Product Description
by Titu Andreescu (Author), Oleg Mushkarov (Author), Luchezar Stoyanov (Author)
This carefully developed problem book takes a unique, intuitive approach to extreme value problems, treating them within the framework of Euclidean geometry. Included is a comprehensive selection of maxima and minima problems, from classical Greek constructions to modern, recently solved problems; detailed, step-by-step solutions to many of the exercises are provided. The reader is exposed to algebra, analysis, combinatorics, and topology, and throughout the text, emphasis is placed on creative techniques for problem solving. Reflecting the authors' experience as professors and Olympiad coaches, this volume is ideal for use at the junior and senior undergraduate level, as well as for enrichment programs and Olympiad training for advanced high school students. The book will also appeal to graduate students, professional mathematicians, and puzzle enthusiasts alike.
Back Jacket
Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme-value problems, examples, and solutions primarily through Euclidean geometry.
Key features and topics:
* Comprehensive selection of problems, including Greek geometry and optics, Newtonian mechanics, isoperimetric problems, and recently solved problems such as Malfatti's problem
* Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning
* Presentation and application of classical inequalities, including Cauchy--Schwarz and Minkowski's Inequality; basic results in calculus, such as the Intermediate Value Theorem; and emphasis on simple but useful geometric concepts, including transformations, convexity, and symmetry
* Clear solutions to the problems, often accompanied by figures
* Hundreds of exercises of varying difficulty, from straightforward to Olympiad-caliber
Written by a team of established mathematicians and professors, this work draws on the authors' experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book's breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzle enthusiasts.
