Kiyoshi Igusa, Brandeis University, Waltham, MA

Higher Franz-Reidemeister Torsion

Expected publication date is November 15, 2002

Description
The book is devoted to the theory of topological higher Franz-Reidemeister torsion in K-theory. The author defines the higher Franz-Reidemeister torsion based on Volodin's K-theory and Borel's regulator map. He describes its properties and generalizations and studies the relation between the higher Franz-Reidemeister torsion and other torsions used in K-theory: Whitehead torsion and Ray-Singer torsion. He also presents methods of computing higher Franz-Reidemeister torsion, illustrates them with numerous examples, and describes various applications of higher Franz-Reidemeister torsion, particularly for the study of homology of mapping class groups.

Packed with up-to-date information, the book provides a unique research and reference tool for specialists working in algebraic topology and K-theory.

Contents

・Other titles in this series
・Cocycles in Volodin K-theory
・Spaces of matrices and higher Franz-Reidemeister torsion
・A model for the Whitehead spaces
・Morse theory and filtered chain complexes
・Homotopy type of the Whitehead space
・The framing principle and Bokstedt's theorem
・Proof of complexified Bokstedt theorem
・Framed graphs
・Bibliography
・Index

Details:

Series: AMS/IP Studies in Advanced Mathematics, Volume: 31
Publication Year: 2002
ISBN: 0-8218-3170-4
Paging: approximately 392 pp.
Binding: Hardcover

A. V. Mel'nikov, S. N. Volkov, and M. L. Nechaev, Steklov Institute of Mathematics, Moscow, Russia

Mathematics of Financial Obligations

Description
Contemporary finance and actuarial calculations have become so mathematically complex that a rigorous exposition is required for an accurate and complete presentation. This volume delivers just that. It gives a comprehensive and up-to-date methodology for financial pricing and modelling. Also included are special cases useful for practical applications.

Beyond the traditional areas of hedging and investment on complete markets (the Black-Scholes and Cox-Ross-Rubinstein models), the book includes topics that are not currently available in monograph form, such as incomplete markets, markets with constraints, imperfect forms of hedging, and the convergence of calculations in finance and insurance.

The book is geared toward specialists in finance and actuarial mathematics, practitioners in the financial and insurance business, students, and post-docs in corresponding areas of study. Readers should have a foundation in probability theory, random processes, and mathematical statistics.

Contents

・Financial systems: Innovations and the risk calculus
・Random processes and the stochastic calculus
・Hedging and investment in complete markets
・Hedging and incomplete markets
・Markets with structural constraints and transaction costs
・Imperfect forms of hedging
・Dynamic contingent claims and American options
・Analysis of "bond" contingent claims
・Economics of insurance and finance: Convergence of quantitative methods of calculations
・Bibliographical notes
・Bibliography
・Subject index

Details:

Series: Translations of Mathematical Monographs, Volume: 212
Publication Year: 2002
ISBN: 0-8218-2945-9
Paging: 194 pp.
Binding: Hardcover

Edited by: Robert Gilman, Stevens Institute of Technology, Hoboken, NJ, Alexei G. Myasnikov, New York City, NY, and Vladimir Shpilrain, City College of New York (CUNY), NY

Computational and Statistical Group Theory

Description

This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ).

It is suitable for graduate students and research mathematicians interested in group theory.

Contents

・R. C. Alperin and G. A. Noskov -- Uniform growth, actions on trees and GL_2
・A. V. Borovik -- Centralisers of involutions in black box groups
・A. V. Borovik, A. G. Myasnikov, and V. Shpilrain -- Measuring sets in infinite groups
・E. M. Freden -- Quantum one-way automata and finitely generated groups
・R. I. Grigorchuk and A. Zuk -- Spectral properties of a torsion-free weakly branch group defined by a three state automaton
・T. Jitsukawa -- Malnormal subgroups of free groups
・C. R. Leedham-Green and S. H. Murray -- Variants of product replacement
・D. V. Osin -- Weakly amenable groups
・C. C. Sims -- The Knuth-Bendix procedure for strings and large rewriting systems

Details:

Series: Contemporary Mathematics, Volume: 298
Publication Year: 2002
ISBN: 0-8218-3158-5
Paging: 124 pp.
Binding: Softcover

Timothy G. Feeman, Villanova University, PA

Portraits of the Earth: A Mathematician Looks at Maps

Expected publication date is October 30, 2002

Description

"Every map is a tool, a product of human effort and creativity, that represents some aspects of our world or universe ... [This] course was powered by the belief that by exploring the mathematical ideas involved in creating and analyzing maps, students would see how mathematics could help them to understand and explain their world."

--from the Preface

Portraits of the Earth exemplifies the AMS's mission to bring the power and vitality of mathematical thought to the nonexpert. It is designed to teach students to think logically and to analyze the technical information that they so readily encounter every day.

Maps are exciting, visual tools that we encounter on a daily basis: from street maps to maps of the world accompanying news stories to geologic maps depicting the underground structure of the earth. This book explores the mathematical ideas involved in creating and analyzing maps, a topic that is rarely discussed in undergraduate courses. It is the first modern book to present the famous problem of mapping the earth in a style that is highly readable and mathematically accessible to most students. Feeman's writing is inviting to the novice, yet also interesting to readers with more mathematical experience. Through the visual context of maps and mapmaking, students will see how contemporary mathematics can help them to understand and explain the world.

Topics explored are the shape and size of the earth, basic spherical geometry, and why one can't make a perfect flat map of the planet. The author discusses different attributes that maps can have and determines mathematically how to design maps that have the desired features. The distortions that arise in making world maps are quantitatively analyzed. There is an in-depth discussion on the design of numerous map projections--both historical and contemporary--as well as conformal and equal-area maps. Feeman looks at how basic map designs can be modified to produce maps with any center, and he indicates how to generalize methods to produce maps of arbitrary surfaces of revolution. Also included are end-of-chapter exercises and laboratory projects. Particularly interesting is a chapter that explains how to use MapleR add-on software to make maps from geographic data points.

This book would make an excellent text for a basic undergraduate mathematics or geography course and would be especially appealing to the teacher who is interested in exciting visual applications in the classroom. It would also serve nicely as supplementary reading for a course in calculus, linear algebra, or differential geometry. Prerequisites include a solid grasp of trigonometry and basic calculus.

Contents

・Geodesy--measuring the earth
・Map projections
・Scale factors
・Distances and shortest paths on the sphere
・Angles, triangles, and area on a sphere
・Curvature of surfaces
・Classical projections
・Equal-area maps
・Conformal maps
・Analysis of map distortion
・Oblique perspectives
・Other worlds: Maps of surfaces of revolution
・Appendix A: Aspects of thematic cartography: Symbolization, data classification, and thematic maps
・Appendix B: Laboratory projects
・Appendix C: Portraits of the earth: How the maps in this book were produced
・Bibliography
・Index

Details:

Series: Mathematical World, Volume: 18
Publication Year: 2002
ISBN: 0-8218-3255-7
Paging: approximately 136 pp.
Binding: Softcover

Edited by: Shuxing Chen, Fudan University, Shanghai, People's Republic of China, and S.-T. Yau, Harvard University, Cambridge, MA

Geometry and Nonlinear Partial Differential Equations

Expected publication date is October 23, 2002

Description

This book presents the proceedings of a conference on geometry and nonlinear partial differential equations dedicated to Professor Buqing Su in honor of his one-hundredth birthday. It offers a look at current research by Chinese mathematicians in differential geometry and geometric areas of mathematical physics.

It is suitable for advanced graduate students and research mathematicians interested in geometry, topology, differential equations, and mathematical physics.

Contents

・C. Gu -- The address on the celebration for the 100th birthday of Professor Su Buqing
・B.-L. Chen and X.-P. Zhu -- A property of Kahler-Ricci solitons on complete complex surfaces
・S. Chen and Y.-G. Wang -- Propagation of singularities in compressible viscous fluids
・Q. Ding -- The Landau-Lifshitz equation and its gauge equivalent structure
・Z. Jiang, D. Fang, H. Liu, and D. Moss -- General flattened Jaffe models for galaxies
・L. Ji -- Scattering matrices and geodesics of locally symmetric spaces
・J. Li -- A note on enumerating rational curves in a K3 surface
・S. Jin and X. Li -- Multi-phase computations of the semiclassical limit of the Schrodinger equation
・B. Lian, K. Liu, and S.-T. Yau -- Towards a mirror principle for higher genus
・F. Lin and T.-C. Lin -- Vortices in two-dimensional Bose-Einstein condensates
・Z. Lin -- Sample path properties of Gaussian processes
・L. Peng -- Wavelets on the Heisenberg group
・Y.-B. Shen -- On complete submanifolds with parallel mean curvature vector
・S.-L. Tan -- Triple covers on smooth algebraic varieties
・W. Wang -- Osculating CR manifolds by nilpotent Lie groups in the theory of several complex variables
・Y. Wang -- Dynamics of commuting holomorphic maps
・Y. Yang, H. Chen, and W. Liu -- Different behaviour for the solutions of 1-dimensional chemotaxis model with exponential   growth
・S. T. Yau -- Some progress in classical general relativity
・H. Yin -- Long shock for supersonic flow past a curved cone
・X. Zhang -- A compactness theorem for Yang-Mills connections
・X. Zhang -- The positive mass theorem in general relativity
・X.-Y. Zhou -- Extension theorems for special holomorphic functions

Details:

Series: AMS/IP Studies in Advanced Mathematics, Volume: 29
Publication Year: 2002
ISBN: 0-8218-3294-8
Paging: 237 pp.
Binding: Softcover