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Mathematics and Physics

Mathematics and Physics

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In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception—the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space—were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence.

A History of Quantum Chemistry

Quantum chemistry--a discipline that is not quite physics, not quite chemistry, and not quite applied mathematics--emerged as a field of study in the 1920s. It was referred to by such terms as mathematical chemistry, subatomic theoretical chemistry, molecular quantum mechanics, and chemical physics until the community agreed on the designation of quantum chemistry.

The classical view of concepts in psychology was challenged in the 1970s when experimental evidence showed that concept categories are graded and thus cannot be represented adequately by classical sets. The possibility of using fuzzy set theory and fuzzy logic for representing and dealing with concepts was recognized initially but then virtually abandoned in the early 1980s. In this volume, leading researchers—both psychologists working on concepts and mathematicians working on fuzzy logic—reassess the usefulness of fuzzy logic for the psychology of concepts.

The Mathematical Foundations of Music

“Mathematics can be as effortless as humming a tune, if you know the tune,” writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.

The Mathematical Foundations of Music

Volume 2 of Musimathics continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform.

A Gentle Introduction

The combination of two of the twentieth century’s most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level.

Zhores Alferov's Life in Communist Science

In 2000, Russian scientist Zhores Alferov shared the Nobel Prize for Physics for his discovery of the heterojunction, a semiconductor device the practical applications of which include LEDs, rapid transistors, and the microchip. The Prize was the culmination of a career in Soviet science that spanned the eras of Stalin, Khrushchev, and Gorbachev--and continues today in the postcommunist Russia of Putin and Medvedev.

The Art of Educated Guessing and Opportunistic Problem Solving

In problem solving, as in street fighting, rules are for fools: do whatever works--don’t just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions.

A Math Tool Kit

This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems.

Robert Reitano’s Introduction to Quantitative Finance offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. This manual provides solutions to the Practice Exercises in the text.

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