Included in series
Studies in Logic and the Foundations of Mathematics, 147
Description
Relation algebras are algebras arising from the study of binary
relations. They form a part of the field of algebraic logic, and
have applications in proof theory, modal logic, and computer
science. This research text uses combinatorial games to study the
fundamental notion of representations of relation algebras. Games
allow an intuitive and appealing approach to the subject, and
permit substantial advances to be made. The book contains many
new results and proofs not published elsewhere. It should be
invaluable to graduate students and researchers interested in
relation algebras and games.
After an introduction describing the authors' perspective on the
material, the text proper has six parts. The lengthy first part
is devoted to background material, including the formal
definitions of relation algebras, cylindric algebras, their basic
properties, and some connections between them. Examples are given.
Part 1 ends with a short survey of other work beyond the scope of
the book. In part 2, games are introduced, and used to axiomatise
various classes of algebras. Part 3 discusses approximations to
representability, using bases, relation algebra reducts, and
relativised representations. Part 4 presents some constructions
of relation algebras, including Monk algebras and the 'rainbow
construction', and uses them to show that various classes of
representable algebras are non-finitely axiomatisable or even non-elementary.
Part 5 shows that the representability problem for finite
relation algebras is undecidable, and then in contrast proves
some finite base property results. Part 6 contains a condensed
summary of the book, and a list of problems. There are more than
400 exercises.
The book is generally self-contained on relation algebras and on
games, and introductory text is scattered throughout. Some
familiarity with elementary aspects of first-order logic and set
theory is assumed, though many of the definitions are given.
Chapter 2 introduces the necessary universal algebra and model
theory, and more specific model-theoretic ideas are explained as
they arise.
Year 2002
Hardbound
ISBN: 0-444-50932-1
712 pages
(Hardback )
0-19-852673-3
Publication date: January 2003
432 pages, none, 234mm x 156mm
Series: London Mathematical Society Monographs (0199611971)
Description
'Reiner's book gives by far the most extensive and most readable
account available of the classical theory of maximal orders. The
book has been written with great care, and is a pleasure to read.
Unlike many books at such an advanced level, it contains many
interesting exercises, with hints where appropriate. It is
essential to the library of every working algebraist. ' -Bulletin
of the American Mathematical Society
'The book certainly fills a gap in the mathematical literature,
since no modern text-book on maximal orders has been available.
The author has succeeded very well in giving a clear and easily
accessible presentation of the subject. ' -Mathematical Reviews
'This book is unique in its role of providing a self-contained
and easily accessible introduction to the theory of orders and
maximal orders in both the local and the global setting. Readers
of the book will also find it valuable as a guide to many basic
algebraic notions such as localizations, completions, the
Jacobson radical, and Morita theory. The text is well-written and
complete, and well-chosen exercises are offered at the end of
each chapter. The book is well-suited as a text for graduate
courses in representation theory, and for many years has filled a
gap in the literature in the area of orders and maximal orders. '
-Professor Tsit-Yuen Lam, University of California at Berkeley.
This is a reissue of a classic text previously published by the
LMS, aimed at beginning postgraduate students in algebra and
number theory. It gives a well-paced introduction to topics
central to several active areas of mathematical research, and
provides a very helpful background reference to researchers.
Readership: Graduate students and researchers in algebra, number
theory, group theory and ring theory.
Contents
(Hardback )
0-19-852592-3
(Paperback )
0-19-852593-1
Publication date: March 2003
170 pages, none, 234mm x 156mm
Series: Oxford Texts in Applied and Engineering Mathematics
An unique text on the application of Monte-Carlo methods to
partial differential equations
Description
This text is aimed at graduate students in mathematics, physics,
engineering, economics, finance, and the biosciences that are
interested in using Monte-Carlo methods for the resolution of
real-life scenarios.
Readership: Graduate students and workers in mathematics,
physics, engineering, economics, finance, and the biosciences
that are interested in using Monte-Carlo methods of probability
for scenario simulation and modelling
Contents
(Hardback )
0-19-850984-7
Publication date: March 2003
320 pages, 46 line, 234mm x 156mm
Series: Oxford Statistical Science Series
Includes worked examples along with data and code, which provides
the reader with easy implementation of methods
Addresses issues in study design and sample size formulas
Contains solid mathematical theory
Comprehensive, discusses a wide range of real-world problems
Description
This book describes statistical techniques for the design and
evaluation of research studies on medical diagnostic tests,
screening tests, biomarkers and new technologies for
classification in medicine.
Readership: Researchers in biostatistics (medical statistics),
statistics, medical science, public health and clinical research.
Contents
(Hardback )
0-19-852602-4
Publication date: March 2003
First complete edition of Harriot's algebra
Layout and notation kept as close as possible to the original
Extended introduction giving the background to the text and an
explanation of its contents
Illustrations of some of the original manuscripts
Description
Thomas Harriot (c.1560-1621) was an innovative thinker who left
behind several hundred manuscript sheets on navigation,
astronomy, optics, geometry and algebra, most of which have never
been published. This book is the first complete edition of
Harriot's work on the structure and solution of equations, an
important new resource for understanding the development of
algebra in seventeenth-century England.
Readership: Historians of mathematics, students and teachers of
mathematics, general readers with an interest in the history of
mathematics and science
Contents