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This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use as a graduate course text, but complete enough for a standard reference work on the basic theory. Thus it will be an essential purchase for combinatorialists, matrix theorists, and those numerical analysts working in numerical linear algebra.

Matrices. --- Combinatorial analysis. --- Combinatorics --- Algebra --- Mathematical analysis --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University. Contents : Tutorial. Applications. Further Reading.

Computer science --- Categories (Mathematics) --- Mathematics --- Mathematics. --- Categories (Mathematics). --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Computer mathematics --- Electronic data processing --- Computer science - Mathematics --- Algebra --- COMPUTER SCIENCE/General

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Algebra, Abstract --- Geometry --- -Mathematics --- Euclid's Elements --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory --- Problems, Famous --- Algebra, Abstract. --- Famous problems. --- -Problems, Famous --- -Abstract algebra --- Famous problems in geometry --- Problems, Famous, in geometry --- Famous problems

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Mathematics --- Algebras, Linear --- -512.64 --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Outlines, syllabi, etc --- Linear and multilinear algebra. Matrix theory --- Outlines, syllabi, etc. --- 512.64 Linear and multilinear algebra. Matrix theory --- Algebra --- algebra --- 512.64 --- Algebras, Linear - Outlines, syllabi, etc. --- Algebras, Linear - Problems, exercises, etc.

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Categories (Mathematics) --- Categorieën (Wiskunde) --- Catégories (Mathématiques) --- Topologie --- Topology --- Computer science --- Mathematics --- 515.1 --- 512.58 --- -Topology --- 681.3*F0 --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Informatics --- Science --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory --- Categories. Category theory --- Computerwetenschap--?*F0 --- Topology. --- Mathematics. --- Categories (Mathematics). --- 512.58 Categories. Category theory --- 515.1 Topology --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer science - Mathematics. --- Informatique --- Catégories (mathématiques) --- Computer science - Mathematics