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    STUDIA MATHEMATICA - Issue no. 2 / 2005  
  Article:   BOOK REVIEWS.

Authors:  .
  Abstract:  This excellent book deals with some important topics of elementary mathematics necessarily in the process of training students for various contests and olympiads. One of the main intention of the authors is to build a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate mathematics. Mathematical Olympiad Treasures re- flects the depth of experience of two seasoned professors and coaches from the USA and Romanian Olympiad teams. The book is organized into three chapters each of them containing eight sections. Each sections contains some suggestive completely solved problems and some proposed problems which are solved in the second part of the book. In what follows we will briefly present each of them. Chapter 1 is entitled Algebra and contains some basic notions and results concerning the following topics: An algebraic identity, Cauchy-Schwartz revisited, Easy ways through absolute values, Parameters, Take the conjugate, Inequalities with convex functions, Induction at work, Roots and coecients. Chapter 2, Geometry and Trigonometry, contains eight sections dealing with Geometric inequalities, An interesting locus, Cyclic quads, Equiangular polygons, More on equilateral triangles, The carpets theorem, Quadrilaterals with an inscribed circle, Dr. Trig learns complex numbers.  
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