Bloch, E. D.,
Bard College,Department of Mathematics, Annadale-on-Hudson, NY, USA
Proofs and Fundamentals
A First Course in Abstract Mathematics
2000. 432 pages. Hardcover
ISBN 3-7643-4111-4
Due in June 2000
This book is designed as a ftransition e textbook to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality.
Serves as a bridge between computational courses, e.g., calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra, and real analysis. It also includes a key section devoted to the proper writing of proofs and over 400 problem sets, which are mostly proofs rather than example problems. The excellent exposition and choice of topics will make this text valuable for classroom use as well as for the general reader who wants to gain a deeper understanding of the language of mathematics.
The material in Proofs and Fundamentals: A First Course in Abstract Mathematics was chosen because it is needed in the advanced mathematics curriculum, yet it is often not taught in any other course at the level of
calculus or below.
Donald E. Knuth
Stanford University
Selected Papers on Discrete Mathematics
Description
Donald Knuth's influence in computer science ranges from the invention of literate programming to the development of the TeX programming language. One of the foremost figures in the field of mathematical sciences, his papers are widely referenced and stand as milestones of development over a wide range of topics. This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics. It includes a variety of topics in combinatorial mathematics (finite geometries, graph theory, enumeration, partitions, tableaux, matroids, codes); discrete algebra (finite fields, groupoids, closure operators, inequalities, convolutions, Pfaffians); and concrete mathematics (recurrence relations, special numbers and notations, identities, discrete probability). Of particular interest are two fundamental papers in which the evolution of random graphs is studied by means of generating functions.
Chapter Contents
1. Discussion of Mr. Riordan paper bel identities and inverse relationsE 2. Duality in addition chains; 3. Combinatorial analysis and computers; 4. Tables of finite fields; 5. Finite semifields and projective planes; 6. A
class of projective planes; 7. Construction of a random sequence; 8. Oriented subtrees of an arc digraph; 9. Another enumeration of trees; 10. Notes on central groupoids; 11. Permutations, matrices, and generalized
Young tableaux; 12. A note on solid partitions; 13. Subspaces, subsets, and partitions; 14. Enumeration of plane
partitions; 15. Complements and transitive closures; 16. Permutations with nonnegative partial sums; 17. Wheels within wheels; 18. The asymptotic number of geometries; 19. Random matroids; 20. Identities from
partition involutions; 21. Huffman's algorithm via algebra; 22. A permanent inequality; 23. Efficient balanced codes; 24. The power of a prime that divides a generalized binomial coefficient; 25. The first cycles in an evolving graph; 26. The birth of the giant component; 27. Polynomials involving the floor function; 28. The
sandwich theorem; 29. Aztec diamonds, checkerboard graphs, and spanning trees. Binding: Paperback
Bibliographic information:
228 x 152 mm 400pp
ISBN: 1 575 86248 4
Publication: c.December 2000
Binding: Hardback
ISBN: 1 575 86249 2
Publication: c.December 2000
Hans Reiter, late Professor of Mathematics,
and Jan D. Stegeman, Department of Mathematics, University of Utrecht
Classical Harmonic Analysis and Locally Compact Groups
Second Edition
New edition of well-known classic text
Topics relevant for today's research
Includes reference to the older literature as well as the most recent
Thorough coverage suitable for graduate students as well as researchers
Stegeman was a student of Hans Reiter who wrote the first edition
320 pages, 234mm x 156mm
Series: London Mathematical Society Monographs
Hardback, 0-19-851189-2
Publication date: 20 July 2000
Description
Readership: Primary Market: Research Mathematicians in harmonic analysis, functional analysis, theory of Banach algebras Secondary Market: Graduate students, research students taking courses in Fourier analysis, harmonic analysis A revised and expanded second edition of Reiter's classic text, this book deals with various developments in analysis centring around around the fundamental work of Wiener, Carleman, and Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study at certain general function algebras, and then discusses functions defined on locally compact groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. The new edition contains relevent material that was unavailable when the first edition was published.
Contents/contributors
1 Classical harmonic analysis and Wiener's theorem
2 Function algebras and the generalization of Wiener's theorem
3 Locally compact groups and Haar measures
4 Locally compact abelian groups and the foundations of harmonic analysis
5 Functions on locally compact abelian groups
6 Wiener's theorem and locally compact abelian groups
7 The spectrum and its applications
8 Functions on general locally compact groups
A. Additional material
B. Notes and additional references
C. Summary of notations
Smith, K.E., University of Michigan, Ann Arbor, MI, USA
Kahanp, L., University of Jyvaeskylae, Finland
Keklinen, P., University of Joensuu, Finland
Traves, W.N., US Naval Academy, USA
An Invitation to Algebraic Geometry
2000. Approx. 160 pp. 45 figs.
0-387-98980-3
The aim of this book is to describe the underlying principles of algebraic geometry, some of its important
developments in the twentieth century, and some of the problems that occupy its practitioners today. It is
intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
Contents: * Affine Algebraic Varieties * Algebraic Foundations * Projective Varieties * Quasi-projective
Varieties * Classical Constructions * Smoothness * Birational Geometry * Maps to Projective Space * Appendix: Sheaves and Abstract Varieties
Fields: Combinatorial Mathematics/Graph Theory and Discrete Mathematics; Number Theory
Written for: Grad math students, mathematicians
Book category: Graduate Textbook
Publication language: English
I.S. Krasil'shchik
Moscow Institute of Municipal Economy and Diffiety Institute, Moscow, Russia
P.H.M. Kersten
Dept. of Applied Mathematics, University of Twente, Enschede, the Netherlands
Symmetries and Recursion Operators
for Classical and Supersymmetric Differential Equations
MATHEMATICS AND ITS APPLICATIONS Volume 507
This book is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions. It contains an original theory of FrölicherNijenhuis brackets which is the basis for a special cohomological theory naturally related to the equation structure. This theory gives rise to infinitesimal deformations of PDE, recursion operators being a particular case of such deformations.
Efficient computational formulas for constructing recursion operators are deduced and, in combination with the theory of coverings, lead to practical algorithms of computations. Using these techniques, previously unknown recursion operators (together with the corresponding infinite series of symmetries) are constructed. In particular, complete integrability of some superequations of mathematical physics (Kortewegde Vries, nonlinear Schrödinger equations, etc.) is proved.
Audience: The book will be of interest to mathematicians and physicists specializing in geometry of differential equations, integrable systems and related topics.
Contents
Preface. 1. Classical symmetries. 2. Higher symmetries and conservation laws. 3. Nonlocal theory. 4. Brackets. 5. Deformations and recursion operators. 6. Super and graded theories. 7. Deformations of supersymmetric
equations. 8. Symbolic computations in differential geometry. Bibliography. Index.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6315-9
May 2000, 400 pp.
Walsh, J.L.
Rivlin, T.J., Chappaqua,
NY, USA Saff, E.B., University of South Florida, Tampa, FL, USA (Eds.)
Walsh, J.L. : Selected Papers
2000. XLIV, 682 pp.
0-387-98782-7
This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".
Contents: Zeros and Critical Points.- Walsh Functions.- Qualitative Approximation.- Conformal Mapping.- Polynomial Approximation Theory.- Rational Approximation.- Spline Functions. Fields: Real Functions,Measure and Integration; Numerical Analysis and Computation; Complex Analysis
Written for: Mathematicians, math graduate students
Book category: Works of a Particular Author
Publication language: English