Contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. This book introduces a theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the

The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Theorie de la Speculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and...

Explains some of the biology and the computational and mathematical challenges we are facing. This book provides examples of how these challenges are met, with particular emphasis on nontraditional mathematical approaches.

The first three chapters of this book introduce the reader to knot theory, topological chirality and molecular symmetry, and DNA topology. The second half of the book is focused on three particular applications of knot theory.

This title begins with several surveys of the main features of tt*-geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. It then moves on to explorations of current foundational issues in Hodge theory.

Presents a collection of articles about fractal geometry. This work covers analysis, number theory, dynamical systems, multifractals, probability and statistical mechanics and applications. It is suitable for graduate students and researchers interested in fractal geometry and its applications.

This volume presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, DC. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field.

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief...