<p>This book contains 500 problems that range over a wide spectrum of mathematics and of levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained by the book. For many problems, more than one solution is supplied so that students can compare the elegance and efficiency of different mathematical approaches. A special mathematical toolchest summarizes the results and techniques needed by competition-level students. Teachers will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. The problems were first published as a series of problem booklets almost twenty years ago. They have stood the test of time and the demand for them has been steady. Their publication in book form is long overdue.</p>

Five Hundred Mathematical Challenges (Spectrum)

Science & Math

Murray S. Klamkin

Edward J. Barbeau

William O. J. Moser

Mathematics

The Mathematical Association of America

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely­ generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e.' .subgroups of es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute for a more extensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer.

Generators and Relations for Discrete Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

H. S. M. Coxeter

Springer

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Books by William O. J. Moser