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Mathematics and Physics

Mathematics and Physics

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Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton’s work that has not been tightly connected to Newton’s actual practice: his philosophy of mathematics.

Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming.

Their Relationship to Energy Balance, Atmospheric Dynamics, and Precipitation

More than half the globe is covered by visible clouds. Clouds control major parts of the Earth’s energy balance, influencing both incoming shortwave solar radiation and outgoing longwave thermal radiation. Latent heating and cooling related to cloud processes modify atmospheric circulation, and, by modulating sea surface temperatures, clouds affect the oceanic circulation. Clouds are also an essential component of the global water cycle, on which all terrestrial life depends.

Devices

This text offers an introduction to quantum computing, with a special emphasis on basic quantum physics, experiment, and quantum devices. Unlike many other texts, which tend to emphasize algorithms, Quantum Computing without Magic explains the requisite quantum physics in some depth, and then explains the devices themselves.

Edited by Michele Emmer

Mathematical forms rendered visually can give aesthetic pleasure; certain works of art—Max Bill's Moebius band sculpture, for example—can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.

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. This book introduces the reader to a wealth of techniques and algorithms in the field. All algorithms are based on a single overarching mathematical foundation.

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.

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