An introduction to many mathematical topics applicable to quantitative finance that teaches how to “think in mathematics” rather than simply do mathematics by rote.

An analysis of Newton’s mathematical work, from early discoveries to mature reflections, and a discussion of Newton’s views on the role and nature of mathematics.

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.

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.

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.

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.

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.

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.

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.

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.

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.