## New AMS-Distributed Publications

Am e r i c A n mAt h e m At i c A l So c i e t y

of finite dimensional algebras and singularities; M. Reineke, Moduli of representations of quivers; A. Skowron´ski and K. Yamagata, Selfinjective algebras of quasitilted type; List of contributors.

EMS Series of Congress Reports, Volume 1

September 2008, 722 pages, Hardcover, ISBN: 978-3-03719-062-3, 2000 Mathematics Subject Classification: 16-02, 16Gxx, 03Cxx, 05Exx, 13Axx, 13Cxx, 13Hxx, 14Lxx, 14Mxx, 16Dxx, 16Exx, 16Sxx, 17Bxx, 18Exx, 18Gxx, 20Cxx, 20Gxx, 20Jxx, 32Sxx, 55Pxx, 57Mxx, 81Rxx, AMS members US$110, List US$138, Order code EMSSCR/1

Discrete Mathematics and Combinatorics

How much math can you cover in five minutes?

Quite a bit, if you have a good guide.

From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis

Christian Lubich, University of Tübingen, Germany

# Five-Minute Mathematics

## Ehrhard Behrends

Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research e orts in numerical analysis in a number of application areas: high-dimensional partial di erential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations.

This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrödinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Contents: Quantum vs. classical dynamics; Reduced models via variational approximation; Numerical methods for the time-dependent Schrödinger equation; Numerical methods for non-linear reduced models; Semi-classical dynamics using Hagedorn wave packets; Bibliography.

## Freie Universität Berlin, Germany

This collection of one hundred short essays offers a tour through contemporary and everyday mathematics that is both entertaining and enlightening.

Translated by David Kramer

2008; 380 pp; softcover; ISBN: 978-0-8218-4348-2; List Price: US$35; Member Price: US$28; Order Code:

MBK/53

Zurich Lectures in Advanced Mathematics, Volume 12

September 2008, 156 pages, Softcover, ISBN: 978-3-03719-067-8, 2000 Mathematics Subject Classification: 65M70, 65Z05, 81-08, AMS members US$31, List US$39, Order code EMSZLEC/12

1-800-321-4AMS (4267), in the U. S. and Canada, or 1-401-455-4000 (worldwide); fax:1-401-455-4046; email: cust-serv@ams.org.

www.ams.org/bookstore

### January 2009

### Notices of the AMS

81