MICHELE AUDIN
University of Strasbourg
ペーパー版出来
A modern view of the role played by algebraic
geometry in classical mechanics has
been established in recent years by many
mathematicians. This book presents some
of these modern techniques, which fall within the
orbit of finite dimensional integrable
systems. The main body of the text presents a rich
assortment of methods and ideas
from algebraic geometry prompted by classical
mechanics. The book is based on
courses for graduate students given by the author
at Strasbourg University but the
wealth of original ideas will make it appeal to
researchers also.
Contents: Introduction; 1. The rigid body with a
fixed point; 2. The symmetric spinning top; 3. The
Kowalevski top; 4. The free rigid body; 5,
Non-compact levels: a Toda lattice: Appendix 1. A
Poisson structure on the dual of a Lie algebra;
Appendix 2. R-matrices and the 'AKS theorem';
Appendix 3, The eigenvector mapping and
linearising flows; Appendix 4. Complex curves, real
curves and their Jacobians; Appendix 5. Prym
varieties; Bibliography; Index.
Selling Points: ･ First book making the subject
accessible to graduate students .
Suited for both pure and applied audiences as lots
of examples
Well-known author (has written related books
before)
comparable Titles:AUDIN/Spi'nning Tops/1 996/0521
561 299
NOVIKOV/Solitons and Geometry/1 994/0521 471 966
GUILLEMIN and STERNBERG/Symplectic Techniques in
Physics/1984/0521248663
MARSDEN/Lectures on Mechanics/1 992/0521 428440
Subject areas: mathematics (geometry, dynamics),
mathematical physics
Market: academic researchers, graduate students
Series: Cambridge Studies in Advanced Mathematics,
51
0521 561299 Hardback 147pp July 1996
0521 779197 Paperback 150pp November1999
THOMAS BETH /
University of Karlsrtne
D. JUNGNICKEL / University of
Giessen
AND H. LENZ / Free University of
Berlin
This is the concluding volume
of the second edition of the standard text on design
theory. Since the first edition
there has been extensive development of the theory and
this book has been thoroughly
rewritten to reflect this. lt is suitable for advanced
courses and as a reference work,
not only for researchers in discrete mathematics or
finite algebra, but also for those
working in computer and communications engineering
and other mathematically oriented
disciplines. Exercises are included throughout, and
the book concludes with an
extensive bibliography of over 1800 items.
Contents: 9. Recursive
constructions; 10. Transversal designs and nets, continued; 11.
Asymptotic existence theory; 12.
Characterisation of classical designs; 13, Applications of
designs; Appendix: Tables.
Selling Points: ･ Updated
version of the standard text on design theory
･ Suitable for an advanced
course and as a reference for many
mathematically-oriented
disciplines
･ Includes extensive
bibliography of over 1800 items
Comparable Titles:BETH/Design
Theory/1 993/HB 0521 333342
ASSMUS and KEY/Designs and Their
Codes/1992/HB 0521 413613
Subject areasmathematics
(combinatorics)
Market: academic researchers,
graduate students
Series: Encyclopedia of
Mathematics and its Applications, 78
0 521 77231 1 Hardback 512pp
November 1999
The development of the
supersymmetry technique has led to significant advances in
the study of disordered metals and
semiconductors. The technique has proved to be
of great use in the analysis of
modern mesoscopic quantum devices, but is also
finding applications in a broad
range of other topics, such as localization and quantum
chaos. This book provides the
first comprehensive treatment of the ideas and uses of
supersymmetry. lt will be of great
interest to graduate students and researchers in
condensed matter physics and
quantum chaos.
'Efetov has done a service to
condensed matter physics by explaining the ins and
outs of his method in a clear and
comprehensive monograph. It is likely to become a
classic in the field. The book is
indispensible for researchers who use or who would
like to use the supersymmetry
technique... I would recommend it to anyone with an
interest in modern techniques of
theoretical physics:
C. W. J. Beenakker, Endeavour
Contents: 1. htroduction; 2.
Supermathematics; 3. Diffusion modes; 4. Nonlinear supermatrix
cr-
model; 5. Perturbation theory and
renormalization group; 6. Energy level statistics; 7. Quantum
size effects in small metal
particles; 8. Persistent currents in mesoscopic rings; 9.
Transport
through mesoscopic devices; 10.
Universal parametric correlations; 1 1. Localization in systems
with one-dimensional geometry; 12.
Anderson meta'1-insulator transition; 13. Disorder in two
dimensions; 14. Afterword.
Selling Points: ･ First book to
cover this important topic
･ Author was the inventor of
these techniques
･ Each topic is covered in a
self-contained way
Comparable Titles:TSVEuK/Quantum
Field Theory in Condensed Matter Physics/1 995/0521 454670
Subject areasr: condensed matter
physics, theoretical physics
Market: graduate students,
academic researchers
0 521 47097 8 Hardback 453pp
February 1997
0 521 66382 2 Paperback 456pp
November 1999
RODOLFO GAMBINI /Universidad de la Republica,
Montevideo
AND JORGE PULLIN /Pennsylvania State University
FOREWORD BY ABHAY ASHTEKAR
This text provides a self-contained introduction to
applications of loop representations
and knot theory in particle physics and quantum gravity. Loop
representations (and
the related topic of knot theory) are of considerable current
interest because they
provide a unified arena for the study of the four fundamental
forces. This text reviews
loop representation theory, Maxwell theory, Yang-Mills theories,
lattice techniques,
knot and braid theory, and describes applications in quantum
gravity. A final chapter
assesses the current status of the theory and points out possible
directions for future
research.
Contents: 1. Holonomies and the group of loops; 2. Loop
coordinates and the extended group of
loops; 3. The loop representation; 4. Maxwell theory; 5.
Yang-Mills theories; 6. Lattice techniques;
7. Quantum gravity; 8. The loop representation of quantum theory;
9. Loop representation: further
developments; 10. Knot theory and physical states of quantum
gravity; 11. The extended loop
representation of quantum gravity; 12. Conclusions: present
status and outlook; References;
Index.
SeIIing Points: ･ It casts several topics from different afreas
of physics in a common language
and a single perspective
･ The book is self-contained from the point of view of a
graduate student who
wants to get started in the field
･ 1t introduces several notions of sophisticated mathematics
that are needed to
discuss the physics in a simple fashion
Comparable Titles:DE FELICE and CLARKE/Relativity on Curved
Manifolds/1992/0521 429080
Subject areas :theoretical physics, applied mathematics
Market: academic researchers, graduate students
Series: Cambridge Monographs on Mathematical Physics
0 521 65475 0 A Paperback 321pp November 1999
HAROLD JEFFREYS /Late Fellow, St John's College,
Cambridge
AND BERTHA JEFFREYS /Fellow , Girton College, Cambridge
This well known text and reference contains an account of
those parts of mathematics
that are most frequently needed in physics. As a working rule, it
includes methods
which have applications in at least two branches of physics.
Examples of the practical
use of the methods developed are given in the text: these are
taken from a wide range
of physics, including dynamics, hydrodynamics, elasticity,
electromagnetism, heat
conduction, waveA motion and quaTIIum theory. Exercises accompany
each chapter.
From reviews of the first edition:
There must be very few major techniques in theoretical physics
which are not
explained here and illustrated by some genuine examples. It
remains, and is likely to
continue for many years, an almost indispensable work of
reference for anyone
attempting research in theoretical physics:
Proceedings of the Physical Society
Contents: 1. The real variable; 2. Scalars and vectors; 3.
Tensors; 4. Matrices; 5. Multiple
integrals; 6. Potential theory; 7, Operational methods; 8.
Physical applications of the operational
method; 9, Numerical methods; 10. Calculus of variatk)ns; 11.
Functions of a complex variable;
12. Contour integration and Bromwich's integral; 13. Contour
integration; 14. Fourier's theorem;
15. The factorial and related functions; 16. Solution of linear
differential equations of the second
order; 17. Asymptotic expansions; 18. The equations of potential,
waves and heat conduction; 19.
Waves in one dimension and waves with spherical symmetry; 20.
Conduction of heat in one and
three dimensions; 21. Bessel functions; 22. Applications of
Bessel functions; 23. The con fluent
hypergeometric function; 24. Legendre functions and associated
functions; 25. EIliptic functions;
Notes; Appendix on notation; lndex.
Selling Points: . Well-known text and reference, now available at
a reduced price
･ Comprehensive coverage of those parts of mathematics most
needed in physics
･ Includes examples of the practical uses of methods discussed
in the text
Comparable Titles:JEFFREYS and JEFFREYS/Methods of Mathematical
Physics, first
edition/1 953/0521 097231
Subject areas :applied mathematics, mathematical physics,
theoretical physics
Market: graduate students, academic researchers, professionals,
undergraduate students
Series: Cambridge Mathematical Library
0 521 66402 0 Paperback 730pp November 1999
LEE PENG YEE /Nanyang Technological University,
Singapore
AND RUDOLF VYBORNY /University of Queensland
Integration has a long history: its roots can be traced as far
back as the ancient
Greeks. The first genuinely rigorous definition of an integral
was that given by
Riemann, and further (more general, and so more useM) definitions
have since been
given by Lebesgue, Denjoy, Perron, Kurzweil and Henstock, and
this culminated in
the work of McShane. This textbook provides an introduction to
this theory, and it
presents a unified-yet-elementary approach that is suitable for
beginning graduate and
final year undergraduate students.
Contents: Preface; 1. Introduction; 2. Basic theory; 3. Theory
development; 4. The SL-integral; 5,
Generalized AC function; 6. lntegration in several dimensions; 7.
Some applications; 8. List of
symbols; Appendices.
Selling Points: . No other texts at this level
･ Vyborny is well known in this area
･ Material is class tested by both authors
Comparable Titles:WEI R/General lntegration and Measure/1
979/0521 2971 5X
Subject areasmathematics (analysis)
Market: graduate students, undergraduate students, academic
researchers
Series: Australian Mathematical Society Lecture Series, 14
0521 779685 Paperback 312pp November1999
ROSARlO N, MANTEGNA / Universita di Palermo
AND H. EUGENE STANLEY / Boston University
ln recent years there has been a reciprocal interest between
physicists and
economists in finding common research approaches. This interest
has been mainly
thggered by the large amount of carefully recorded economic data
now easily
available, and by the emergence in physics of new results and
paradigms in the study
of critical phenomena, disordered systems and n-onlinear
dynamical systems. This
book introduces the concepts and methods that are emerging from
this renewed
activity, in a straightforward direct style designed to appeal to
individuals with either a
science or economics background.
Contents: 1. Introduction; 2. EfRcient market hypothesis; 3.
Random walks; 4. Levy stochastic
processes and limit theorems; 5. Scales in financial data; 6.
Stationarity and time correlation; 7.
Stochastic models of price dynamics; 8. Scaling and its
breakdowns; 9. ARCH and GARCH
processes; 10. Financial markets and turbulence; 11. Correlation
inside a financial market; 12.
Taxonomy of a stock portfolio; 13. Options and derivatives; 14.
BIack and Scholes in practice.
Selling Points: ･ First-ever book on important field of
econophysics, which applies ideas from
statistical physics to economics and finance
･ Gene Stanley is a distinguished and very well known physicist
and author
･ This work was highlighted in a page 1 article in the Wall
Street Journal on November 6, 1998
Comparable Titles:BAXTER and RENNIE/Financial Calculus/1996/0521
552893
Subject areasphysics (statistical), economics, finance
Market: graduate students, professionals, academic researchers
0521620082 Hardback 176pp November1999
KURT MEHLHORN / Max-Planck Institute for lnformatics,
Saarbruecken
AND STEFAN NAHER / University of Halle
LEDA is a library of effcient data types and algorithms and a
platform for
combinatorial and geometric computing. ln each of the core areas
of data structures,
graph and network algorithms, and computational geometry, LEDA
covers all (and
more) that is found in the standard textbooks.
LEDA is the first such library and this is the first book devoted
to it. Written by the
main authors of LEDA, it is the definitive account, making the
book essential for all
workers in algorithms, data structures and computational
geometry.
Contents: Preface; 1. lntroduction; 2. Foundations; 3. Basic data
types; 4. Numbers and matrices;
5. Advanced data types; 6. Graphs and their data structures; 7.
Graph algorithms; 8. Embedded
graphs; 9. The geometry kernels; 10. Geometry algorithms; 11.
Windows and panels; 12.
GraphWin; 13. On the implementation of LEDA; 14. Manual pages and
documentation;
Bibliography; Index.
Selling Points: ･ Definitive book on the only software library
for geometric computing
･ Written by authors of the library .i
･ Covers the details of the library plus its use through
examples
Comparable Titles:PRESS et al./Numerical Recipes in C/1993/0521
431085
0'ROURKE/ComputationaI Geometry in C/1 994/0521 445922
Subject areascomputer science (algorithms, data structures,
computational geometry)
Market: professionals, academic researchers
0521 56329 1 Hardback 1040pp November1999
ALEXANDER VILENKIN / Tufts University
AND E. PAUL S. SHELLARD / University of Cambridge
パーパー版出来
Now in paperback, this book is the first comprehensive and
coherent introduction to
the role of cosmic strings and other topological defects in the
universe. This study has
been one of the major driving forces in cosmology over the last
decade, and lies at the
fruitful intersection of particle physics and cosmology. Ample
introductory material is
included to make the book accessible to the wide audience of
particle physicists,
astrophysicists and cosmologists for whom this topic is of
immediate interest.
Contents: Preface; 1. lntroduction; 2. Phase transitions in the
early universe; 3. Topological
defects; 4. String field theory; 5. Superconducting strings; 6.
String dynamics; 7. String gravity; 8.
String interactions; 9. String evolution; 10. Cosmological
implications of strings; 11. Structure
formation with strings; 12. Cosmology of superconducting and
global strings; 13. Domain walls;
14. Monopoles; 15. Textures; 16. Topological defects and
inflation; References; lndex.
Selling Points: ･ The first coherent text on cosmic strings
･ First author is leading researcher in this area
･ Particularly thorough bibliography which is very valuable for
graduate students
Comparable Titles:BIRREL and DAVIES/Quantum Fields in Curved
Space/1984/0521 278589
VILENKIN and SHELLARD/Cosmic Strings and other Topological
Defects/1 994/0521 391 539
Subject areastheoretical physics, particle physics, astrophysics,
cosmology
Market: academic researchers, graduate students
Series: Cambridge Monographs on Mathematical Physics
0 521 39153 9 Hardback 537pp September 1994
0521 654769 Paperback 517pp c November 1999