Author: Jiří Matoušek
Publisher: American Mathematical Soc.
ISBN: 0821849778
Category : Mathematics
Languages : en
Pages : 196
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Book Description
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)
Author: Jiří Matoušek
Publisher: American Mathematical Soc.
ISBN: 9781470416362
Category : MATHEMATICS
Languages : en
Pages : 182
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Book Description
This book presents interesting problems and theorems as a collection of independent, intriguing issues. These applications of linear algebra are mainly in the areas of combinatorics, geometry and algorithms. The text can serve as supplementary reading for an undergraduate linear algebra course or as the main text for a special-topics course on linear algebraic methods.
Author: Jiří Matoušek
Publisher: American Mathematical Soc.
ISBN: 0821884697
Category : Mathematics
Languages : en
Pages : 196
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Book Description
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. --from publisher description
Author: Joachim von zur Gathen
Publisher: Cambridge University Press
ISBN: 1107039037
Category : Computers
Languages : en
Pages : 811
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Book Description
Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.
Author: William Younger Fletcher
Publisher:
ISBN:
Category : Book collectors
Languages : en
Pages : 544
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Book Description
Author: Elizabeth Fennema
Publisher: Teachers College Press
ISBN: 9780807730010
Category : Education
Languages : en
Pages : 214
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Book Description
This edited collection describes how the Autonomous Learning Behaviours (ALB) model, formulated by Fennema and Peterson, specifically relates to gender differences in mathematics education, learning and performance. The book provides a background to the debate on gender differences; considers the interactions between internal beliefs and external influences, as well as their effects on learning math; and provides a summary of the latest research relevant to the ALB model. Gender differences in learning mathematics is examined from a variety of perspectives, strengthened by longitudinal studies and a cross-cultural American and Australian perspective..
Author: Ida Kantor
Publisher: American Mathematical Soc.
ISBN: 1470422611
Category : MATHEMATICS
Languages : en
Pages : 343
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Book Description
Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.
Author: Helen J. Swift
Publisher: Oxford University Press
ISBN: 0199232237
Category : Art
Languages : en
Pages : 302
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Book Description
Helen Swift examines late-medieval and early-modern French imaginative literature written by men in defence of women of great popularity in its own time - including catalogues of virtuous women, allegorical narratives, and debate poems.
Author: Sirarpie Der Nersessian
Publisher: Dumbarton Oaks
ISBN: 9780884022022
Category : Art
Languages : en
Pages : 228
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Book Description
Sirarpie Der Nersessian's scholarship has influenced the understanding of Armenian art and its Byzantine context. These two volumes are the culmination of six decades devoted to the exploration of Armenian art, and reflect a deep knowledge of the manuscripts and their creators.
Author: Owen Byer
Publisher: American Mathematical Soc.
ISBN: 0883857634
Category : Mathematics
Languages : en
Pages : 461
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Book Description
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
