Lecture Notes In Logic, 20
Summary
A compilation of papers presented at the 2001 European Summer
Meeting of the Association for Symbolic Logic, Logic Colloquium
f01 includes surveys and research articles from some of the
worldfs preeminent logicians. Two long articles are based on
tutorials given at the meeting and present accessible expositions
of research in two active areas of logic, geometric model theory
and descriptive set theory of group actions.
The remaining articles cover seperate research topics in many
areas of mathematical logic, including applications in Computer
Science, Proof Theory, Set Theory, Model Theory, Computability
Theory, and aspects of Philosophy.
This collection will be of interest not only to specialists in
mathematical logic, but also to philosophical logicians,
historians of logic, computer scientists, formal linguists and
mathematicians in the areas of algebra, abstract analysis and
topology. A number of the articles are aimed at non-specialists
and serve as good introductions for graduate students.
Details
ISBN: 1-56881-247-7/Format: Hardcover
ISBN: 1-56881-248-5/Format: Paperback
Year: 2005
Pages: 496
Lecture Notes in Logic, 18
Summary
In fall 2000, the Notre Dame logic community hosted Greg Hjorth,
Rodney G. Downey, Zoe Chatzidakis, and Paola DfAquino as
visiting lecturers. Each of them presented a month long series of
expository lectures at the graduate level. The articles in this
volume are refinements of these excellent lectures.
Details
ISBN: 1-56881-249-3
Format: Hardcover
ISBN: 1-56881-250-7
Format: Paperback
Pages: 200
2005, X, 228 p., Softcover
ISBN: 3-7643-7259-1
About this book
Universal Logic is not a new logic, but a general theory of
logics, considered as mathematical structures. The name was
introduced about ten years ago, but the subject is as old as the
beginning of modern logic: Alfred Tarski and other Polish
logicians such as Adolf Lindenbaum developed a general theory of
logics at the end of the 1920s based on consequence operations
and logical matrices. The subject was revived after the flowering
of thousands of new logics during the last thirty years: there
was a need for a systematic theory of logics to put some order in
this chaotic multiplicity.
This book contains recent works on universal logic by first-class
researchers from all around the world. The book is full of new
and challenging ideas that will guide the future of this exciting
subject. It will be of interest for people who want to better
understand what logic is. Tools and concepts are provided here
for those who want to study classes of already existing logics or
want to design and build new ones.
Table of contents
Preface.- Universal Logic: Frameworks and Structures.- Identity
and Nature of Logical Structures.- Tools and Concepts for
Universal Logic.
Series: Operator Theory: Advances and Applications, Vol. 157
2005, XII, 316 p., Hardcover
ISBN: 3-7643-7212-5
A Birkhauser book
About this book
Operator theory, system theory, scattering theory, and the theory
of analytic functions of one complex variable are deeply related
topics, and the relationships between these theories are well
understood. When one leaves the setting of one operator and
considers several operators, the situation is much more involved.
There is no longer a single underlying theory, but rather
different theories, some of them loosely connected and some not
connected at all. These various theories, which one could call
"multidimensional operator theory", are topics of
active and intensive research.
The present volume contains a selection of papers in
multidimensional operator theory. Topics considered include the
non-commutative case, function theory in the polydisk, hyponormal
operators, hyperanalytic functions, and holomorphic deformations
of linear differential equations.
The volume will be of interest to a wide audience of pure and
applied mathematicians, electrical engineers and theoretical
physicists.
Table of contents
Editorial Introduction.- Contributions by J. Ball and V. Vinnikov
/ T. Banks, T. Constantinescu and J.L. Johnson / M. Bessmertnyi /
S. Eidelman and Y. Krasnov / D.S. Kalyuzhnyi-Verbovetzkii / V.
Katsnelson and D. Volok / M.E. Luna-Elizarraras and M. Shapiro /
P. Muhly and B. Solel / M. Putinar / M. Reurings and L. Rodman /
F.H. Szafraniec.
Hardback (ISBN 0521831660)
Paperback (ISBN 0521539374)
Textbook
Lecturers can request inspection copies of this title.
Courses: Probability, Stochastic Processes, Functional Analysis
This text is designed both for students of probability and
stochastic processes, and for students of functional analysis.
For the reader not familiar with functional analysis a detailed
introduction to necessary notions and facts is provided. However,
this is not a straight textbook in functional analysis; rather,
it presents some chosen parts of functional analysis that can
help understand ideas from probability and stochastic processes.
The subjects range from basic Hilbert and Banach spaces, through
weak topologies and Banach algebras, to the theory of semigroups
of bounded linear operators. Numerous standard and nonstandard
examples and exercises make the book suitable as a course
textbook or for selfstudy.
Contents
1. Preliminaries, notations, conventions; 2. Basic notations in
functional analysis; 3. Conditional expectation; 4. Brownian
motion and hilbert spaces; 5. Dual spaces and convergence of
probability measures; 6. The Gelfand transform and its
applications; 7. Semigroups of operators and Levy processes; 8.
Markov processes and semigroups of operators; 9. Appendixes;
References; Index.
2 Paperback books (ISBN 0521672295)
Textbook
Lecturers can request inspection copies of this title.
Courses: String Theory Introductory String Theory The Geometry of
String Theory
Levels: GRADUATE LEVEL
Available for the first time in paperback, String Theory
comprises two volumes which give an uptodate, comprehensive and
pedagogic account of the subject. Volume 1, An Introduction to
the Bosonic String, gives a thorough introduction to the bosonic
string, based on the Polyakov path integral and conformal field
theory. Volume 2, Superstring Theory and Beyond, begins with an
introduction to supersymmetric string theories and goes on to a
broad presentation of the important advances of recent years.
Both volumes contain an annotated reference section, emphasizing
references that will be useful to the student, as well as a
detailed glossary of important terms and concepts. Many exercises
are included which are intended to reinforce the main points of
the text and to bring in additional ideas. These volumes provide
an essential text and reference for graduate students and
researchers in theoretical physics, particle physics and
relativity.
Contents
Volume I: 1. A first look at strings; 2. Conformal field theory;
3. The Polyakov path integral; 4. The string spectrum; 5. The
string S-matrix; 6. Tree level amplitudes; 7. One loop
amplitudes; 8. Toroidal compactification and T-duality; 9. Higher
order amplitudes; Appendix A. A short course on path integrals;
References; Glossary; Index. Volume 2: 10. Type I and type II
superstrings; 11. The heterototic string; 12. Superstring
interactions; 13. D-branes; 14. Strings at strong coupling; 15.
Advanced conformal field theory; 16. Orbifolds; 17. Calabi-Yau
compactification; 18. Spacetime physics; 19. Advanced topics;
Appendix B. Spinors and SUSY in various dimensions; References;
Glossary; Index.
Reviews
'c this is an impressive book. It is notable for its consistent
line of development and the clarity and insight with which topics
are treated c It is hard to think of a better text in an
advanced graduate area, and it is rare to have one written by a
master of the subject. It is worth pointing out that the book
also contains a collection of useful problems, a glossary, and an
unusually complete index.' Physics Today
'c the most comprehensive text addressing the discoveries of
the superstring revolutions of the early to mid 1990s, which mark
the beginnings of 'modern' string theory.' Donald Marolf,
University of California Santa Barbara, American Journal of
Physics
'Physicists believe that the best hope for a fundamental theory
of nature - including unification of quantum mechanics with
general relativity and elementary particle theory - lies in
string theory. This elegant mathematical physics subject is
expounded by Joseph Polchinski in two volumes from Cambridge
University Press c Written for advanced students and
researchers, this set provides thorough and up-to-date knowledge.'
American Scientist
'We would like to stress the pedagogical value of the present
book. The approach taken is modern and pleasantly systematic, and
it covers a broad class of results in a unified language. A set
of exercises at the end of each chapter complements the
discussions in the main text. On the other hand, the introduction
of techniques and concepts essential in the context of
superstrings makes it a useful reference for researchers in the
field.' Mathematical Reviews
'It amply fulfils the need to inspire future string theorists on
their long slog and is destined to become a classic. It is a
truly exciting enterprise and one hugely served by this
magnificent book.' David Bailin, The Times Higher Education
Supplement