Topics in algebra and analysis : preparing for the Mathematical Olympiad /

Bulajich Manfrino and Delgado (both, Univ. Autónoma del Estado de Morelos, Mexico), and Ortega (Univ. Nacional Autónoma de Mexico) have put together a very enjoyable collection of high school mathematics competition problems in algebra and analysis, the level of which ranges from local contests to the International Mathematical Olympiads. This means that there is no prerequisite that goes beyond high school mathematics, but some of the problems are still extremely challenging because of the deep thought or clever tricks that are needed for their solution. The topics are, not surprisingly, polynomials, sums, progressions, sequences, functional equations, complex numbers, and mathematical induction. The last section contains problems that bridge several categories; they are typically the most difficult to solve. All problems come with full solutions. The book is extremely useful for high school students preparing for competitions. For everyone above that level, it is a very welcome collection of problems that have elementary, but often very difficult, solutions. Strongly recommended. Essential for libraries used by high school students. Summing Up: Highly recommended. Lower-division undergraduates through researchers/faculty. --Miklos Bona, University of Florida