Thirty-three Miniatures

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Jiří Matoušek: Charles University, Prague, Czech Republic

出版者:American Mathematical Socity
作者:Jiří Matoušek
出品人:
页数:182
译者:
出版时间:2010-6-18
价格:USD 24.60
装帧:平装
isbn号码:9780821849774
丛书系列:Student Mathematical Library
图书标签:
  • 数学 
  • 线性代数 
  • 算法 
  • Linear_Algebra 
  • 数学科学 
  • 代数 
  • Trick 
  • Mathematics 
  •  
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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 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)

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类似数学天书中的证明,都是鬼斧神工般的精妙证明。

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很好玩的书:每个定理基本上一两页左右...好多看上去让人无处下手的问题竟然用基本的线性代数的工具简单利落的处理掉,觉得真是好奇妙啊~

评分

类似数学天书中的证明,都是鬼斧神工般的精妙证明。

评分

很好玩的书:每个定理基本上一两页左右...好多看上去让人无处下手的问题竟然用基本的线性代数的工具简单利落的处理掉,觉得真是好奇妙啊~

评分

类似数学天书中的证明,都是鬼斧神工般的精妙证明。

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