Thirty-Three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra

Thirty-Three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra

by Jiri Matousek
     
 

This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The

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Overview

This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations.

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Product Details

ISBN-13:
9780821849774
Publisher:
American Mathematical Society
Publication date:
05/28/2010
Series:
Student Mathematical Library, #53
Edition description:
New Edition
Pages:
182
Product dimensions:
5.60(w) x 8.40(h) x 0.40(d)

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