Series: Universitext
2005, VIII, 189 p. 65 illus., 15 in colour., Softcover
ISBN: 3-540-22908-6
About this textbook
This book presents a survey of the field of dynamical systems and
its significance for research in complex systems and other
fields, based on a careful analysis of specific important
examples. It also explains the fundamental underlying
mathematical concepts, with a particular focus on invariants of
dynamical systems, including a systematic treatment of Morse-Conley
theory. Entropy and related concepts in the topological, metric,
measure theoretic and smooth settings and some connections with
information theory are discussed, and cellular automata and
random Boolean networks are presented as specific examples.
Table of contents
Series: Statistics and Computing
2005, XXII, 444 p. 31 illus., Softcover
ISBN: 0-387-26109-5
About this book
This book explains the basics of S-PLUS in a clear style at a
level suitable for people with little computing or statistical
knowledge. Unlike the manuals, it is not comprehensive, but
instead introduces the most important ideas of S-PLUS and R, its
companion in implementing the S language.
The authors take the reader on a journey into the world of
interactive computing, data exploration, and statistical analysis.
They explain how to approach data sets and teach the
corresponding S-PLUS commands.
A collection of exercises summarizes the main ideas of each
chapter. The exercises are accompanied by solutions that are
worked out in full detail, and the code is ready to use and to be
modified.
The volume is rounded off with practical hints on how efficient
work can be performed in S-PLUS, for example by pointing out how
to set up a good working environment and how to integrate S-PLUS
with office products.
The book is well suited for self-study and as a textbook. It
serves as an introduction to S-PLUS as well as R. A separate
chapter points out the major differences between R and S-PLUS.
Over the last editions, the book has been updated to cover
important changes like the inclusion of S Language Version 4,
Trellis graphics, a graphical user interface, and many useful
tips and tricks. The fourth edition is based on S-PLUS Version 7.0
for Windows and UNIX and has been updated and revised accordingly.
Table of contents
Series: Encyclopaedia of Mathematical Sciences, Vol. 11
1st ed. 1990. 3rd printing, 2005, IV, 258 p., Hardcover
ISBN: 3-540-25177-4
About this book
Wholeheartedly recommended to every student and user of
mathematics, this is an extremely original and highly informative
essay on algebra and its place in modern mathematics and science.
From the fields studied in every university maths course, through
Lie groups to cohomology and category theory, the author shows
how the origins of each concept can be related to attempts to
model phenomena in physics or in other branches of mathematics.
Required reading for mathematicians, from beginners to experts.
Table of contents
Preface.- 1 What is Algebra?- 2 Fields.- 3 Commutative Rings.- 4
Homomorphisms and Ideals.- 5 Modules.- 6 Algebraic Aspects of
Dimension.- 7 The Algebraic View of Infinitesimal Notions.- 8
Noncommutative Rings.- 9 Modules and Noncommutative Rings.- 10
Semisimple Modules and Rings.- 11 Division Algebras of Finite
Rank.- 12 The Notion of a Group.- 13 Examples of Groups: Finite
Groups.- 14 Examples of Groups: Infinite Discrete Groups.- 15
Examples of Groups : Lie Groups and Algebraic Groups.- 16 General
Results of Group Theory.- 17 Group Representations.- 18 Some
Applications of Groups.- 19 Lie Algebras and Nonassociative
Algebra.- 20 Categories.- 21 Homological Algebra.- 22 K-Theory.-
Comments on the Literature.- References.- Indices
Description
The book addresses many important new developments in the field.
All the topics covered are of great interest to the readers
because such inequalities have become a major tool in the
analysis of various branches of mathematics.
Audience
University libraries, research institutes, engineering and
technological institutes, mathematical economics insitutes,
computer science institutes and physical science institutes
Contents
Preface.
Introduction.
1. Inequalities Involving Convex Functions.
2. Inequalities Related to Hardy?s Inequality.
3. Opial-Type Inequalities.
4. Poincare- and Sobolev-Type Inequalities.
5. Levin- and Lyapunov-type Inequalities.
Reference.
Index.
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-51795-2, 484 pages, publication date: 2005
Cloth | 2005 | ISBN: 0-691-12279-2
536 pp. | 6 x 9 | 39 line illus.
Table of Contents
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject.
In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics.
The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.
Eric Schechter, Associate Professor of Mathematics at Vanderbilt University, is the author of Handbook of Analysis and Its Foundations.
Endorsements:
"Offering a rich combination and breadth of material, this book is practically an encyclopedia of schools of logic; it is a convenient reference, lucidly describing complex ideas in various schools of logic that are traditionally not treated in a single book. The writing is fluent, clear, and detailed; the exposition is solid and successfully clarifies topics that are usually difficult for beginners to understand."--Iraj Kalantari, Western Illinois University
"This is a fine introduction to relevance and intuitionist logics and the basic notions of metalogic, with classical logic introduced as a necessary contrast. It will be a valuable addition to the literature, especially as some of the topics covered have long been the preserve of specialists. Though I have worked in philosophical logic for many years, it taught me things I should have known long ago."--Bernard Linsky, University of Alberta, author of Russell's Metaphysical Logic
"This is a very good introduction to a broad array of logics. Particularly interesting is the treatment of algebraic and topological semantics, which are only found in more advanced treatments of the same topics. The author does a great job motivating, presenting, and addressing the different formalisms."--G. Aldo Antonelli, University of California, Irvine; Editor, Journal of Philosophical Logic