Required text: Proofs from the Book, by M. Aigner and G. Ziegler, to be published in August 1998 by Springer-Verlag.

Comment about required text: The title comes from the idea of Paul Erdös that God has The Book containing the best (i.e., most elegant or most instructive) proofs of all theorems, and that working mathematicians are only occasionally lucky or skillful enough to discover one of these proofs. The Aigner-Ziegler book is devoted to proofs that were thought by Erdös or the authors to meet this high standard. The topics covered are Geometry, Number Theory, Combinatorics, and Graph Theory. We'll concentrate on the material from Discrete Geometry, on parts of the other topics that have interesting applications in Discrete Geometry, and on supplementary material from research papers and from the book mentioned below.

Comment about supplementary text: Recommended but not required is Old and New Unsolved Problems in Plane Geometry and Number Theory, V. Klee and S. Wagon, Math. Assoc. Amer., 1992.

Comment about the level of both books: From preface of Aigner- Ziegler book: "A little linear algebra, some basic analysis and number theory, and a healthy dollop of elementary concepts and reasonings from discrete mathematics should be sufficient to understand and enjoy everything in this book."

Conduct of course: There will be no examinations, but a number of exercises will be assigned. In addition to the emphasis on elegant or revealing proofs, there will be a special focus on the statement of related unsolved problems, explaining their background and partial results, why they are interesting, etc. Each student will be expected to keep a notebook containing solutions of exercises, details of any attacks on unsolved problems, etc., and these will be turned in for grading at the end of the quarter.

Previewing of required and recommended text: The preface and table of contents of the Aigner-Ziegler book will be posted on the door to my office (PDL C-551). The Klee-Wagon book is on reserve in the Math Research library.