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Thirty-Three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library, 53, Band 53) - Softcover
Inhaltsangabe
Matousek started gathering these succinct applications of linear algebra some years ago, and has decided to share his collection with students. Each problem can be covered in a typical 90-minute class, he says, the earlier ones suitable for undergraduates and the latter ones for graduates. He assumes a background in basic linear algebra, a bit of familiarity with polynomials, and some terminology of graph-theory and geometry. Readers are free to notice recurring patterns, and features of linear algebra as a whole, but he does not point them out. Nothing here is original, he says. Among his topics are Fibonacci numbers, equi-angular lines, covering a cube minus one vertex, walking in the yard, turning a ladder over a finite field, the secret agent and the umbrella, and cutting cheaply using eigenvectors. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
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Über die Autorin bzw. den Autor
Jiří Matoušek, Charles University, Prague, Czech Republic
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Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra
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American Mathematical Society, 2010
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Paperback. Zustand: Good. Contains a collection of mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof, and assumes only a modest background in linear algebra. The topics include Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture. Bestandsnummer des Verkäufers CIN0821849778G
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Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra
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ISBN 13: 9780821849774
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Paperback. Zustand: Good. Contains a collection of mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof, and assumes only a modest background in linear algebra. The topics include Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture. Bestandsnummer des Verkäufers CIN0821849778G
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Paperback. Zustand: New. 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. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53). Bestandsnummer des Verkäufers LU-9780821849774
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Paperback. Zustand: new. Paperback. 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. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53) Contains a collection of mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof, and assumes only a modest background in linear algebra. The topics include Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780821849774