C R Borges (University of California, Davies)

ELEMENTARY TOPOLOGY AND APPLICATIONS

The material in this book is organized in such a way that the reader gets to significant applications quickly, and the emphasis is on the geometric understanding and use of new concepts. The theme of the book is that topology is really the language of modern mathematics.

Contents:
Sets and Numbers
Metric and Topological Spaces
From Old to New Spaces
Very Special Spaces
Function Spaces
Topological Groups
Special Groups
Normal and Paracompact Spaces
The Fundamental Group
Cauchy Schwarz and Minkowski Inequalities
Binomial Equalities

Readership: Graduates and undergraduates in differential geometry and topology.

220pp (approx.)
Pub. date: Scheduled Summer 2000
ISBN 981-02-4240-9

edited by Marco Avellaneda (Courant Institute, New York University)

QUANTITATIVE ANALYSIS IN FINANCIAL MARKETS
Collected Papers of the New York University Mathematical Finance Seminar

This invaluable book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.

The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.

Contents:
Deriving Closed-Form Solutions for Gaussian Pricing Models: A Systematic Time-Domain Approach (A Levin)
Static Hedging of Exotic Options (P Carr et al.)
Closed Form Formulas for Exotic Options and Their Lifetime Distribution (R Douady)
Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution (S E Posner & M A Milevsky)
Pricing and Hedging American Options: A Recursive Integration Method (M G Subrahmanyam et al.)
Piecewise Convex Function Estimation: Pilot Estimators (K S Riedel)
E-ARCH Model for Implied Volatility Term-Structure of FX Options (Y-Z Zhu & M Avellaneda)
Calibrating Volatility Surfaces via Relative-Entropy Minimization (M Avellaneda et al.)
Portfolio-Based Risk Pricing: Pricing Long-Term Put Options with GJR-GARCH(1,1)/Jump Diffusion Process (D-J Guo & S Esipov)
Portfolio Generating Functions (R Fernholz)
and other papers

Readership: Students and researchers in economics, finance and applied mathematics.

388pp
Pub. date: Oct 1999
ISBN 981-02-3788-X
ISBN 981-02-3789-8(pbk)

edited by H-D Doebner, J-D Henning, W Leke
& V K Dobrev (Bulgarian Academy of Sciences, Sofia & Technical University of Clausthal)

QUANTUM THEORY AND SYMMETRIES
Proceedings of the International Symposium Goslar, Germany 18 - 22 July 1999

This volume gives an overview of the recent representative developments in relativistic and non-relativistic quantum theory, which are related to the application of various mathematical notions of various symmetries. These notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. The emphasis is on results in the following areas: foundation of quantum physics, quantization methods, nonlinear quantum mechanics,
algebraic quantum field theory, gauge and string theories, discrete spaces, quantum groups and generalized symmetries.

Contents:
New Developments in the Interaction Between Stochastic Analysis, Geometry and Quantum Field Theory (S Albeverio) Relativistic Resonances, Relativistic Gamow Vectors, and Semigroup Representations of the PoincarrGroup (A B)m) More Understanding of the Hydrogen Atom: Yangian Symmetry and Effect (M-L Ge)
Spacetime Metric from Linear Electrodynamics (F W Hehl) The Lax-Phillips Semigroup for Resonances of a Model in Relativistic Quantum Field Theory (L Horwitz) Divergence Operators and Odd Poisson Brackets (Y Kosmann-Schwarzbach) Group Theoretical Methods Applied to Condensed Matter Problems (J Lmtmer-Strathmann) From Athens to Clausthal (The Route Covered) (Y Ne'eman) Supersymmetric Noether Currents (L O'Raifeartaigh) A New Description of the Quantum Superalgebra Uq[sl(n/m)] and Related Quantum Statistics (T D Palev) Review of Some Recent Developments in String Theory (S Randjbar-Daemi)
Quantization of Classical Mechanics (F E Schroeck, Jr.) General Deformations and General Coherent States (A I Solomon) New Results and Questions in Entanglement Theory (R Werner) and other papers

Readership: Mathematical and theoretical physicists and mathematicians.

620pp (approx.)
Pub. date: Scheduled Summer 2000
ISBN 981-02-4237-9

edited by K Lehnertz, C E Elger (University of Bonn, Germany), J Arnhold
& P Grassberger (NIC, Forschungszentrum Jcich, Germany)

CHAOS IN BRAIN?
Proceedings of the Workshop University of Bonn, Germany 10 - 12 March 1999

There has been a heated debate about whether chaos theory can be applied to the dynamics of the human brain. While it is obvious that nonlinear mechanisms are crucial in neural systems, there has been strong criticism of attempts to identify at strange attractors in brain signals and to measure their fractal dimensions, Lyapunov exponents, etc. Conventional methods analyzing brain dynamics are largely based on linear models and on Fourier spectra. Regardless of the existence of strange attractors in brain activity, the neurosciences should benefit greatly from alternative methods that have been developed in recent years for the analysis of nonlinear and chaotic behavior.

Contents:
Cortical Dynamics - Experiments and Models (S Rotter & A Aertsen) Is Nonlinearity Evident in Time Series of Brain Electrical Activity? (T Schreiber) Finding and Characterizing Unstable Fixed Points by Controlling System Dynamics (D T Kaplan) Detection of Phase Locking from Noisy Data: Application to Magnetoencephalography (M Rosenblum et al.) Dynamical Analysis in Clinical Practice (P E Rapp & T I Schmah) Rhythms of the Brain: Between Randomness and Determinism (F H Lopes da Silva et al.)
Pre-ictal Changes of the EEG Dynamics in Epileptic Patients: Clinical and Neurobiological Implications (M Baulac et al.) Spatio-Temporal Dynamics of Epileptogenic Networks (M Le van Quyen et al.)
Pre-ictal Changes and EEG Analyses Within the Framework of Lyapunov Theory (H R Moser et al.)
Epilepsy - When Chaos Fails (J C Sackellares et al.) Possible Clinical and Research Applications of Nonlinear EEG Analysis in Humans (K Lehnertz et al.) Dynamics of EEG Signals During Petit-Mal Epileptic Seizures (R Friedrich) Detection of Epileptic Dynamics in Neuromagnetic Signals: Spectral Analyses Versus Characteristics of Correlation Function (E Bohl et al.) Nonlinear Methods for Evoked Potential Analyses and Modeling (B H Jansen) From Slow Potentials to Chaos: Processing in the Brain and Controlling the Brain (H Preibl & W Lutzenberger) and other papers

Readership:
Neural scientists, physicists, statisticians and mathematicians interested in applying nonlinear dynamical system theory to brain research.

384pp
Pub. date: Jan 2000
ISBN 981-02-4222-0

Hans Sallhofer (Sallhofer GmbH, Austria) & Dennis Radharose (Munich, Germany)

HERE ERRED EINSTEIN

The emergence of modern physics in the first three decades of the 20th century was accompanied by a loss of determinism. That loss is embodied in the Copenhagen interpretation and the theory of relativity. The development of physics-based technologies, both constructive and destructive, occurred shortly thereafter at so dizzying a rate that scientists rarely took a critical look at the logical foundations of the Copenhagen interpretation and the theory of relativity, or at the consequences of the loss of determinism.

This book contains a dialogue between a physicist and a philosopher on that issue. The dialogue is strongly contextualized with respect to the main players in physics during the first sixty years of the 20th century, and to the prevailing political conditions in Western Europe and the USA. It was galvanized by the debate and the subsequent abandonment of the Superconducting Super Collider, and also affords a lively understanding of Greek epistemology. Questioned by the philosopher, the physicist provides an account of the directions
taken by physicists and the roads not traveled, as well as his own understanding of the nature of matter.

Contents:
First Conversation
Second Conversation
Third Conversation
Fourth Conversation
Fifth Conversation
The Physical Interpretation of the Wave Function
Theory of Relativity
Particle Physics Today

Readership: Researchers and general readers.

180pp (approx.)
Pub. date: Scheduled Summer 2000
ISBN 981-02-4242-5
ISBN 981-02-4243-3(pbk)

C Swartz (New Mexico State University, Las Cruces)

INTRODUCTION TO GAUGE INTEGRALS

This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces.

A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.

Readership: Upper level undergraduates and mathematicians interested in gauge integrals.

150pp (approx.)
Pub. date: Scheduled Summer 2000
ISBN 981-02-4239-5