September 2004 | Hardback | 394 pages 41
line diagrams 22
tables 279 exercises | ISBN: 0-521-83329-9
September 2004 | Paperback | 394 pages 41
line diagrams 22 tables
279 exercises | ISBN: 0-521-54036-4
Chance events are commonplace in our daily
lives. Every day we
encounter many situations where the outcome
is uncertain, and,
perhaps without realizing it, we make a guess
about the
likelihood of one outcome or another. But
mastering the concepts
of probability can cast a new light on situations
where
randomness and chance appear to rule. Here
the reader can learn
about the world of probability in an informal
way. Lotteries and
casino games provide a natural source of
motivation, and these
are carefully discussed with many worked
examples to illustrate
the key concepts and ideas from probability
theory. The emphasis
is on why probability works and how it can
be applied. The author
introduces the reader to the law of large
numbers, betting
systems, random walks, the bootstrap, rare
events, the central
limit theorem, the multivariate normal distribution,
the Bayesian
approach, generating functions, and more.
Written with wit and
clarity, this book can easily be read by
anyone who is not put
off by a few numbers and some high school
algebra. It is also
ideally suited to students of engineering
or computer science
undertaking a first course in probability.
Contents
Part I. Probability in Action: 1. Probability
questions; 2. The
law of large numbers and simulation; 3. Probabilities
in everyday
life; 4. Rare events and lotteries; 5. Probability
and
statistics; 6. Chance trees and Bayes’ rule;
Part II: 7.
Foundations of probability theory; 8. Conditional
probability and
Bayes; 9. Basic rules for discrete random
variables; 10.
Continuous random variables; 11. Jointly
distributed random
variables; 12. Multivariate normal distribution;
13. Conditional
distributions; 14. Generating functions.
Solving Polynomial Equation Systems II
Macaulay's Paradigm and Grobner Technology
Publication is planned for September 2004
| Hardback | 700
pages | ISBN: 0-521-81156-2
The second volume of this comprehensive treatise
focusses on
Buchberger theory and its application to
the algorithmic view of
commutative algebra. In distinction to other
works, the
presentation here is based on the intrinsic
linear algebra
structure of Groebner bases, and thus elementary
considerations
lead easily to the state-of-the-art in issues
of implementation.
The same language describes the applications
of Groebner
technology to the central problems of commutative
algebra. The
book can be also used as a reference on elementary
ideal theory
and a source for the state-of-the-art in
its algorithmization.
Aiming to provide a complete survey on Groebner
bases and their
applications, the author also includes advanced
aspects of
Buchberger theory, such as the complexity
of the algorithm,
Galligo's theorem, the optimality of degrevlex,
the Gianni-Kalkbrener
theorem, the FGLM algorithm, and so on. Thus
it will be essential
for all workers in commutative algebra, computational
algebra and
algebraic geometry.
Contents
Preface; Part III. Gauss, Euclid, Buchberger
- Elementary Grobner
Bases: 20. Hilbert; 21. Gauss; 22. Buchberger;
23. Macaulay I; 24.
Grobner I; 25. Gebauer and Traverso; 26.
Spear; Part IV. Duality:
27. Noether; 28. Moller I; 29. Lazard; 30.
Macaulay II; 31.
Grobner II; 32. Grobner III; 33. Moller II;
Part IV. Beyond
Dimension Zero: 34. Grobner IV; 35. Gianni
Trager Zacharias; 36.
Macaulay III; 37. Galligo; 38. Giusti; Bibliography;
Index.
*
October 2004 | Hardback | 320 pages 5 tables
48 figures | ISBN:
0-521-84045-7
This book applies the mathematics and concepts
of quantum
mechanics and quantum field theory to the
modelling of interest
rates and the theory of options. Particular
emphasis is placed on
path integrals and hamiltonians. Financial
mathematics is
currently almost completely dominated by
stochastic calculus. The
present book is unique in that it offers
a formulation that is
completely independent of that approach.
As such many new results
emerge from the ideas developed by the author.
This pioneering
work will be of interest to physicists and
mathematicians working
in the field of finance, to quantitative
analysts in banks and
finance firms and to practitioners in the
field of fixed income
securities and foreign exchange. The book
can also be used as a
graduate text for courses in financial physics
and financial
mathematics.
Contents
Foreword; Preface; 1. Synopsis; Part I. Fundamental
Concepts of
Finance: 2. Introduction to finance; 3. Derivative
securities;
Part II. Systems with finite number of degrees
of freedom: 4.
Hamiltonians and stock options; 5. Path integrals
and stock
options; 6. Stochastic interest rates’ Hamiltonians
and path
integrals; Part III. Quantum field theory
of interest rates
models: 7. Quantum field theory of forward
interest rates; 8.
Empirical forward interest rates and field
theory models; 9.
Field theory of derivatives and hedging of
treasury bonds; 10.
Field theory Hamiltonian of forward interest
rates; 11.
Conclusions; A. Mathematical Background;
Brief glossary of
financial terms; Brief glossary of physics
terms; List of main
symbols
October 2004 | Paperback | 350 pages 100
line diagrams | ISBN:
0-521-54831-4
October 2004 | Hardback | 350 pages 100 line
diagrams | ISBN: 0-521-83947-5
Knot theory is the study of embeddings of
circles in space. It is
a subject in which naturally occurring questions
are often so
simple to state that they can be explained
to a child, yet
finding answers may require ideas from the
forefront of research.
Peter Cromwell has written a textbook designed
for use at on
advanced undergraduate or beginning graduate
level courses. The
exposition is detailed and careful yet engaging
and full of
motivation. Numerous examples and exercises
serve to help
students through the material, while an instructor’s
manual is
available online.
Contents
1. Introduction; 2. A Topologist’s toolkit;
3. Link diagrams; 4.
Constructions and decompositions of links;
5. Spanning surfaces
and genus; 6. Matrix invariants; 7. The Alexander-Conway
polynomial; 8. Rational tangles; 9. More
polynomials; 10. Closed
braids and arc presentations.
*
October 2004 | Hardback | 250 pages 53 line
diagrams 35
exercises | ISBN: 0-52-183186-5
Ideas of projective geometry keep reappearing
in seemingly
unrelated fields of mathematics. The authors'
main goal is to
emphasize connections between classical projective
differential
geometry and contemporary mathematics and
mathematical physics.
They also give new results and new proofs
of classic theorems.
Exercises play a prominent role: historical
and cultural comments
set the basic notions in a broader context.
The book opens by
discussing the Schwarzian derivative and
its connection to the
Virasoro algebra. One-dimensional projective
differential
geometry features strongly. Related topics
include differential
operators, the cohomology of the group of
diffeomorphisms of the
circle, and the classical four-vertex theorem.
The classical
theory of projective hypersurfaces is surveyed
and related to
some very recent results and conjectures.
A final chapter
considers various versions of multi-dimensional
Schwarzian
derivative. In sum, here is a rapid route
for graduate students
and researchers to the frontiers of current
research in this
evergreen subject.
Contents
Preface: why projective? 1. Introduction;
2. The geometry of the
projective line; 3. The algebra of the projective
line and
cohomology of Diff(S1); 4. Vertices of projective
curves; 5.
Projective invariants of submanifolds; 6.
Projective structures
on smooth manifolds; 7. Multi-dimensional
Schwarzian derivatives
and differential operators; Appendix 1. Five
proofs of the Sturm
theorem; Appendix 2. The language of symplectic
and contact
geometry; Appendix 3. The language of connections;
Appendix 4.
The language of homological algebra; Appendix
5. Remarkable
cocycles on groups of diffeomorphisms; Appendix
6. The
Godbillon?Vey class; Appendix 7. The Adler?Gelfand?Dickey
bracket
and infinite-dimensional Poisson geometry;
Bibliography; Index.
November 2004 | Hardback | 342 pages 148
exercises | ISBN: 0-521-84397-9
The techniques that can be used to solve
non-linear problems are
far different than those that are used to
solve linear problems.
Many courses in analysis and applied mathematics
attack linear
cases simply because they are easier to solve
and do not require
a large theoretical background in order to
approach them.
Professor Schechter’s book is devoted to
non-linear methods
using the least background material as possible
and the simplest
linear techniques. An understanding of the
tools for solving non-linear
problems is developed whilst demonstrating
their application to
problems in one and then leading to, higher
dimensions. The
reader is guided using simple exposition
and proof, assuming a
minimal set of pre-requisites. For completion,
a set of
appendices covering essential basics in functional
analysis and
metric spaces is included, making this ideal
as an accompanying
text on an upper-undergraduate or graduate
course, or even for
self-study.
Contents
1. Extrema; 2. Critical points; 3. Boundary
value problems; 4.
Saddle points; 5. Calculus of variations;
6. Degree theory; 7.
Conditional extrema; 8. Minimax methods;
9. Jumping
nonlinearities; 10. Higher Dimensions;