Thirtythree Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library) (Student Mat,Used

Thirtythree Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library) (Student Mat,Used

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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 wellknown mathematical gems, such as Hamming codes, the matrixtree theorem, the Lovsz 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 linearalgebraic methods or for seminar presentations.

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