Winning solutions / Edward Lozansky, Cecil Rousseau

This preparation book for high school competitors in national and international Olympiads covers techniques and background in key nongeometric areas. The first chapter, “Numbers”, treats induction, congruence, complex numbers, progressions and diophantine equations. The second, “Algebra”, includes material on polynomials and inequalities. The final chapter, “Combinatorics”, handles recurrences, generating functions, combinatorial avaraging and extremal problems along with standard elementary topics. Each section has illustrative worked examples as well as exercises, many from Olympiad and Putnam papers, for which an appendix contains hints and answers. Each chapter concludes with ten “Olympiad problems”. This is a valuable resource for capable secondary students and their teachers. (Zentralblatt)