Geometric Problems on Maxima and Minima

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.
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.

List of contents

From the contents:
Preface
- Methods for Solving Geometric Problems on Maxima and Minima
- Selected Types of Geometric Problems on Maxima and Minima
- Miscellaneous Problems
- Hints and Solutions
- Glossary

Summary

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.

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.

Additional text

From the reviews:

"As an avid problem solver with a strong interest in inequalities…I am delighted to supplement my repertoire with the techniques illustrated in this volume…. The book contains hundreds of problems, classical and modern, all with hints or complete solutions…. Over the years, Titu Andreescu and various collaborators have used their experiences as teachers and as Olympiad coaches to produce a series of excellent problem-solving manuals…. The present volume continues that tradition and should appeal to a wide audience ranging from advanced high school students to professional mathematicians."   –MAA

"The whole exposition of the book is kept at a sufficiently elementary level, so that it can be understood by high-school students. Apart from trying to be comprehensive in terms of types of problems and techniques for their solutions, the authors have tried to offer various different levels of difficulty making the book possible to use by people with different interests in mathematics, different abilities, and of different age groups." —V. Oproiu, Analele Stiintifice

"This excellent book, Geometric problems on maxima and minima, deals not only with these famous problems, but well over a hundred other such problems, many of which were completely novel and new to me. ... This book will certainly greatly appeal to highschool students, mathematics teachers, professional mathematicians, and puzzle enthusiasts. I would regard it as absolutely essential reading for students preparing for mathematics competitions around the world." (Michael de Villiers, The Mathematical Gazette, Vol. 92 (525), 2008)

Report

From the reviews:
"As an avid problem solver with a strong interest in inequalities...I am delighted to supplement my repertoire with the techniques illustrated in this volume.... The book contains hundreds of problems, classical and modern, all with hints or complete solutions.... Over the years, Titu Andreescu and various collaborators have used their experiences as teachers and as Olympiad coaches to produce a series of excellent problem-solving manuals.... The present volume continues that tradition and should appeal to a wide audience ranging from advanced high school students to professional mathematicians."   -MAA
"The whole exposition of the book is kept at a sufficiently elementary level, so that it can be understood by high-school students. Apart from trying to be comprehensive in terms of types of problems and techniques for their solutions, the authors have tried to offer various different levels of difficulty making the book possible to use by people with different interests in mathematics, different abilities, and of different age groups." -V. Oproiu, Analele Stiintifice
"This excellent book, Geometric problems on maxima and minima, deals not only with these famous problems, but well over a hundred other such problems, many of which were completely novel and new to me. ... This book will certainly greatly appeal to highschool students, mathematics teachers, professional mathematicians, and puzzle enthusiasts. I would regard it as absolutely essential reading for students preparing for mathematics competitions around the world." (Michael de Villiers, The Mathematical Gazette, Vol. 92 (525), 2008)

Product details

• Authors: Tit Andreescu, Titu Andreescu, Ole Mushkarov, Oleg Mushkarov, Luchezar Stoyanov
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 05.01.2006
• EAN: 9780817635176
• ISBN: 978-0-8176-3517-6
• No. of pages: 264
• Dimensions: 157 mm x 239 mm x 14 mm
• Weight: 450 g
• Illustrations: X, 264 p. 262 illus.
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Analysis, Algebra, A, Optimization, geometry, Combinatorics, Mathematics and Statistics, Topology, Discrete Mathematics, Combinatorics & graph theory, Calculus & mathematical analysis, Mathematical optimization, Analysis (Mathematics), Mathematical analysis