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
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
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
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
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