In the 1950s, von Neumann and Morgenstern's theory of games and economic behaviour created a new area of mathematics concerned with the formal problems of rational decision as experienced by multiple agents. In the 21st century, game theory is all around us. Here, Mehlmann presents mathematical foundations and concepts illustrated via social quandaries, mock political battles, evolutionary confrontations, economic struggles, and literary conflict. Most of the standard models - the prisoners' dilemma, the arms race, evolution, duels, the game of chicken, etc. - are here. Many non-standard...

Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. This title includes chapters that deal with discrete probability spaces, random variables, conditioning, Markov chains, and filtering of discre

Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric t

Ramanujan is recognized as one of the great number theorists of the twentieth century. This book provides an introduction to his work in number theory. It also examines subjects that have a rich history dating back to Euler and Jacobi, and they continue to

This is the sequel to Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (volume 4 in the AMS series, the Student Mathematical Library). As in the first volume, this book is divided into two parts. The first is a collection of exercises and problems, and the second contains their solutions. The book mainly deals with real functions of one real variable. Topics include: properties of continuous functions, intermediate value property, uniform continuity, mean value theorems, Taylor's formula, convex functions, sequences and series of functions.

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. Th

It is rarely taught in undergraduate or even graduate curricula that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. This fact is taught in most complex analysis courses. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof, due to Nevanlinna, in general dimension and a differential geometric proof in dimension three. For...

Gives an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. In particular, this book includes a detailed construction of the Lebesgue measure on the real line and an introduction t

Surfaces are among the most common and easily visualized mathematical objects. This book covers various ways of representing surfaces, combinatorial structure and topological classification of surfaces, topology and smooth structure, and much more.

This work is based on an undergraduate course taught at the IAS/Park City Mathematics Institute, on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses travelling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small...