When Less is More: Visualizing Basic Inequalities (Dolciani Mathematical Expositions) - Hardcover

Alsina, Claudi; Nelsen, Roger

Hardcover

ISBN 10: 0883853426 ISBN 13: 9780883853429

Publisher: The Mathematical Association of America, 2009

Synopsis

Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they don't possess the richness and variety that one finds with inequalities. The objective of this book is to illustrate how use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and we would like to convince you that the same is true when working with inequalities. We show how to produce figures in a systematic way for the illustration of inequalities; and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument can not only show two things unequal, but also help the observer see just how unequal they are.

About this title

Book Description

An introduction to basic inequalities in mathematics (including numbers, functions and geometry) motivated and illustrated by drawings that make it possible to 'see' the results in an elegant manner. Applications of the inequalities, historical details, and exercises for the reader (with solutions) are also included.

About the Author

Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. His post-doctoral studies were at the University of Massachusetts, Amherst. He is Professor of Mathematics at the Technical University of Catalonia and has developed a wide range of international activities, research papers, publications and hundreds of lectures on mathematics and mathematics education. His latest books include Associative Functions: Triangular Norms and Copulas with M. J. Frank and B. Schweizer, WSP, 2006; Math Made Visual. Creating Images for Understanding Mathematics with Roger B. Nelsen, MAA, 2006; Vitaminas Matemáticas and El Club de la Hipotenusa, Ariel, 2008.

Edition details

• Publisher: The Mathematical Association of America
• Publication date: 2009
• ISBN 10: 0883853426
• ISBN 13: 9780883853429
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 199