Geometry of Convex Sets free ebook download.

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Geometry of Convex Sets free ebook download

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Catalogue

Author(s):	I. E. Leonard and J. E. Lewis

Date:	2017	Format:	PDF	Language:	English	ISBN/ASIN:	1119022665
Pages:	1	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	8/27/2018 6:12:20 AM

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A gentle introduction to the geometry of convex sets in n-dimensional space

Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting.

Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on an n-dimensional space.

Geometry of Convex Sets also features:

An introduction to n-dimensional geometry including points  lines  vectors  distance  norms  inner products  orthogonality  convexity  hyperplanes  and linear functionals
Coverage of n-dimensional norm topology including interior points and open sets  accumulation points and closed sets  boundary points and closed sets  compact subsets of n-dimensional space  completeness of n-dimensional space  sequences  equivalent norms  distance between sets  and support hyperplanes 
Basic properties of convex sets  convex hulls  interior and closure of convex sets  closed convex hulls  accessibility lemma  regularity of convex sets  affine hulls  flats or affine subspaces  affine basis theorem  separation theorems  extreme points of convex sets  supporting hyperplanes and extreme points  existence of extreme points  KreinMilman theorem  polyhedral sets and polytopes  and Birkhoffs theorem on doubly stochastic matrices
Discussions of Hellys theorem  the Art Gallery theorem  Vincensinis problem  Hadwigers theorems  theorems of Radon and Caratheodory  Kirchbergers theorem  Helly-type theorems for circles  covering problems  piercing problems  sets of constant width  Reuleaux triangles  Barbiers theorem  and Borsuks problem

Geometry of Convex Sets is a useful textbook for upper-undergraduate level courses in geometry of convex sets and is essential for graduate-level courses in convex analysis. An excellent reference for academics and readers interested in learning the various applications of convex geometry, the book is also appropriate for teachers who would like to convey a better understanding and appreciation of the field to students.

I. E. Leonard, PhD, was a contract lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta. The author of over 15 peer-reviewed journal articles, he is a technical editor for the Canadian Applied Mathematical Quarterly journal.

J. E. Lewis, PhD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004 as well as the PIMS Education Prize in 2002.

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	Title	Link	Password	Size (MB)	Thank to	Inform Admin
2253921	Book	http://k2s.cc/file/f539bea974f30/1119022...		2.00	eternal

Tags: Convex Geometry Sets

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