Atjaunināt sīkdatņu piekrišanu

Selected Papers on Discrete Mathematics [Hardback]

4.40/5 (5 ratings by Goodreads)
(Stanford University, California)
Citas grāmatas par šo tēmu:
Selected Papers on Discrete MathematicsPalielināt
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781575862491.html
Keywords:
Donald Knuth's influence in computer science ranges from the invention of literate programming to the development of the TeX programming language. One of the foremost figures in the field of mathematical sciences, his papers are widely referenced and stand as milestones of development over a wide range of topics. This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics. It includes a variety of topics in combinatorial mathematics (finite geometries, graph theory, enumeration, partitions, tableaux, matroids, codes); discrete algebra (finite fields, groupoids, closure operators, inequalities, convolutions, Pfaffians); and concrete mathematics (recurrence relations, special numbers and notations, identities, discrete probability). Of particular interest are two fundamental papers in which the evolution of random graphs is studied by means of generating functions.

This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics.

Sixth in a series of collected works, Selected Papers on Discrete Mathematics is devoted to Knuth's purely mathematical work. Over forty of Knuth's classic papers spanning the entire range of discrete mathematics are collected in this volume, all brought up to date with extensive revisions and the addition of new material.

The papers emphasize general techniques of problem solving and explore the creation of mathematical patterns. Knuth's prize-winning expositions of mathematical notation, his accounts of episodes in the history of mathematics, and his fundamental papers on tableaux and random graphs are all found here, along with fifty new illustrations. Scholars and students of mathematics will find this an indispensable collection.


Sixth in a series of collected works, Selected Papers on Discrete Mathematics is devoted to Knuth's purely mathematical work. Over forty of Knuth's classic papers spanning the entire range of discrete mathematics are collected in this volume, all brought up to date with extensive revisions and the addition of new material.

The papers emphasize general techniques of problem solving and explore the creation of mathematical patterns. Knuth's prize-winning expositions of mathematical notation, his accounts of episodes in the history of mathematics, and his fundamental papers on tableaux and random graphs are all found here, along with fifty new illustrations. Scholars and students of mathematics will find this an indispensable collection.

1. Discussion of Mr. Riordan's paper 'Abel identities and inverse
relations';
2. Duality in addition chains;
3. Combinatorial analysis and
computers;
4. Tables of finite fields;
5. Finite semifields and projective
planes;
6. A class of projective planes;
7. Construction of a random
sequence;
8. Oriented subtrees of an arc digraph;
9. Another enumeration of
trees;
10. Notes on central groupoids;
11. Permutations, matrices, and
generalized Young tableaux;
12. A note on solid partitions;
13. Subspaces,
subsets, and partitions;
14. Enumeration of plane partitions;
15. Complements
and transitive closures;
16. Permutations with nonnegative partial sums;
17.
Wheels within wheels;
18. The asymptotic number of geometries;
19. Random
matroids;
20. Identities from partition involutions;
21. Huffman's algorithm
via algebra;
22. A permanent inequality;
23. Efficient balanced codes;
24.
The power of a prime that divides a generalized binomial coefficient;
25. The
first cycles in an evolving graph;
26. The birth of the giant component;
27.
Polynomials involving the floor function;
28. The sandwich theorem;
29. Aztec
diamonds, checkerboard graphs, and spanning trees.