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Mathematics and Physics

Mathematics and Physics

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An Essay on Modern Bayesian Methods

The problem of how to estimate probabilities has interested philosophers, statisticians, actuaries, and mathematicians for a long time. It is currently of interest for automatic recognition, medical diagnosis, and artificial intelligence in general. The main purpose of this monograph is to review existing methods, especially those that are new or have not been written up in a connected manner. The need for nontrivial theory arises because our samples are usually too small for us to rely exclusively on the frequency definition of probability.

As a result of a lunchtime conversation with Professor Wendell Garner concerning the productiveness of the sacrifice bunt, Earnshaw Cook took on the three-year task of presenting a formal analysis of baseball. His analysis, explained in terms perfectly clear to anyone with college freshman level mathematics, suggests that no one has ever known the true percentages, and if anyone did know them he could manage almost any team into the top ranks of major league baseball.

In writing the first book-length study of ancient Egyptian mathematics, Richard Gillings presents evidence that Egyptian achievements in this area are much more substantial than has been previously thought. He does so in a way that will interest not only historians of Egypt and of mathematics, but also people who simply like to manipulate numbers in novel ways. He examines all the extant sources, with particular attention to the most extensive of these—the Rhind Mathematical Papyrus, a collection of training exercises for scribes.

Finite Groups

Richard Brauer (1901-1977) was one of the leading algebraists of this century. Although he contributed to a number of mathematical fields, Brauer devoted the major share of his efforts to the study of finite groups, a subject of considerable abstract interest and one that underlies many of the more recent advances in combinatorics and finite geometries.

Modeling and Simulation with Incomplete Knowledge

This book presents, within a conceptually unified theoretical framework, a body of methods that have been developed over the past fifteen years for building and simulating qualitative models of physical systems—bathtubs, tea kettles, automobiles, the physiology of the body, chemical processing plants, control systems, electrical systems—where knowledge of that system is incomplete. The primary tool for this work is the author's QSIM algorithm, which is discussed in detail.

A Search for the Hidden Meaning of Science

Nature has secrets, and it is the desire to uncover them that motivates the scientific quest. But what makes these "secrets" secret? Is it that they are beyond human ken? that they concern divine matters? And if they are accessible to human seeking, why do they seem so carefully hidden? Such questions are at the heart of Peter Pesic's enlightening effort to uncover the meaning of modern science.

Creating a Professional Identity in Post-World War II America

Women Becoming Mathematicians looks at the lives and careers of thirty-six of the approximately two hundred women who earned Ph.D.s in mathematics from American institutions from 1940 to 1959. During this period, American mathematical research enjoyed an unprecedented expansion, fueled by the technological successes of World War II and the postwar boom in federal funding for education in the basic sciences. Yet women's share of doctorates earned in mathematics in the United States reached an all-time low.

Theory and Practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics.

In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy.

Efficient Algorithms

Algorithmic Number Theory provides a thorough introduction to the design and analysis of algorithms for problems from the theory of numbers. Although not an elementary textbook, it includes over 300 exercises with suggested solutions. Every theorem not proved in the text or left as an exercise has a reference in the notes section that appears at the end of each chapter. The bibliography contains over 1,750 citations to the literature.

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