Description
One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894 the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. The success of high school competitions led the Mathematical Society to found a college level contest, named after Mikls Schweitzer. The problems of the Schweitzer Contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in the contests between 1962 and 1991 which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, topology, to set theory. The second part contains the solutions. The Schweitzer competition is one of the most unique in the world. The experience shows that this competition helps to identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research level problems might be of interest for more mature mathematicians and historians of mathematics as well. 1. Problems of the Contests.- 2. Results of the Contests.- 3. Solutions to the Problems.- 3.1 Algebra (Jzsef Pelikn).- 3.2 Combinatorics (Ervin Gy?ri).- 3.3 Theory of Functions (Jnos Bognr and Vilmos Totik).- 3.4 Geometry (Balzs Csiks).- 3.5 Measure Theory (Jnos Bognr).- 3.6 Number Theory (Imre Z. Ruzsa).- 3.7 Operators (Jnos Bognr).- 3.8 Probability Theory (Gabriella Szp).- 3.9 Sequences and Series (Jen? Tr?csik).- 3.10 Topology (Gbor Moussong).- 3.11 Set Theory (Pter Komjth).- Index of Names.
