Maxima and Minima Without Calculus (Dolciani Mathematical Expositions)

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		Maxima and Minima Without Calculus (Dolciani Mathematical Expositions)
		Maxima and Minima Without Calculus (Dolciani Mathematical Expositions)

基本信息·出版社：Mathematical Association of America (MAA)
·页码：303 页
·出版日期：1981年12月
·ISBN：088385306X
·International Standard Book Number：088385306X
·条形码：9780883853061
·EAN：9780883853061
·装帧：精装
·正文语种：英语
·丛书名：Dolciani Mathematical Expositions
·分册名：6

内容简介 The purpose of the this book is to put together in one place the basic elementary techniques for solving problems in maxima and minima other than the methods of calculus and linear programming. The emphasis is not on individual problems, but on methods that solve large classes of problems. These methods are organized in terms of the mathematical ideas used, whether from algebra, geometry, the theory of inequalities, and so on. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.
作者简介 Ivan Niven published over sixty papers, some with well-known co-authors such as Samuel Eilenberg, Paul Erdos (6 times), Nathan J. Fine, R. D. James, and H. S. Zuckerman (7 times). His areas of expertise were number theory, especially the areas of diophantine approximation and questions of irrationality and transcendance of numbers, and combinatorics. He wrote seven books, including the Carus Monograph "Irrational Numbers and "Numbers: Rational and Irrational" and "Mathematics of Choice/How to Count without Counting," and "Maxima and Minima Without Calculus," for the MAA. In 1989 he was presented the MAA's highest award for achievement, the Award for Distinguished Service to Mathematics (now called the Yueh-Gin Gung and Charles Y. Hu Award for Distinguished Service to Mathematics). Ivan Niven died in May 1999 in Eugene, Oregon
媒体推荐 A book superb in its exposition and teeming with a variety of elegant mathematical results. -- G. D. Chakerian, Mathematical Reviews

A book superb in its exposition and teeming with a variety of elegant mathematical results. --G. D. Chakerian, Mathematical Reviews

An endless source of fascinating problems with elegant and easily understandable solutions by the methods given in the text. -- John Abram, The Mathematical Gazette

An endless source of fascinating problems with elegant and easily understandable solutions by the methods given in the text. --John Abram, The Mathematical Gazette

This is a book which deserves to be read very widely. -- P.T. Johnstone, Times High Education Supplement, London

This is a book which deserves to be read very widely. --P.T. Johnstone, Times High Education Supplement, London
目录
Preface; 1. Background material; 2. Simple algebraic results; 3. Elementary geometric questions; 4. Isoperimetric results; 5. Basic trigonometric inequalities; 6. Polygons inscribed and circumscribed; 7. Ellipses; 8. The bees and their hexagons; 9. Further geometric results; 10. Applied and miscellaneous problems; 11. Euclidean three-space; 12. Isoperimetric results not assuming existence; Postscript on calculus; Solutions of problems; References; Index.
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