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Mathematics and Physics

Mathematics and Physics

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Probabilistic robotics is a new and growing area in robotics, concerned with perception and control in the face of uncertainty. Building on the field of mathematical statistics, probabilistic robotics endows robots with a new level of robustness in real-world situations.

Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twenty-four-page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry.

An Essay on the Sources and Meaning of Mathematical Unsolvability

In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim.

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.

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.

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.

Dynamic Nonlinear Models

Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations.

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.

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