Publication is planned for June 2004 | Hardback | 416 pages
133 exercises | ISBN: 0-521-83263-2
Levy processes form a wide and rich class of random process, and
have many applications ranging from physics to finance.
Stochastic calculus is the mathematics of systems interacting
with random noise. For the first time in a book, Applebaum ties
the two subjects together. He begins with an introduction to the
general theory of Levy processes. The second part develops the
stochastic calculus for Levy processes in a direct and accessible
way. En route, the reader is introduced to important concepts in
modern probability theory, such as martingales, semimartingales,
Markov and Feller processes, semigroups and generators, and the
theory of Dirichlet forms. There is a careful development of
stochastic integrals and stochastic differential equations driven
by Levy processes. The book introduces all the tools that are
needed for the stochastic approach to option pricing, including
Ito's formula, Girsanovfs theorem and the martingale
representation theorem.
June 2004 | Hardback | 316 pages 37 line diagrams 1 half-tone | ISBN: 0-88385-542-9
For many years, famed mathematics historian and master teacher
Howard Eves collected stories and anecdotes about mathematics and
mathematicians, gathering them together in six Mathematical
Circles books. Thousands of teachers of mathematics have read
these stories and anecdotes for their own enjoyment and used them
in the classroom - to add entertainment, to introduce a human
element, to inspire the student, and to forge some links of
cultural history. All six of the Mathematical Circles books have
been reissued as a three-volume edition. This three-volume set is
a must for all who enjoy the mathematical enterprise, especially
those who appreciate the human and cultural aspects of
mathematics.
Reviews
eThe 360 different anecdotes compiled in these delightful
volumes will add zest to every teacherfs mathematical classes.
There are appropriate selections for all levels of students. They
are short, succinct, and at the same time given in simple
settings which enable the reader to identify with the story and
its implications. Here is presented the kind of material that
makes the difference to the undecided student. I highly recommend
you putting a copy next to your worktable.f The Mathematics
Teacher
Publication is planned for August 2004 | Hardback | 288 pages
| ISBN: 0-521-80160-5
Though its relationship with electromagnetic boundary value
problems has long been recognized, topology is still a largely
unexploited tool in problem formulation and computational methods
for electromagnetic fields. The development of algebraic topology
since the time of Maxwell provides a framework for linking data
structures, algorithms, and computation to topological aspects of
3-dimensional electromagnetic boundary value problems. This book
exposes the link between Maxwell and a modern approach to
algorithms through algebraic topology. The first chapters lay out
relevant structures from homology theory, differential forms, and
Hodge decompositions with an interpretation for electromagnetism.
These topological structures are subsequently linked to
variational formulations in electromagnetics, the finite element
method, algorithms, and certain aspects of the associated
numerical linear algebra. While not directed primarily towards
applications, a recurring theme is formulation of and algorithms
for the problem of making branch cuts for computing magnetic
scalar potentials and eddy currents.
Publication is planned for July 2004 | Hardback | 200 pages 12
figures | ISBN: 0-521-83660-3
The bilinear, or Hirotafs direct, method was invented in the
early 1970s as an elementary means of constructing soliton
solutions that avoided the use of the heavy machinery of the
inverse scattering transform and was successfully used to
construct the multisoliton solutions of many new equations. In
the 1980s the deeper significance of the tools used in this
method - Hirota derivatives and the bilinear form - came to be
understood as a key ingredient in Satofs theory and the
connections with affine Lie algebras. The main part of this book
concerns the more modern version of the method in which solutions
are expressed in the form of determinants and pfaffians. While
maintaining the original philosophy of using relatively simple
mathematics, it has, nevertheless, been influenced by the deeper
understanding that came out of the work of the Kyoto school. The
book will be essential for all those working in soliton theory.
July 2004 | Paperback | 450 pages 10 tables 400 exercises 120
figures | ISBN: 0-521-54310-X
Recent years have seen the development of powerful tools for
verifying hardware and software systems, as companies worldwide
realise the need for improved means of validating their products.
There is increasing demand for training in basic methods in
formal reasoning so that students can gain proficiency in logic-based
verification methods. The second edition of this successful
textbook addresses both those requirements, by continuing to
provide a clear introduction to formal reasoning which is both
relevant to the needs of modern computer science and rigorous
enough for practical application. Improvements to the first
edition have been made throughout, with extra and expanded
sections on SAT solvers, existential/universal second-order
logic, micro-models, programming by contract and total
correctness. The coverage of model-checking has been
substantially updated. Further exercises have been added.
Internet support for the book includes worked solutions for all
exercises for teachers, and model solutions to some exercises for
students.
Reviews
ec an unusual, inspiring and remarkable book c one can find
in it all the material which is suitable for undergraduate and
beginning graduate students in computer science and electrical
engineering who will profit by using it in their professional
activities in the near future.f Zentralblatt MATH