Convexity

Hardcover | February 1, 1993

byRoger Webster

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Convexity provides a wide-ranging introduction for final year undergraduates and graduate students. Convex sets and functions are studied in the Euclidean space IRn, thus allowing an exposition demanding only an elementary knowledge of analysis and linear algebra, and enabling concepts to bemotivated through simple geometric examples. The fundemental ideas of convexity are natural and appealing, and does not have to travel far along its path, before meeting significant, aesthetically pleasing results. It develops geometric intuition, and is a showcase for displaying interconnections amongst different parts of mathematics, inaddition to have ties with economics, science and engineering. Despite being an active research field, it abounds in unsolved problems having an instant intuitive appeal. One distinctive feature of the book is the diverse applications that it highlights: number theory, geometric extremum problems, combinatorial geometry, linear programming, game theory, polytopes, bodies of constant width, the gamma function, minimax approximation, and linear, classical and matrixinequalities. Several topics make their first appearance in a general introduction to convexity, while a few have not appeared outside research journals. The account has a self-contained treatment of volume, thus permitting a rigorous discussion of mixed volumes, is operimetry and Brunn-Minkowskitheory. Full solutions to most of the 241 exercises are provided and detailed suggestions for further reading are given.

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Convexity provides a wide-ranging introduction for final year undergraduates and graduate students. Convex sets and functions are studied in the Euclidean space IRn, thus allowing an exposition demanding only an elementary knowledge of analysis and linear algebra, and enabling concepts to bemotivated through simple geometric examples. ...

Roger Webster is at Sheffield University.

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Format:HardcoverDimensions:462 pages, 9.21 × 6.14 × 1.14 inPublished:February 1, 1993Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198531478

ISBN - 13:9780198531470

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Table of Contents

Inroduction1. The Euclidean space2. Convex sets3. Convex polytopes4. Linear programming5. Convex functions6. Mixed volumes and extremum problems7. Selected topics8. Solutions to exercises9. Notes on further readingBibliographyIndex of symbols and notation

Editorial Reviews

`This is a well-written introduction to convexity and to a variety of its applications. It is written in a clear style, reader-friendly, and with great care. This book, which requires only elementary prerequisites and provides many exercises, is well suited as a text for an introductory courseon convexity and selected applications.'Zentrallblatt for Mathematik, Band 835/96.