Computational Finance: a Scientific Perspective.

Dec. 2000 380 pp.

Computational finance deals with the mathematics of computer programs that realize financial models or systems. This book outlines the epistemic risks associated with the current valuations of different financial instruments and discusses the corresponding risk management strategies. It covers most of the research and practical areas in computational finance. Starting from traditional fundamental analysis and using algebraic and geometric tools, it is guided by the logic of science to explore information from financial data without prejudice. In fact, this book has the unique feature that it is structured around the simple requirement of objective science: the geometric structure of the data = the information contained in the data.


School on Space-Time Chaos:
Characterization, Control and Synchronization Pamplona, 2000.

May 2001 250 pp.

This book provides a comprehensive overview of the topics related to characterization, control and synchronization of complex spatiotemporal phenomena, from both a theoretical and an experimental point of view. It describes applications of these processes in applied mathematics, signal analysis, nonlinear optics, fluid dynamics, chemical reactions, electronic circuits, etc.


Quantum Information, III:
Proceedings of the Int'l Conference Meijo Univ., 2000.

May 2001 250 pp.

Over the last decade the theory of quantum information has developed into an important and active research area in mathematics, physics and other fields of science. It has established a link among those fields. This volume covers the following topics: Quantum Computation, NP-Complete Problem, Quantum Communication, Quantum Stochastic Processes, Quantum Field Theory, Classical and Quantum White Noise Analysis, Infinite Dimensional Stochastic Analysis, Gaussian Random Fields, Probabilistic Control in Microorganisms, Complexity in Nature, etc.NP-Complete Problem


Lectures on Finsler Geometry.

May 2001 200 pp.

In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced a new quantity --- Berwald curvature. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.


Introduction to Matrix Theory: with Applications to Business and Economics.

May 2001 420 pp.


In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields. Contents: Elements of Matrix Algebra; The Fundamentals of Matrix Analysis and Linear Algebra; Applications Are Presented in input-output Systems; Dynamic Economic Systems; Growth Models etc.


Superstrings and Related Matters:
Proceedings of the ICTP Spring Workshop ICTP, Trieste, 2000.

Aug. 2001 350 pp.

In this volume, topics such as the AdS/CFT correspondence, non-BPS states, noncommutative gauge theories and the Randall-Sundrum scenario are discussed. For the AdS/CFT correspondence, some of its generalizations, including examples of non-AdS/nonconformal backgrounds, are described. Myer's effect in this context and otherwise is also treated. Recent results in the context of non-BPS states are reviewed, in particular the use of open string field theory in understanding the related problem of tachyon condensation. Instantons and solitons in noncommutative gauge theories are described, as are various issues in the framework of the Randall-Sundrum scenario.


Galois' Theory of Algebraic Equations.

Aug. 2001 400 pp.

Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field". A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way what the most technical details can be skilled by readers who are interested primarily in a broad survey of the theory.