Classical Recursion Theory

Lectures on Electromagnetic Theory provides a concise, self-contained introduction to graduate-level electromagnetic theory, organized for a one-semester course. Written in a "theoretical minimum" style, the text emphasizes clear physical insight and mathematical precision. The five chapters cover Maxwell equations and fundamental theorems; wave propagation, plane-wave expansion, and guided waves; electromagnetic radiation and Green functions; analytical scattering theory for canonical targets; and an introduction to relativistic electrodynamics linking classical electrodynamics with special relativity. The book serves both beginning graduate students and researchers seeking a compact reference.

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.

In ancient times, scholars such as Confucius and Aristotle expounded on the virtue of the “middle way” or “intermediate,” an ideal point of moderation or balance between the extremes of human behavior. Adam Smith, widely considered the father of modern economics as we know it, also encouraged propriety in his first work, The Theory of Moral Sentiments. Since then, different schools of economics have continued to incorporate the idea of propriety into their theories, for example in such concepts as equilibrium and bounded rationality, though few economists have defined it explicitly. In light of growing uncertainty and polarization around the world, propriety economics offers alternative solutions for markets, governments, and everyday citizens.This book embarks on a thorough review of Eastern and Western philosophies of propriety over the past 2,500 years, followed by an investigation of the ideas of propriety found in five key schools of economics: classical, neoclassical, institution

This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continu

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.

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups.This text a