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The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary
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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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