a CD-ROM that contains: * a complete hypertext version of the full printed book. * the source code and URLs for all cited implementations. * over 30 hours of audio lectures on the design and analysis of algorithms are provided, all keyed to on-line lecture notes.

    It allows one to gain information by discarding information, namely, the individuality of the observations. Stigler s second pillar, information measurement, challenges the importance of big data by noting that observations are not all equally important: the amount of information in a data set is often proportional to only the square root of the number of observations, not the absolute number. The third idea is likelihood, the calibration of inferences with the use of probability. Intercomparison is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is regression, both a paradox (tall parents on average produce shorter children; tall children on average have shorter parents) and the basis of inference, including Bayesian inference and causal reasoning. The sixth concept captures the importance of experimental design for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the residual the notion that a complicated phenomenon can be simplified by subtracting the effect of known causes, leaving a residual phenomenon that can be explained more easily.The Seven Pillars of Statistical Wisdom presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician."

    Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further."