Publication is planned for April 2004 | Hardback
| 315 pages
25 line diagrams | ISBN: 0-521-82925-9
Part two of the authors’ comprehensive and
innovative work on
multidimensional real analysis. This book
is based on extensive
teaching experience at Utrecht University
and gives a thorough
account of integral analysis in multidimensional
Euclidean space.
It is an ideal preparation for students who
wish to go on to more
advanced study. The notation is carefully
organized and all
proofs are clean, complete and rigorous.
The authors have taken
care to pay proper attention to all aspects
of the theory. In
many respects this book presents an original
treatment of the
subject and it contains many results and
exercises that cannot be
found elsewhere. The numerous exercises illustrate
a variety of
applications in mathematics and physics.
This combined with the
exhaustive and transparent treatment of subject
matter make the
book ideal as either the text for a course,
a source of problems
for a seminar or for self study.
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Contents
1. Integration; 2. Integration over submanifolds;
3. Oriented
integration; Exercises.
November 2003 | Hardback | 365 pages 118
line diagrams 4
tables 43 exercises | ISBN: 0-521-82150-9
November 2003 | Paperback | 365 pages 118
line diagrams 4 tables
43 exercises | ISBN: 0-521-52902-6
The paradigm of deterministic chaos has influenced
thinking in
many fields of science. Chaotic systems show
rich and surprising
mathematical structures. In the applied sciences,
deterministic
chaos provides a striking explanation for
irregular behaviour and
anomalies in systems which do not seem to
be inherently
stochastic. The most direct link between
chaos theory and the
real world is the analysis of time series
from real systems in
terms of nonlinear dynamics. Experimental
technique and data
analysis have seen such dramatic progress
that, by now, most
fundamental properties of nonlinear dynamical
systems have been
observed in the laboratory. Great efforts
are being made to
exploit ideas from chaos theory wherever
the data displays more
structure than can be captured by traditional
methods. Problems
of this kind are typical in biology and physiology
but also in
geophysics, economics, and many other sciences.
Reviews
From reviews of the first edition: ‘… any
serious physics
institute should have such a book on its
shelves. It will be of
use to any experimental scientist dealing
with nonlinear data or
a theoretical physicist who desires a feeling
of ‘how one does
it in an experiment’. The clear course of
presentation should
make it accessible to undergraduate students.’
Daniel Wojcik,
Pageoph
‘This book will be of value to any graduate
student or
researcher who needs to be able to analyse
time series data,
especially in the fields of physics, chemistry,
biology,
geophysics, medicine, economics and the social
sciences.’
Mathematical Reviews
Contents
Part I. Basic Topics: 1. Introduction: why
nonlinear methods?; 2.
Linear tools and general considerations;
3. Phase space methods;
4. Determinism and predictability; 5. Instability:
Lyapunov
exponents; 6. Self-similarity: dimensions;
7. Using nonlinear
methods when determinism is weak; 8. Selected
nonlinear
phenomena; Part II. Advanced Topics: 9. Advanced
embedding
methods; 10. Chaotic data and noise; 11.
More about invariant
quantities; 12. Modelling and forecasting;
13. Non-stationary
signals; 14. Coupling and synchronisation
of nonlinear systems;
15. Chaos control; Appendix A Using the TISEAN
programs; Appendix
B Description of the experimental data sets.
Publication is planned for November 2003
| Hardback | 208
pages | ISBN: 0-521-82964-X
Publication is planned for November 2003
| Paperback| 208 pages |
ISBN: 0-521-53650-2
The interplay between algebra and geometry
is a beautiful (and
fun!) area of mathematical investigation.
Recent advances in
computing and algorithms make it possible
to tackle many
classical problems in a down-to-earth and
concrete fashion. This
opens wonderful new vistas and allows us
to pose, study and solve
problems that were previously out of reach.
Suitable for graduate
students, the objective of this book is to
bring advanced algebra
to life with lots of examples. The first
chapters provide an
introduction to commutative algebra and connections
to geometry.
The rest of the book focuses on three active
areas of
contemporary algebra: Homological Algebra
(the snake lemma, long
exact sequence inhomology, functors and derived
functors (Tor and
Ext), and double complexes); Algebraic Combinatorics
and
Algebraic Topology (simplicial complexes
and simplicial homology,
Stanley-Reisner rings, upper bound theorem
and polytopes); and
Algebraic Geometry (points and curves in
projective space,
Riemann-Roch, Cech cohomology, regularity).
Contents
Preface; 1. Basics of commutative algebra;
2. Projective space
and graded objects; 3. Free resolutions and
regular sequences; 4.
Grobner bases; 5. Combinatorics and topology;
6. Functors:
localization, hom, and tensor; 7. Geometry
of points; 8.
Homological algebra, derived functors; 9.
Curves, sheaves and
cohomology; 10. Projective dimension; A.
Abstract algebra primer;
B. Complex analysis primer; Bibliography.
Publication is planned for November 2003
| Hardback | 303
pages 45 line diagrams | ISBN: 0-521-45054-3
This is a self-contained account of how some
modern ideas in
differential geometry can be used to tackle
and extend classical
results in integral geometry. The authors
investigate the
influence of total curvature on the metric
structure of complete,
non-compact Riemannian 2-manifolds, though
their work, much of
which has never appeared in book form before,
can be extended to
more general spaces. Many classical results
are introduced and
then extended by the authors. The compactification
of complete
open surfaces is discussed, as are Busemann
functions for rays.
Open problems are provided in each chapter,
and the text is
richly illustrated with figures designed
to help the reader
understand the subject matter and get intuitive
ideas about the
subject. The treatment is self-contained,
assuming only a basic
knowledge of manifold theory, so is suitable
for graduate
students and non-specialists who seek an
introduction to this
modern area of differential geometry.
Contents
1. Riemannian geometry; 2. Classical results
by Cohn-Vossen and
Huber; 3. The ideal boundary; 4. The cut
loci of complete open
surfaces; 5. Isoperimetric inequalities;
6. Mass of rays; 7.
Poles and cut loci of a surface of revolution;
8. Behaviour of
geodesics.