2004 | Paperback | 446 pages 16 tables 320
exercises | ISBN: 0-521-54011-9
2004 | Hardback | 446 pages 16 tables 320
exercises | ISBN: 0-521-83250-0
Algebraic number theory is a subject which
came into being
through the attempts of mathematicians to
try to prove Fermat's
last theorem and which now has a wealth of
applications to
diophantine equations, cryptography, factoring,
primality testing
and public-key cryptosystems. This book provides
an introduction
to the subject suitable for senior undergraduates
and beginning
graduate students in mathematics. The material
is presented in a
straightforward, clear and elementary fashion,
and the approach
is hands on, with an explicit computational
flavor. Prerequisites
are kept to a minimum, and numerous examples
illustrating the
material occur throughout the text. References
to suggested
readings and to the biographies of mathematicians
who have
contributed to the development of algebraic
number theory are
given at the end of each chapter. There are
over 320 exercises,
an extensive index, and helpful location
guides to theorems and
lemmas in the text.
Contents
Introduction; 1. Integral domains; 2. Euclidean
domains; 3. Noetherian domains; 4. Elements
integral over a domain; 5. Algebraic extensions
of a field; 6. Algebraic number fields; 7.
Integral bases; 8. Dedekind domains; 9. Norms
of ideals; 10. Decomposing primes in a number
field; 11. Units in real quadratic fields;
12. The ideal class group; 13. Dirichlet's
unit theorem; 14. Applications to diophantine
equations.
2004 | Hardback | 288 pages | ISBN: 0-521-82654-3
Almost all the results available in the literature
on
multivariate t-distributions published in
the last 50 years are
now collected together in this comprehensive
reference. Because
these distributions are becoming more prominent
in many
applications, this book is a must for any
serious researcher or
consultant working in multivariate analysis
and statistical
distributions. Much of this material has
never before appeared in
book form. The first part of the book emphasizes
theoretical
results of a probabilistic nature. In the
second part of the
book, these are supplemented by a variety
of statistical aspects.
Various generalizations and applications
are dealt with in the
final chapters. The material on estimation
and regression models
is of special value for practitioners in
statistics and economics.
A comprehensive bibliography of over 350
references is included.
February 2004 | Hardback | 416 pages 3 tables
102 exercises 81
figures | ISBN: 0-521-81185-6
February 2004 | Paperback | 416 pages 3 tables
102 exercises 81
figures | ISBN: 0-521-01069-1
Thoroughly revised and updated, this textbook
provides a
pedagogical introduction to relativity. It
is self-contained, but
the reader is expected to have a basic knowledge
of theoretical
mechanics and electrodynamics. It covers
the most important
features of both special and general relativity,
as well as
touching on more difficult topics, such as
the field of charged
pole-dipole particles, the Petrov classification,
groups of
motions, gravitational lenses, exact solutions
and the structure
of infinity. The necessary mathematical tools
(tensor calculus,
Riemannian geometry) are provided, most of
the derivations are
given in full, and exercises are included
where appropriate.
Written as a textbook for undergraduate and
introductory graduate
courses, it will also be of use to researchers
working in the
field. The bibliography gives the original
papers and directs the
reader to useful monographs and review papers.
Contents
Foreword; Part I. Special Relativity: 1.
Introduction: inertial
systems and Galilei invariance; 2. Light
propagation and Lorenz
transformations; 3. Our world as a Minkowski
space; 4. Mechanics
of special relativity; 5. Optics of plane
waves; 6. Four-dimensional
vectors and tensors; 7. Electrodynamics in
vacuo; 8.
Transformation properties of electromagnetic
fields: examples; 9.
Null vectors and algebraic properties of
electromagnetic fields;
10. Charged point particles and their field;
11. Pole-dipole
particles and their field; 12. Electodynamics
in media; 13.
Perfect fluids and other physical theories;
Part II. Riemannian
Geometry: 14. The force-free motion of particles;
15. Why
Riemannian geometry?; 16. Riemannian space;
17. Tensor algebra;
18. The covariant derivative and parallel
transport; 19. The
curvature tensor; 20. Differential operators,
integrals and
integral laws; 21. Fundamental laws of physics
in Riemannian
spaces; Part III. Foundations of Einstein's
Theory of Gravitation:
22. The fundamental equations of Einstein's
theory of
gravitation; 23. The Schwarzschild solution;
24. Experiments to
verify the Schwarzschild metric; 25. Gravitational
lenses; 26.
The interior Schwarzschild solution; Part
IV. Linearized Theory
of Gravitation, Far Fields and Gravitational
Waves: 27. The
linearized Einstein theory of gravity; 28.
Far fields and balance
equations; 29. Gravitational waves; 30. The
Cauchy problem for
the Einstein field equations; Part V. Invariant
Characterization
of Exact Solutions: 31. Preferred vector
fields and their
properties; 32. The Petrov classification;
33. Killing vectors
and groups of motion; 34. A survey of some
selected classes of
exact solutions; Part VI. Gravitational Collapse
and Black Holes:
35. The Schwarzschild singularity; 36. Gravitational
collapse of
spherically-symmetric stars; 37. Rotating
black holes; 38. Black
holes are not black; 39. The conformal structure
of infinity;
Part VII. Cosmology: 40. Robertson-Walker
metrics and their
properties; 41. The dynamics of R-W metrics
and the Friedmann
universes; 42. Our Universe as a Friedmann
model; 43. General
cosmological models; Bibliography; Index.
2004 | Paperback | 600 pages 50 line diagrams
1 half-tone |
ISBN: 0-521-54049-6
The symposium held in honour of the 60th
birthday of Graeme Segal
brought together leading physicists and mathematicians.
Its
topics were centred around string theory,
M-theory, and quantum
gravity on the one hand, and K-theory, elliptic
cohomology,
quantum cohomology and string topology on
the other. Geometry and
quantum physics developed in parallel since
the recognition of
the central role of non-abelian gauge theory
in elementary
particle physics in the late seventies and
the emerging study of
super-symmetry and string theory. With its
selection of survey
and research articles these proceedings fulfil
the dual role of
reporting on recent developments in the field
and defining
directions for future research. For the first
time Graeme Segal痴
manuscript 禅he definition of Conformal Field
Theory・is
published, which has been greatly influential
over more than ten
years. An introduction by the author puts
it into the present
context.
Contributors
Michael Atiyah, Michael Hopkins, Nils Baas,
Bjorn Dundas, John
Rognes, David Ben-Zvi, Edward Frenkel, Yuri
Berest, George
Wilson, Ralph Cohen, Veronique Godin, Robbert
Dijkgraaf, Dusa
McDuff, Gregory Moore, Jack Morava, Stephan
Stolz, Peter
Teichner, Dennis Sullivan, Constantin Teleman,
Michael S. Weiss,
Edward Witten, Graeme Segal
Contents
Part I. Contributions: 1. A variant of K-theory
Michael Atiyah
and Michael Hopkins; 2. Two-vector bundles
and forms of elliptic
cohomology Nils Baas, Bjorn Dundas and John
Rognes; 3. Geometric
realisation of the Segal-Sugawara construction
David Ben-Zvi and
Edward Frenkel; 4. Differential isomorphism
and equivalence of
algebraic varieties Yuri Berest and George
Wilson; 5. A polarized
view of string topology Ralph Cohen and Veronique
Godin; 6.
Random matrices and Calabi-Yau geometry Robbert
Dijkgraaf; 7. A
survey of the topological properties of symplectomorphism
groups
Dusa McDuff; 8. K-theory from a physical
perspective Gregory
Moore; 9. Heisenberg groups and algebraic
topology Jack Morava;
10. What is an elliptic object? Stephan Stolz
and Peter Teichner;
11. Open and closed string field theory interpreted
in classical
algebraic topology Dennis Sullivan; 12. K-theory
of the moduli of
principal bundles on a surface and deformations
of the Verlinde
algebra Constantin Teleman; 13. Cohomology
of the stable mapping
class group Michael S. Weiss; 14. Conformal
field theory in four
and six dimensions Edward Witten; Part II.
The Definition of
Conformal Field Theory by Graeme Segal: 15.
Definition of a
conformal field theory Graeme Segal.