Noted expert’s clearly written discussions of essential ideas of highly useful mathematical approach to human behavior and decision-making. Lucid, accessible treatment of such concepts as "utility," "strategy," and the difference between "non-zero" and "zero-sum" games. Minimum of mathematical prerequisites makes it accessible to non-mathematicians.
N-person game theory analyzes contests in which there are more than two sets of conflicting interests, e.g. a hand of poker or wide-scale warfare. In this sequel to his Two-Person Game Theory, the author introduces the necessary mathematical notation (mainly set theory), presents basic concepts, discusses a variety of models, and provides applications to social situations.
This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions.
The material from function theory, up to the residue calculus, is developed in a lively and vivid style, well motivated throughout by examples and practice exercises. Additionally, there is ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations (original language together with English translation) from their classical works. Yet the book is far from being a mere history of function theory. Even experts will find here few new or long forgotten gems, like Eisenstein's novel approach to the circular functions.
The Theory of Differential Equations: Classical and Qualitative
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations.
