Klaus Mainzer

Heinz-Dieter Ebbinghaus

Friedrich Hirzebruch

Max Koecher

Jürgen Neukirch

Reinhold Remmert

Hans Hermes

Alexander Prestel

A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.

Numbers

Thomas Berger

Rainer Jung

This book provides a comprehensive introduction to the theory of elliptic genera due to Ochanine, Landweber, Stong, and others. The theory describes a new cobordism invariant for manifolds in terms of modular forms. The book evolved from notes of a course given at the University of Bonn. After providing some background material elliptic genera are constructed, including the classical genera signature and the index of the Dirac operator as special cases. Various properties of elliptic genera are discussed, especially their behaviour in fibre bundles and rigidity for group actions. For stably almost complex manifolds the theory is extended to elliptic genera of higher level. The text is in most parts self-contained. The results are illustrated by explicit examples and by comparison with well-known theorems. The relevant aspects of the theory of modular forms are derived in a seperate appendix, providing also a useful reference for mathematicians working in this field.

Manifolds and Modular Forms

Shiing-Shen Chern

Wolf Prize in Mathematics

Topological Methods in Algebraic Geometry

335. Sitzung am 5. November 1986 in Düsseldorf (F. Hirzebruch) / 359. Sitzung am 7. Juni 1989 in Düsseldorf (D. Zagier)

Codierungstheorie und ihre Beziehung zu Geometrie und Zahlentheorie. Primzahlen: Theorie und Anwendung

Peter Hilton

Mathematics has a certain mystique, for it is pure and ex- act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in- dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz G|tze,who has dedicated his life to scientific pu- blishing, took up this challenge with his typical enthusi- asm. This Festschrift celebrates his invaluable contribu- tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz G|tze's life-longsupport of mathematics.

Miscellanea Mathematica

Joachim Schwermer

Silke Suter

Proceedings of the Meeting held by the Max-Planck-Institut für Mathematik, Bonn, June 15-22, 1984

Arbeitstagung Bonn 1984

Friedrich Hirzebruch

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