Herman J., Kucera R., Simsa J. Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory

Springer, 2000. — 357 pages.This book presents methods of solving problems in three areas of classical elementary mathematics: Equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises, which range from routine to rather challenging problems. There are approximately 330 examples and 760 exercises.An excellent source of problems, the book would make a good supplement to many lower-division undergraduate courses and would assist in preparing students for mathematics competitions. Highly recommended for virtually any mathematics course involving problem solving.