An Introduction to Modern Mathematical Computing

In this concise yet comprehensive guide to the mathematics of modern portfolio theory the authors discuss mean-variance analysis, factor models, utility theory, stochastic dominance, very long term investing, the capital asset pricing model, risk measures including VAR, coherence, market efficiency, rationality and the modelling of actuarial liabilities. Each topic is clearly explained with assumptions, mathematics, limitations, problems and solutions presented in turn. Joshi's trademark style of clarity and practicality is here brought to classical financial mathematics. The book is suitable for mathematically trained students in actuarial studies, business and economics as well as mathematics and finance, and it can be used for both self-study and as a course text. The authors' experience as both academics and practitioners brings clarity and relevance to the book, whilst ensuring that the limitations of models are highlighted.

An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

This textbook builds up General Relativity in a modern way that shows the marvellous unity in physics. Einstein's gravity can be understood as the theory of matter interacting with a massless spin-2 particle (the graviton), just as electromagnetism is the theory of charges interacting with a massless spin-1 particle (the photon). Starting with scalar gravity and electromagnetism, General Relativity is developed step by step, highlighting all the key ideas and equations. The text develops many applications of enduring interest, including solar-system effects and cosmological expansion, as well as important cutting-edge topics such as black hole imaging and gravitational wave detection. In-chapter exercises and end-chapter problems allow readers to test their understanding, with selected solutions available to instructors online. The textbook provides essential material for the beginning – and experienced – physicist or astronomer interested in modern developments in gravitation, astroph

For nearly four decades, Trancework has been the definitive textbook for thousands of professionals undergoing training in the art and science of clinical hypnosis. Now in its 5th edition, this classi