Notices of the American Mathematical Society

... the progress of physics will to a large extent depend on the progress of nonlinear mathe­ matics, of methods to solve nonlinear equations... and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe­ maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction­ diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems. Cover Contents Union Mathematique lnternationale Mathematics Program Review: Problems and Opportunities, James G. Glimm Primes, Codes and the National Security Agency, Susan Landau Queries Letters to the Editor News and Announcements NSF News & Reports Future Meetings of the Society Denver, January 3-9 Mathematical Sciences Employment Register Norman, March 18-19 New York City, April 14-15 Summer Research Institute AMS-SIAM Summer Seminar AMS Summer Research Conferences Invited Speakers and Special Sessions Special Meetings New AMS Publications Miscellaneous Personal Items Deaths Visiting Mathematicians (Supplement) AMS Reports and Communications Recent Appointments Reports of Past Meetings: Toronto Advertisements Registration Form (New York City)