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Author: Jiří Matoušek Publisher: American Mathematical Soc. ISBN: 0821849778 Category : Mathematics Languages : en Pages : 196
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: 0821849778 Category : Mathematics Languages : en Pages : 196
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: Ian Anderson Publisher: Courier Corporation ISBN: 9780486422572 Category : Mathematics Languages : en Pages : 276
Book Description
Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
Author: Ida Kantor Publisher: American Mathematical Soc. ISBN: 1470422611 Category : Mathematics Languages : en Pages : 359
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: Jennifer P. Kingsley Publisher: Penn State Press ISBN: 0271077646 Category : Art Languages : en Pages : 489
Book Description
Few works of art better illustrate the splendor of eleventh-century painting than the manuscript often referred to as the “precious gospels” of Bishop Bernward of Hildesheim, with its peculiar combination of sophistication and naïveté, its dramatically gesturing figures, and the saturated colors of its densely ornamented surfaces. In The Bernward Gospels, Jennifer Kingsley offers the first interpretive study of the pictorial program of this famed manuscript and considers how the gospel book conditioned contemporary and future viewers to remember the bishop. The codex constructs a complex image of a minister caring for his diocese not only through a life of service but also by means of his exceptional artistic patronage; of a bishop exercising the sacerdotal authority of his office; and of a man fundamentally preoccupied with his own salvation and desire to unite with God through both his sight and touch. Kingsley insightfully demonstrates how this prominent member of the early medieval episcopate presented his role to the saints and to the communities called upon to remember him.
Author: Flor Peeters Publisher: Alfred Music ISBN: 1457403617 Category : Music Languages : en Pages : 66
Book Description
These 35 contemporary style miniatures for organ selected by James Conely are lovely improvisatory pieces written in various styles and moods, in most major, minor and modal keys. Several pieces are marked 'con Ped.,' but since they are generally easy and most are written on two staves instead of three, they may be played on two manuals alone. Registration suggestions are included.
Author: Peter Kidd Publisher: Ad Ilissum ISBN: 9781912168132 Category : Illumination of books and manuscripts, Central European Languages : en Pages : 247
Book Description
This substantial catalogue is the second of a two-volume set exploring a remarkable collection of leaves and miniatures from medieval manuscripts. Richly detailed with plentiful illustrations, this notable contribution to medieval scholarship covers a period from c. 1100 to the late 15th century.
Author: Jiří Matoušek
Author: Jiří Matoušek
Author: Jiří Matoušek
Author: Ian Anderson
Author: Ida Kantor
Author: William Younger Fletcher
Author: Jennifer P. Kingsley
Author: Flor Peeters
Author: Richard P. Stanley
Author: Peter Kidd
Author: Alfred W. Pollard