Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library) (Student Mathematical Library, 53) - Softcover

Jiri Matousek

Softcover

ISBN 10: 0821849778 ISBN 13: 9780821849774

Publisher: American Mathematical Society, 2010

Synopsis

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 Lovász 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.

About this title

About the Author

Ji í Matou ek: Charles University, Prague, Czech Republic

Review

Finding examples of "linear algebra in action" that are both accessible and convincing is difficult. Thirty-three Miniatures is an attempt to present some usable examples. . . . For me, the biggest impact of the book came from noticing the tools that are used. Many linear algebra textbooks, including the one I use, delay discussion of inner products and transpose matrices till later in the course, which sometimes means they don't get discussed at all. Seeing how often the transpose matrix shows up in Matousek's miniatures made me realize space must be made for it. Similarly, the theorem relating the rank of the product of two matrices to the ranks of the factors plays a big role here. Most linear algebra instructors would benefit from this kind of insight. . . . Thirty-three Miniatures would be an excellent book for an informal seminar offered to students after their first linear algebra course. It may also be the germ of many interesting undergraduate talks. And it's fun as well. --Fernando Q. Gouvêa, MAA Reviews

[This book] is an excellent collection of clever applications of linear algebra to various areas of (primarily) discrete/combinatiorial mathematics. ... The style of exposition is very lively, with fairly standard usage of terminologies and notations. ... Highly recommended. --Choice

Edition details

• Publisher: American Mathematical Society
• Publication date: 2010
• ISBN 10: 0821849778
• ISBN 13: 9780821849774
• Binding: Paperback
• Language: English
• Number of pages: 182