Selected papers on discrete mathematics

Donald E. Knuth

812 pages, parution le 07/04/2004

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Résumé

Donald Knuth's influence in computer science ranges from the invention of methods for translating and defining programming languages to the mathematical analysis of algorithms and the creation of theT£X typesetting system.

His award-winning textbooks have become classics that are often given credit for shaping the field; his scientific papers are widely referenced and stand as milestones of development over a wide range of topics. The present volume, which is the sixth in a series of his collected papers, is devoted to his purely mathematical work, which spans the entire range of discrete mathematics: permutations, partitions, identities, recurrences, and combinatorial designs; matrix theory, number theory, graph theory, probability theory, and a bit of algebra.

More than forty of Knuth's classic papers on the subject are collected in this book, brought up to date with extensive revisions and dozens of pages of new material. The papers emphasize general techniques that apply to many different kinds of problems, together with the joy of discovery associated with beautiful mathematical patterns. Knuth's prize-winning expositions of mathematical notation, his accounts of fascinating episodes in the history of mathematics, and his fundamental papers on tableaux and random graphs all are found here, accompanied by 50 newly created illustrations. Everyone who enjoys mathematics will take pleasure in this unusually readable collection.

L'auteur - Donald E. Knuth

Donald E. Knuth est professeur émérite à l'université de Stanford, membre de l'Académie des sciences des États-Unis, titulaire de la Médaille des sciences et du Prix Turing. Auteur d'une centaine de publications, notamment The Art of Computer Programming en trois volumes dont la section "Préliminaires mathématiques" a inspiré ce livre, il est également le créateur des systèmes TEX et Metafont auxquels il a déjà consacré cinq ouvrages.

Sommaire

Combinatorial Analysis and Computers
Two Notes on Notation
Bracket Notation for the Coefficient of Operator
Johann Faulhaber and Sums of Powers
Notes on Thomas Hariot
A Permanent Inequality
Overlapping Pfaffians
The Sandwich Theorem
Combinatorial Matrices
Aztec Diamonds, Checkerboard Graphs, and Spanning Trees
Partitioned Tensor Products and Their Spectra
Oriented Subtrees of an Arc Digraph
Another Enumeration of Trees
Abel Identities and Inverse Relations
Convolution Polynomials
Polynomials Involving the Floor Function
Construction of a Random Sequence
An Imaginary Number System
Tables of Finite Fields
Finite Semifields and Projective Planes
A Class of Projective Planes
Notes on Central Groupoids
Huffman's Algorithm via Algebra
Wheels Within Wheels
Complements and Transitive Closures
Random Matroids
The Asymptotic Number of Geometries
Permutations with Nonnegative Partial Sums
Efficient Balanced Codes
The Knowlton-Graham Partition Problem
Permutations, Matrices, and Generalized Young Tableaux
Enumeration of Plane Partitions
A Note on Solid Partitions
Identities from Partition Involutions
Subspaces, Subsets, and Partitions
The Power of a Prime That Divides a Generalized Coefficient
An Almost Linear Recurrence
Recurrence Relations Based on Minimization
A Recurrence Related to Trees
The First Cycles in an Evolving Graph
The Birth of the Giant Component

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Caractéristiques techniques

	PAPIER
Éditeur(s)	CSLI
Auteur(s)	Donald E. Knuth
Parution	07/04/2004
Nb. de pages	812
Format	15 x 22,8
Couverture	Broché
Poids	1083g
Intérieur	Noir et Blanc
EAN13	9781575862484
ISBN13	978-1-57586-248-4