Facts and Formulae
Probability and its Applications
2002. 688 pages. Hardcover
ISBN 3-7643-6705-9
English
The purpose of this book is to give an easy
reference to a large
number of facts and formulae associated Brownian
motion. The
collection contains more than 2500 numbered
formulae.
This book is of value as a basic reference
material to
researchers, graduate students, and people
doing applied work
with Brownian motion and diffusions. It can
also be used as a
source of explicit examples when teaching
stochastic processes.
Compared with the first edition published
in 1996, this second
edition has been revised and considerably
expanded. More than
1000 new formulae have been added to the
tables and, in
particular, geometric Brownian motion is
covered both in the
theoretical and the formula part of the book.
"This is an extremely useful handbook
(...) It is without
any previous example in its own subject matter:
the very first of
its kind. The primary aim of this handbook
is to serve as an
easily accessible reference for an incredibly
large number of
facts concerning the distribution of various
functionals of
Brownian motion and some related stochastic
processes."
Mathematical Reviews (review of 1st edition)
"In every respect, this most reliable
handbook on Brownian
motion and its friends is a volume to cherish.
I can highly
recommend it to researchers and users of
probability alike. The
authors are to be congratulated on their
great job in bringing
all of these facts and formulas together."
Journal of the American Statistical Association
(review of 1st
edition)
The book consists of two parts. The first
one - theory part - is
devoted to properties of linear diffusions
in general and
Brownian motion in particular. Results are
given mainly without
proofs. The second one - formula part - is
a table of
distributions of functionals of Brownian
motion and related
processes.
This book is of value as a basic reference
material to
researchers, graduate students, and people
doing applied work
with Brownian motion and diffusions. It can
also be used as a
source of explicit examples when teaching
stochastic processes.
Compared with the first edition published
in 1996, this second
edition has been revised and considerably
expanded. More than
1000 new formulae have been added to the
tables and, in
particular, geometric Brownian motion is
covered both in the
theoretical and the formula part of the book.
Progress in Mathematical Physics
2002. Approx. 200 pages. Hardcover
ISBN 0-8176-4298-6
English
Due in August 2002
Dirac operators play an important part in
several domains of
mathematics and mathematical physics, for
example: index theory,
theory of elliptic pseudodifferential operators,
theory of
electromagnetism, particle physics, and representation
theory of
Lie groups.
In this work, the basic theories underlying
the concept of Dirac
operators are explored. Starting with the
requisite material on
Clifford algebras and differential geometry,
the text focuses on
the two main properties of Dirac operators:
conformal invariance,
which determines the local behavior of the
operator, and the
unique continuation property dominating global
behavior. Spin
groups and spin or bundles are covered, as
well as the relations
with their classical counterparts, orthogonal
groups and Clifford
bundles.
The chapters on Clifford algebra and the
fundamentals of
differential geometry can be used as an introduction
to the above
topics, and are suitable for senior undergraduates
and graduates.
The other chapters are also accessible at
this level. Thus, this
self-contained book requires very little
previous knowledge of
the domains covered, although the reader
will benefit from
knowledge of complex analysis, which gives
the basic example of a
Dirac operator. More advanced readers - mathematical
physicists,
physicists and mathematicians from diverse
areas - will
appreciate the fresh approach to the theory,
as well as the new
results on boundary value theory.
Contents:
・IntroductionClifford Algebras
・Manifolds
・Dirac Operators
・Conformal Maps
・Unique Continuation and the Cauchy Kernel
・Boundary Values
・Appendix. General Manifolds
・List of Symbols
・Bibliography
・Index
May 2002 | Paperback | 368 pages 55 line
diagrams | ISBN: 0-521-00758-5
May 2002 | Hardback | 368 pages 55 line diagrams
| ISBN: 0-521-80975-4
This fourth edition of one of the classic
logic textbooks has
been thoroughly revised by John Burgess.
The aim is to increase
the pedagogical value of the book for the
core market of students
of philosophy and for students of mathematics
and computer
science as well. This book has become a classic
because of its
accessibility to students without a mathematical
background, and
because it covers not simply the staple topics
of an intermediate
logic course such as Godel’s Incompleteness
Theorems, but also
a large number of optional topics from Turing’s
theory of
computability to Ramsey’s theorem. John
Burgess has now
enhanced the book by adding a selection of
problems at the end of
each chapter, and by reorganising and rewriting
chapters to make
them more independent of each other and thus
to increase the
range of options available to instructors
as to what to cover and
what to defer.
Contents
Part I. Computability Theory: 1. Enumerability;
2.
Diagonalization; 3. Turing computability;
4. Uncomputability; 5.
Abacus computability; 6. Recursive functions;
7. Recursive sets
and relations; 8. Equivalent definitions
of computability; Part
II. Basic Metalogic: 9. A precis of first-order
logic: syntax; 10.
A precis of first-order logic: semantics;
11. The undecidability
of first-order logic; 12. Models; 13. The
existence of models; 14.
Proofs and completeness; 15. Arithmetization;
16.
Representability of recursive functions;
17. Indefinability,
undecidability, incompleteness; 18. The unprovability
of
consistency; Further topics: 19. Normal forms;
20. The Craig
interpolation theorem; 21. Monadic and dyadic
logic; 22. Second-order
logic; 23. Arithmetical definability; 24.
Decidability of
arithmetic without multiplication; 25. Non-standard
models; 26.
Ramsey’s theorem; 27. Modal logic and provability.
ISBN: 1-58488-347-2
Publication Date: 8/28/2002
Number of Pages: 3008
More than 1000 new pages of terms defined,
illustrated, and
referenced
A thorough update of all original entries
Thousands of references to related topics,
sources in the
literature, and Internet resources and links
Rigorous but highly readable technical definitions
enhanced with
the most useful, intersting, and fun aspects
of the topic
Upon publication, the first edition of the
CRC Concise
Encyclopedia of Mathematics received overwhelming
accolades for
its unparalleled scope, readability, and
utility. It soon took
its place among the top selling books in
the history of Chapman
& Hall/CRC, and its popularity continues
unabated.
Yet also unabated has been the dedication
of author Eric
Weisstein to collecting, cataloging, and
referencing mathematical
facts, formulas, and definitions. He has
now updated most of the
original entries and expanded the Encyclopedia
to include 1000
additional pages of illustrated entries.
The accessibility of the Encyclopedia along
with its broad
coverage and economical price make it attractive
to the widest
possible range of readers and certainly a
must for libraries,
from the secondary to the professional and
research levels. For
mathematical definitions, formulas, figures,
tabulations, and
references, this is simply the most impressive
compendium
available.
2002 \ 886,000
The Microfilm Collection
This microfilm collection of Godel’s papers (38 microfilm reels)
includes documents spanning his life, from
1906-1978. It includes notebooks, drafts, unpublished
manuscripts, notes, and legal records. Absent from this
collection is his correspondence.
Godel’s topical notebooks in this collection include: sixteen
mathematical notebooks, fourteen general notebooks,
nine history notebooks, six logic and foundation notebooks, four
on “results on foundations” and fifteen
philosophical notebooks. The philosophical notebooks date from
before May 1941 to the end of Godel’s life.
Unpublished drafts include: 1951 Gibb’s lecture, a fuller
version of his essay on relativity theory and idealistic
philosophy, and an English revised version dated 1972 of his
Dialectica paper (1958.) Godel’s drafts and offprints
also include typescript manuscripts, lectures and reviews in
English, German and in Gabelsberger shorthand. The
remainder of the collection includes notes, photographs,
financial and medical records, legal and political records,
and ephemera.
Organization of the Collection
Outline of Series: I. Personal and Scientific Correspondence. II.
Institutional, Commercial, and Incidental
Correspondence. III. Topical Notebooks. IV. Drafts and Offprints.
V. Bibliographic Notes and Memoranda. VI.
Other Loose Manuscript Notes. VII. Academic Records and Notices.
VIII. Legal and Political Documents. IX.
Financial Records. X. Medical Records .XI. Photographs. XII.
Ephemera. XIII. Oversize Items and Addenda. XIV.
Extra Large Items. XV. Preprints and Offprints.
( IDC Publishers )