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This chapter chronicles the development of permutation statistical methods from 1940 to 1959. This period may be considered a bridge between the early years of 1920–1939 where permutation tests were first conceptualized and the next period, 1960–1979, in which gains in computer technology provided the necessary tools to successfully employ permutation tests. The recognition of permutation methods as the gold standard against which conventional statistical methods were to be evaluated, while often implicit in the 1920s and 1930s, is manifest in many of the publications on permutation methods that appeared between 1940 and 1959. Also, a number of researchers turned their attention during this time period to rank tests, which simplified the calculation of exact probability values; other researchers continued work on calculating exact probability values, creating tables for small samples; and still others continued the theoretical work begun in the 1920s.

In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles inNumber-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers,Number-Crunchingwill appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.