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Geometry and convexity : a study in mathematical methods

Author: Paul J Kelly; Max L Weiss
Publisher: New York : John Wiley & Sons, ©1979.
Series: Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Convex body theory offers important applications in probability and statistics, combinatorial mathematics, and optimization theory. Although this text's setting and central issues are geometric in nature, it stresses the interplay of concepts and methods from topology, analysis, and linear and affine algebra. From motivation to definition, the authors present concrete examples and theorems that identify convex  Read more...
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Additional Physical Format: Online version:
Kelly, Paul Joseph.
Geometry and convexity.
New York : Wiley, ©1979
(OCoLC)610217337
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Paul J Kelly; Max L Weiss
ISBN: 047104637X 9780471046370
OCLC Number: 4497192
Notes: "A Wiley-Interscience publication."
Description: x, 261 pages : illustrations ; 24 cm.
Contents: Introductory metric topology and Euclidean n-space --
The structure of Euclidean n-space --
Dimension and basic structure of convex bodies and surfaces --
The general theory of convex bodies --
Convex spans and independence, related classical theorems --
Linear combinations of sets and the Hausdorff metric.
Series Title: Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Responsibility: Paul J. Kelly, Max L. Weiss.

Abstract:

Convex body theory offers important applications in probability and statistics, combinatorial mathematics, and optimization theory. Although this text's setting and central issues are geometric in nature, it stresses the interplay of concepts and methods from topology, analysis, and linear and affine algebra. From motivation to definition, the authors present concrete examples and theorems that identify convex bodies and surfaces and establish their basic properties. The easy-to-read treatment employs simple notation and clear, complete proofs. Introductory chapters establish the basics of metric topology and the structure of Euclidean n-space. Subsequent chapters apply this background to the dimension, basic structure, and general geometry of convex bodies and surfaces. Concluding chapters illustrate nonintuitive results to offer students a perspective on the wide range of problems and applications in convex body theory.

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