Hans Walser / ETH Zentrum, Switzerland
Translated by Peter Hilton / Jean Pedersen

99 Points of Intersection

Series: Spectrum
Hardback (ISBN-13: 9780883855539 | ISBN-10: 0883855534)

The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some examples of this from basic elementary geometry - the intersection of medians, altitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples - some for figures other than triangles, some where even more than three straight lines pass through a common point. The main part of the book presents 99 points of intersection purely visually, developed in a sequence of figures. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods of proving their existence.

* Translated from the original German
* Readily accessible to students at the undergraduate level but will appeal to anyone interested in geometry
* The examples given have both geometrical interest and an intriguing aesthetic aspect

Contents

Part I. What's It All About?: 1. If three lines meet; 2. Flowers for Fourier; 3. Chebyshev and the Spirits; 4. Sheaves generate curves; Part II. The 99 points of intersection: Part III. The Background: 1. The four classical points of intersection; 2. Proof strategies; 3. Central projection; 4. Ceva’s Theorem; 5. Jacobi’s Theorem; 6. Remarks on selected points of intersection; References.

Gobel, Rudiger / Trlifaj, Jan

Approximations and Endomorphism Algebras of Modules

24 x 17 cm. Approx. 624 pages. Cloth. ISBN 3-11-011079-2

Series: de Gruyter Expositions in Mathematics 41

Subjects: Mathematics / Algebra, Number theory

Language: English

to be published July 2006

This monograph provides a thorough treatment of two important parts of contemporary module theory:

Approximations of modules and their applications, notably to infinite dimensional tilting theory, and
Realizations of algebras as endomorphism algebras of groups and modules. Attention is also given to E-rings and free modules with distinguished submodules.
The monograph starts from basic facts and gradually develops the theory to its present frontiers. It is suitable for graduate students interested in algebra as well as experts in module and representation theory.

Hofmann, Karl H. / Morris, Sidney A.

The Structure of Compact Groups, 2nd. rev. ed.
A Primer for Students - A Handbook for the Expert

24 x 17 cm. Approx. 886 pages. Cloth.
ISBN 3-11-019006-0

Series: de Gruyter Studies in Mathematics 25
Subjects: Mathematics / Algebra, Number theory
Mathematics / Geometry and Topology

Language: English

Dealing with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups.

The first edition of 1998 was well received by reviewers and has been frequently quoted in the areas of instruction and research.

For the present new edition the text has been improved in various sections. New material has been added in order to reflect ongoing research.

Joseph C. Varilly (Universidad de Costa Rica):

An Introduction to Noncommutative Geometry

EMS Series of Lectures in Mathematics

ISBN 978-3-03719-024-1
June 2006, 121 pages, softcover, 17.0 cm x 24.0 cm.

Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras, and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples.

This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the condiditons on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples.

The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.

Contents

S. Akbulut, T. Onder, and R.J. Stern (editors)

Proceedings of Gokova Geometry-Topology Conference 2005

ISBN-10: 1-57146-152-3
ISBN-13: 978-1-57146-152-0
Year Published: 2006
Pages: 212 pages
Binding: Hardcover

Description:

Dedicated to the memory of Raoul Bott, a great mathematician of the 20th Century, this proceedings volume contains articles from both eleventh and twelfth Gokova Conferences, held in Gokova, Turkey.

Contents:

Seven short stories on blowups and resolutions, H. HAUSER
Real algebraic structures, S. AKBULUT
Lefschetz decomposition and the cd-index of fans, K. KARU
Some remarks on G2-structures, R. L. BRYANT
The exceptional holonomy groups and calibrated geometry, D. JOYCE
Ricci-flat deformations of asymptotically cylindrical Calabi?Yau manifolds, A. KOVALEV
Deformations of Special Lagrangian submanifolds: an approach via Fredholm alternative, S. SALUR
Plane curves and contact geometry, L. NG
An open book decomposition compatible with rational contact surgery, B. OZBAGCI
Virtual links and orientations of chord diagrams, O. VIRO