Switzer, R.M., Georg-August-Universitat Gottingen, Germany

Algebraic Topology

Reprint of the 1st ed. Berlin Heidelberg New York 1975. 2002. XIII, 526 pp. Softcover
3-540-42750-3

From the reviews:
"The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. ... The author has sought to make his treatment complete and he has succeeded. The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. ... This book is, all in all, a very admirable work and a valuable addition to the literature...
(S.Y. Husseini in Mathematical Reviews, 1976)

Keywords: Algebraic topology, homology theories, cohomology theories, momotopy theory ,homotopy groups, fibre bundles, spectral sequences, operations MSC-Classification ( 2001 ): 5502, 57A55, 57A65, 57D75

"This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book. ... (It is) suitable for specialists, or for those who already know what algebraic topology is for, and want a guide to the principal methods of stable homotopy theory."
R. Brown in Bulletin of the London Mathematical Society, 1980

Series: Classics in Mathematics.

Ern, A., CERMICS, ENPC, Marne la Vallee, France;
Guermond, J.-L., LIMSI, CNRS, Orsay, France

Elements finis: theorie, applications, mise en oeuvre

2002. X, 430 p. Broche
3-540-42615-9
Publication language: French

Ces notes de cours (Ecole Nationale des Ponts et Chaussees, DEA de Mecanique de Paris VI) presentent la methode des elements finis dans un cadre mathematique rigoureux. En accordant une place fondamentale aux conditions inf-sup, elles s'affranchissent du cadre reducteur Lax-Milgram/Galerkin standard. Elles couvrent un spectre d'applications relativement large et apportent de nombreuses precisions sur la mise en oeuvre numerique. Trois plans de lecture sont proposes: le premier concu pour un lecteur interesse par les aspects mathematiques, le deuxieme s adressant aux ingenieurs et le troisieme limite aux aspects elementaires. Les prerequis mathematiques, de niveau 2eme cycle universitaire, sont rappeles dans deux annexes.

Keywords: calcul scientifique, mathematiques appliquees, mecanique et science d ' ingenieur Mathematics Subject Classification 2000 : 65N30, 35A35, 65M60, 65-01, 76M10, 74S05, 80M10, 65N50, 65F10, 68U20 Computing Reviews : G . 1 . 8, G . 1 . 1, G . 1 . 3, I . 6 . M . A . 1

Contents: Introduction.- Partie I. Fondements. Interpolation par elements finis. Problemes bien poses.- Partie II. Applications. Problemes coercifs. Problemes mixtes. Problemes du premier ordre. Problemes d'evolution en temps.- Partie III. Mise en oeuvre. Maillages. Quadratures numeriques, assemblage et stockage. Algebre lineaire. Estimation d'erreur a posteriori.- Annexes: A. Conventions de notation.- B. Espaces de Banach et de Hilbert.- Elements d'analyse fonctionnelle.

Series: Mathematiques & Applications. VOL. 36

Dietrich, B., IBM TJ Watson Research Center, Yorktown Heights, NY, USA;
Vohra, R.V., Northwestern University, Evanston, IL, USA;
Brick, P., Institute for Math. and its Applications, Minneapolis, MN, USA (Eds.)

Mathematics of the Internet
E-Auction and Markets

2002. XI, 161 pp. 18 figs. Hardcover
0-387-95359-0

The use of the internet for commerce has spawned a variety of auctions, marketplaces, and exchanges for trading everything from bandwidth to books. Mechanisms for bidding agents, dynamic pricing, and combinatorial bids are being implemented in support of internet-based auctions, giving rise to new versions of optimization and resource allocation models. This volume, a collection of papers from an IMA "Hot Topics" workshop in internet auctions, includes descriptions of real and proposed auctions, complete with mathematical model formulations, theoretical results, solution approaches, and computational studies.
This volume also provides a mathematical programming perspective on open questions in auction theory, and provides a glimpse of the growing area of dynamic pricing.

Contents: Modeling opportunities in auctions.- A column generation approach for combinatorial auctions.- Price negotiations for procurement of direct inputs.- An iterative online auction for airline seats.- An integer programming formulation of the bid evaluation problem for coordinated tasks.- Linear programming and Vickrey auctions.- Auctioning telecommunications bandwidth with guaranteed quality of service.- Pricebot dynamics.- Threshold pricing for selling network capacity through forward contracts.- List of workshop participants.

Series: The IMA Volumes in Mathematics and its Applications. VOL. 127

Emery, M., Universite Louis Pasteur, Strasbourg, France;
Yor, M., Universite de Paris VI, Paris, France (Eds.)

Seminaire de Probabilites 1967-1980
A Selection in Martingale Theory

2002. IX, 553 p. Broche
3-540-42813-5
Publication language: French, English

Twenty-five articles have been selected from the first 14 volumes of the "Seminaire de Probabilites", all out of print, for their historical and/or mathematical interest. Among the many articles devoted to Martingale theory in the early volumes of the Seminaire, we have chosen to reprint those that are particularly significant from a historical point of view, as well as those that can still be useful today. They are reprinted here verbatim, with a short retrospective comment, for the benefit of researchers in the theory of stochastic processes, in mathematical finance, or in history of mathematics.

Keywords: General theory of processes, stochastic calculus, Martingale, history of probability theory Mathematics Subject Classifications ( 2000 ): 01A60, 01A75 ,60G07, 60G42, 60G48, 60H05, 60H10

Series: Lecture Notes in Mathematics. VOL. 1771

Burstall, F.E., University of Bath, UK/ Ferus, D., Technische Universitat Berlin, Germany;
Leschke, K., Technische Universitat Berlin, Germany/ Pedit, F., University of Massachusetts, Amherst, MA, USA/ Pinkall, U., Technische Universitat Berlin, Germany

Conformal Geometry of Surfaces in S4 and Quaternions

2002. VIII, 89 pp. Softcover
3-540-43008-3

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Backlund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Keywords: Conformal surface theory, Willmore functional, Twistor projection, Backlund tranform, Darboux transform Mathematics Subject Classification ( 2000 ): 53C42, 53A30

Contents: Quaternions.- Linear algebra over the quaternions.- Projective spaces.- Vector bundles.- The mean curvature sphere.- Willmore Surfaces.- Metric and affine conformal geometry.- Twistor projections.- Backlund transforms of Willmore surfaces.- Willmore surfaces in S3.- Spherical Willmore surfaces in HP1.- Darboux transforms.- Appendix: The bundle L. Holomorphicity and the Ejiri theorem.

Series: Lecture Notes in Mathematics. VOL. 1772

Arad, Z., Netanya Academic College, Netanya, Israel;
Muzychuk, M., Netanya Academic College, Netanya, Israel (Eds.)

Standard Integral Table Algebras Generated
by a Non-real Element of Small Degree

2002. IX, 126 pp. Softcover
3-540-42851-8

This book is addressed to the researchers working in the theory of table algebras and association schemes. This area of algebraic combinatorics has been rapidly developed during the last decade. The volume contains further developments in the theory of table algebras. It collects several papers which deal with a classification problem for standard integral table algebras (SITA). More precisely, we consider SITA with a faithful non-real element of small degree. It turns out that such SITA with some extra conditions may be classified. This leads to new infinite series of SITA which has interesting properties. The last section of the book uses a part of obtained results in the classification of association schemes. This volume summarizes the research which was done at Bar-Ilan University in the academic year 1998/99.

Contents:
1. Introduction (Z.Arad, M. Muzychuk):
1.1 Main Definitions
1.2 Basic examples
1.3 Basic properties
1.4 Basic constructions
2. ITA with a Faithful Nonreal Element of Degree 4
(Z.Arad, M.Muzychuk, H. Arisha, E. Fishman)
2.1 Known examples
2.2 Proof of the main results
3. SITA with a Faithful Nonreal Element of Degree 5
(Z. Arad, F. Bunger, E. Fishman, M. Muzuychuk)
3.1 Introduction
3.2 General facts and known results
3.3 Degree 5
3.4 Case 3
3.5 Case 5
4. SITA with a Faithful Real Element of Degree 5 and Width 3 (F. Bunger)
4.1 Introduction
4.2 Case 1
4.3 Case 2

5. The Enumeration of Primitive Commutative Association Schemes (M. Hirasaka)
5.1 Introduction
5.2 The case of valency 1 or 2
5.3 The case of valency 3
5.4 The case of valency 4
References
Index

Series: Lecture Notes in Mathematics. VOL. 1773