April 2003 | Hardback | 800 pages | ISBN:
0-521-59271-2
The standard rules of probability can be
interpreted as uniquely
valid principles in logic. In this book,
E. T. Jaynes dispels the
imaginary distinction between ‘probability
theory’ and ‘statistical
inference’, leaving a logical unity and
simplicity, which
provides greater technical power and flexibility
in applications.
This book goes beyond the conventional mathematics
of probability
theory, viewing the subject in a wider context.
New results are
discussed, along with applications of probability
theory to a
wide variety of problems in physics, mathematics,
economics,
chemistry and biology. It contains many exercises
and problems,
and is suitable for use as a textbook on
graduate level courses
involving data analysis. The material is
aimed at readers who are
already familiar with applied mathematics
at an advanced
undergraduate level or higher. The book will
be of interest to
scientists working in any area where inference
from incomplete
information is necessary.
Contents
Foreword; Preface; Part I. Principles and
Elementary Applications:
1. Plausible reasoning; 2. The quantitative
rules; 3. Elementary
sampling theory; 4. Elementary hypothesis
testing; 5. Queer uses
for probability theory; 6. Elementary parameter
estimation; 7.
The central, Gaussian or normal distribution;
8. Sufficiency,
ancillarity, and all that; 9. Repetitive
experiments, probability
and frequency; 10. Physics of ‘random experiments’;
Part II.
Advanced Applications: 11. Discrete prior
probabilities, the
entropy principle; 12. Ignorance priors and
transformation
groups; 13. Decision theory: historical background;
14. Simple
applications of decision theory; 15. Paradoxes
of probability
theory; 16. Orthodox methods: historical
background; 17.
Principles and pathology of orthodox statistics;
18. The Ap
distribution and rule of succession; 19.
Physical measurements;
20. Model comparison; 21. Outliers and robustness;
22.
Introduction to communication theory; References;
Appendix A.
Other approaches to probability theory; Appendix
B. Mathematical
formalities and style; Appendix C. Convolutions
and cumulants.
Publication is planned for April 2003 | Hardback
| 456 pages |
ISBN: 0-521-80831-6
This book contains eight expository articles
by well-known
authors of the theory of Galois groups and
fundamental groups.
They focus on presenting recent developments,
avoiding classical
aspects which have already been described
at length in the
standard literature. The volume grew from
the special semester
held at the MSRI in Berkeley in 1999 and
many of the new results
are due to work accomplished during that
program. Among the
subjects covered are elliptic surfaces, Grothendieck’s
anabelian conjecture, fundamental groups
of curves and
differential Galois theory in positive characteristic.
Although
the articles contain original results, the
authors have striven
to make them as introductory as possible,
making them accessible
to graduate students as well as researchers
in algebraic geometry
and number theory. The volume also contains
a lengthy overview by
Leila Schneps that sets the individual articles
into the broader
context of contemporary research in Galois
groups.
Contributors
Fedor Bogomolov, Yuri Tschinkel, Shinichi
Mochizuki, Richard
Hain, Makoto Matsumoto, Leila Schneps, Akio
Tamagawa, B. H.
Matzat, Robert Guralnick, Florian Pop, Mohamed
Saidi
Contents
1. Monodromy of elliptic surfaces; 2. Topics
surrounding the
anabelian geometry of hyperbolic curve; 3.
Tannakian fundamental
groups associated to Galois groups; 4. Automorphisms
of curves
and special loci in genus zero moduli spaces;
5. On the tame
fundamental groups of curves over algebraically
closed fields of
characteristic 0; 6. Constructive differential
Galois theory; 7.
Monodromy groups of coverings of curves;
8. On the specialization
homomorphism of fundamental groups of curves
in positive
characteristic.
April 2003 | Hardback | 500 pages 169 line
diagrams 173
exercises | ISBN: 0-521-81658-0
April 2003 | Paperback| 500 pages 169 line
diagrams 173 exercises
| ISBN: 0-521-01687-8
Finding and interpreting the solutions of
differential equations
is a central and essential part of applied
mathematics. This book
aims to enable the reader to develop the
required skills needed
for a thorough understanding of the subject.
The authors focus on
the business of constructing solutions analytically,
and
interpreting their meaning, using rigorous
analysis where needed.
MATLAB is used extensively to illustrate
the material. There are
many worked examples based on interesting
and unusual real world
problems. A large selection of exercises
is provided, including
several lengthier projects, some of which
involve the use of
MATLAB. The coverage is broad, ranging from
basic second-order
ODEs and PDEs, through to techniques for
nonlinear differential
equations, chaos, asymptotics and control
theory. This broad
coverage, the authors’ clear presentation
and the fact that the
book has been thoroughly class-tested will
increase its
attraction to undergraduates at each stage
of their studies.
Contents
Preface; Part I. Linear Equations: 1. Variable
coefficient,
second-order, linear ordinary differential
equations; 2. Legendre
functions; 3. Bessel functions; 4. Boundary
value problems, Green’s
functions and Sturm?Liouville theory; 5.
Fourier series and the
Fourier transform; 6. Laplace transforms;
Part II. Nonlinear
Equations and Advanced Techniques: 7. Existence,
uniqueness,
continuity and comparison of solutions of
ordinary differential
equations; 8. Nonlinear ordinary differential
equations; 9. Group
theoretical methods; 10. Asymptotic methods:
basic ideas; 11.
Asymptotic methods: differential equations;
12. Stability,
instability and bifurcations; 13. Time-optimal
control in the
phase plane; 14. An introduction to chaotic
systems; Appendix 1.
Linear algebra; Appendix 2. Continuity and
differentiability;
Appendix 3. Power series; Appendix 4. Sequences
of functions;
Appendix 5. Ordinary differential equations;
Appendix 6. Complex
variables; Appendix 7. A short introduction
to MATLAB;
Bibliography; Index.
April 2003 | Paperback | 320 pages 154 line
diagrams 303
exercises | ISBN: 0-521-53104-7
When new ideas like chaos first move into
the mathematical
limelight, the early textbooks tend to be
very difficult. The
concepts are new and it takes time to find
ways to present them
in a form digestible to the average student.
This process may
take a generation, but eventually, what originally
seemed far too
advanced for all but the most mathematically
sophisticated
becomes accessible to a much wider readership.
This book takes
some major steps along that path of generational
change. It
presents ideas about chaos in discrete time
dynamics in a form
where they should be accessible to anyone
who has taken a first
course in undergraduate calculus. More remarkably,
it manages to
do so without discarding a commitment to
mathematical substance
and rigour. The book evolved from a very
popular one-semester
middle level undergraduate course over a
period of several years
and has therefore been well class-tested.
Contents
Preface; 1. Making predictions; 2. Mappings
and orbits; 3.
Periodic orbits; 4. Asymptotic orbits I:
linear and affine
mappings; 5. Asymptotic orbits II: differentiable
mappings; 6.
Families of mappings and bifurcations; 7.
Graphical composition,
wiggly iterates and zeros; 8. Sensitive dependence;
9.
Ingredients of chaos; 10. Schwarzian derivatives
and ‘woggles’;
11. Changing coordinates; 12. Conjugacy;
13. Wiggly iterates,
Cantor sets and chaos; Index.
288 pages , 6 1/8 x 9 , paperback
ISBN: 3-7643-3211-5
expected release date: 03/30/2003
ABOUT THIS BOOK
For the past several decades the theory of
automorphic forms has become a major focal
point of development in number theory and
algebraic geometry, with applications in
many diverse areas, including combinatorics
and mathematical physics.
The six chapters of this monograph present
a broad, user-friendly introduction to the
Langlands program, that is, the theory of
automorphic forms and its connection with
the theory of L-functions and other fields
of mathematics.
Key features of this self-contained presentation:
-- A variety of areas in number theory from
the classical zeta function up to the Langlands
program are covered
-- The exposition is systematic, with each
chapter focusing on a particular topic devoted
to special cases of the program: Basic zeta
function of Riemann and its generalizations
to Dirichlet and Hecke L-function, class
field theory and some topics on classical
automorphic functions (E. Kowalski) * A study
of the conjectures of Artin and Shimura--Taniyama--Weil
conjectures (E. de Shalit) * An examination
of classical modular (automorphic) L-functions
as GL(2) functions, bringing into play the
theory of representations (S. Kudla) * Selberg's
theory of the trace formula, which is a way
to study representations (D. Bump) * Discussion
of cuspidal automorphic representions of
GL(2,(A)) leads to Langlands theory for GL(n,(A))
and the importance of the Langlands' dual
group (J. Cogdell) * An introduction to the
geometric Langlands program, a new and active
area of research that permits using powerful
methods of algebraic geometry to construct
automorphic sheaves (D. Gaitsgory)
First-year graduate students and researchers
will benefit from this beautiful text.
TABLE OF CONTENTS
Preface * E. Kowalski - Elementary Theory
of L-Functions I * E. Kowalski - Elementary
Theory of L-Functions II * E. Kowalski -
Classical Automorphic Forms * E. DeShalit
- Artin L-Functions * E. DeShalit - L-Functions
of Elliptic Curves and Modular Forms * S.
Kudla - Tate's Thesis * S. Kudla - From Modular
Forms to Automorphic Representations * D.
Bump - Spectral Theory and the Trace Formula
* J. Cogdell - Analytic Theory of L-Functions
for GLn * J. Cogdell - Langlands Conjectures
for GLn * J. Cogdell - Dual Groups and Langlands
Functoriality * D. Gaitsgory - Informal Introduction
to Geometric Langlands