Presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). This book describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction.

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...