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内容大纲
《离散与组合数学手册》出版的目的是为需要离散与组合数学信息的计算机科学家、工程师、数学家和学生、物理与社会科学家,以及相关的图书管理员提供一本全方位的参考书。本书的第一版是以准参考资料的形式,为在工作或学习中用到与本书主题相关知识的人准备的展现这类信息的第一手资料,第二版是对第一版的重大修订。它包括了大量的添加和更新,这些添加与更新在本书前言的后半部分进行了总结。本书的范围包括通常被认为是离散数学的一部分的许多领域,集中于被认为在计算机科学、工程和其他学科的应用中至关重要的信息。本书是一部大型的工具书。本书呈现材料的方式可以让读者快速、轻松地找到和使用关键信息。每章都包含一个词汇表,用来对该章节中最重要的术语提供简洁的定义。单独的主题包含在每章的各个部分和小节中,每个部分都是清晰可辨的:定义、事实和示例。 -
作者介绍
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目录
1. FOUNDATIONS
1.1 Propositional and Predicate Logic - Jerrold W. Grossman
1.2 Set Theory - Jerrold W. Grossman
1.3 Functions - Jerrold W. Grossman
1.4 Relations - John G. Michaels
1.5 Proof Techniques - Susanna S. Epp
1.6 Axiomatic Program Verification - David Riley
1.7 Logic-Based Computer Programming Paradigms - Mukesh Dalal
2. COUNTING METHODS
2.1 Summary of Counting Problems - John G. Michaels
2.2 Basic Counting Techniques - Jay Yellen
2.3 Permutations and Combinations - Edward W. Packel
2.4 Inclusion/Exclusion - Robert G. Rieper
2.5 Partitions - George E. Andrews and Andrew V. Sills
2.6 Burnside/Pólya Counting Formula - Alan C. Tucker
2.7 M?bius Inversion Counting - Edward A. Bender
2.8 Young Tableaux - Bruce E. Sagan
3. SEQUENCES
3.1 Special Sequences - Thomas A. Dowling and Douglas R. Shier
3.2 Generating Functions - Ralph P. Grimaldi
3.3 Recurrence Relations - Ralph P. Grimaldi
3.4 Finite Differences - Jay Yellen
3.5 Finite Sums and Summation - Victor S. Miller
3.6 Asymptotics of Sequences - Edward A. Bender and Juanjo Rué
3.7 Mechanical Summation Procedures - Kenneth H. Rosen
4. NUMBER THEORY
4.1 Basic Concepts - Kenneth H. Rosen
4.2 Greatest Common Divisors - Kenneth H. Rosen
4.3 Congruences - Kenneth H. Rosen
4.4 Prime Numbers - Jon F. Grantham and Carl Pomerance
4.5 Factorization - Jon F. Grantham and Carl Pomerance
4.6 Arithmetic Functions - Kenneth H. Rosen
4.7 Primitive Roots and Quadratic Residues - Kenneth H. Rosen
4.8 Diophantine Equations - Bart E. Goddard
4.9 Diophantine Approximation - Jeff Shalit
4.10 Algebraic Number Theory - Lawrence C. Washington
4.11 Elliptic Curves - Lawrence C. Washington
5. ALGEBRAIC STRUCTURES - John G. Michaels
5.1 Algebraic Models
5.2 Groups
5.3 Permutation Groups
5.4 Rings
5.5 Polynomial Rings
5.6 Fields
5.7 Lattices
5.8 Boolean Algebras
6. LINEAR ALGEBRA
6.1 Vector Spaces - Joel V. Brawley
6.2 Linear Transformations - Joel V. Brawley
6.3 Matrix Algebra - Peter R. Turner
6.4 Linear Systems - Barry Peyton and Esmond Ng
6.5 Eigenanalysis - R. B. Bapat
6.6 Combinatorial Matrix Theory - R. B. Bapat and Geir Dahl
6.7 Singular Value Decomposition - Carla D. Martin
7. DISCRETE PROBABILITY
7.1 Fundamental Concepts - Joseph R. Barr
7.2 Independence and Dependence - Joseph R. Barr
7.3 Random Variables - Joseph R. Barr
7.4 Discrete Probability Computations - Peter R. Turner
7.5 Random Walks - Patrick Jaillet
7.6 System Reliability - Douglas R. Shier
7.7 Discrete-Time Markov Chains - Vidyadhar G. Kulkarni
7.8 Hidden Markov Models — Narada Warakagoda
7.9 Queueing Theory - Vidyadhar G. Kulkarni
7.10 Simulation - Lawrence M. Leemis
7.11 The Probabilistic Method - Niranjan Balachandran
8. GRAPH THEORY
8.1 Introduction to Graphs - Lowell W. Beineke
8.2 Graph Models - Jonathan L. Gross
8.3 Directed Graphs - Stephen B. Maurer
8.4 Distance, Connectivity, Traversability, & Matchings - Edward R. Scheinerman and Michael D. Plummer
8.5 Graph Isomorphism and Reconstruction - Bennet Manvel, Adolfo Piperno and Josef Lauri
8.6 Graph Colorings, Labelings, & Related Parameters - Arthur T. White, Teresa W. Haynes, Michael A. Henning, Glenn Hurlbert, and Joseph A. Gallian
8.7 Planar Drawings - Jonathan L. Gross
8.8 Topological Graph Theory - Jonathan L. Gross
8.9 Enumerating Graphs - Paul K. Stockmeyer
8.10 Graph Families - Maria Chudnovsky, Michael Doob, Michael Krebs, Anthony Shaheen, Richard Hammack, Sandi Klavzar, and Wilfried Imrich
8.11 Analytic Graph Theory - Stefan A. Burr
8.12 Hypergraphs — András Gyárfás
9. TREES
9.1 Characterizations and Types of Trees - Lisa Carbone
9.2 Spanning Trees - Uri Peled
9.3 Enumerating Trees - Paul K. Stockmeyer
10. NETWORKS AND FLOWS
10.1 Minimum Spanning Trees - J. B. Orlin and Ravindra K. Ahuja
10.2 Matchings - Douglas R. Shier
10.3 Shortest Paths - J. B. Orlin and Ravindra K. Ahuja
10.4 Maximum Flows — J. B. Orlin and Ravindra K. Ahuja
10.5 Minimum Cost Flows - J. B. Orlin and Ravindra K. Ahuja
10.6 Communication Networks - David Simchi-Levi, Sunil Chopra, and M. Gisela Bardossy
10.7 Difficult Routing and Assignment Problems - Bruce L. Golden, Bharat K Kaku, and Xingyin Wang
10.8 Small-World Networks - Vladimir Boginski, Jongeun Kim, and Vladimir Stozhkov
10.9 Network Representations and Data Structures - Douglas R. Shier
11. PARTIALLY ORDERED SETS
11.1 Basic Poset Concepts - Graham Brightwell and Douglas B. West
11.2 Poset Properties - Graham Brightwell and Douglas B. West
12. COMBINATORIAL DESIGNS
12.1 Block Designs - Charles J. Colbourn and Jeffrey H. Dinitz
12.2 Symmetric Designs and Finite Geometries - Charles J. Colbourn and Jeffrey H. Dinitz
12.3 Latin Squares and Orthogonal Arrays - Charles J. Colbourn and Jeffrey H Dinitz
12.4 Matroids - James G. Oxley
13. DISCRETE AND COMPUTATIONAL GEOMETRY
13.1 Arrangements of Geometric Objects - lleana Streinu
13.2 Space Filling - Karoly Bezdek
13.3 Combinatorial Geometry - János Pach
13.4 Polyhedra - Tamal K. Dey
13.5 Algorithms and Complexity in Computational Geometry - Jianer Chen
13.6 Geometric Data Structures and Searching - Dina Kravets
13.7 Computational Techniques - Nancy M. Amato
13.8 Applications of Geometry - W. Randolph Franklin
14. CODING THEORY - Alfred J. Menezes, Paul C. van Oorschot, David Joyner, and Tony Shaska
14.1 Communication Systems and Information Theory
14.2 Basics of Coding Theory
14.3 Linear Codes
14.4 Cyclic Codes
14.5 Bounds for Codes
14.6 Nonlinear Codes
14.7 Convolutional Codes
14.8 Quantum Error-Correcting Codes
15. CRYPTOGRAPHY - Charles C. Y. Lam (Chapter Editor)
15.1 Basics of Cryptography - Charles C. Y. Lam
15.2 Classical Cryptography - Charles C. Y. Lam
15.3 Modern Private Key Cryptosystems - Khoongming Khoo
15.4 Hash Functions - Charles C. Y. Lam
15.5 Public Key Cryptography - Shaoquan Jiang and Charles C. Y. Lam
15.6 Cryptographic Mechanisms - Shaoquan Jiang
15.7 High-Level Applications of Cryptography - Charles C. Y. Lam
16. DISCRETE OPTIMIZATION
16.1 Linear Programming -- Beth Novick
16.2 Location Theory — S. Louis Hakimi and Maria Albareda
16.3 Packing and Covering - Sunil Chopra and David Simchi-Levi
16.4 Activity Nets - S. E. Elmaghraby
16.5 Game Theory - Mike Mesterton-Gibbons
16.6 Sperner's Lemma and Fixed Points - Joseph R. Barr
16.7 Combinatorial Auctions - Robert W. Day
16.8 Very Large-Scale Neighborhood Search - Douglas Altner
16.9 Tabu Search - Manuel Laguna
17. THEORETICAL COMPUTER SCIENCE
17.1 Computational Models - Wayne Goddard
17.2 Computability - Wiliam Gasarch
17.3 Languages and Grammars — Aarto Salomaa
17.4 Algorithmic Complexity - Thomas Cormen
17.5 Complexity Classes — Lane A. Hemaspaandra
17.6 Randomized Algorithms - Milena Mihail
18. INFORMATION STRUCTURES
18.1 Abstract Datatypes - Charles H. Goldberg
18.2 Concrete Data Structures - Jonathan L. Gross
18.3 Sorting and Searching - Jianer Chen
18.4 Hashing - Viera Krnanova Proulx
18.5 Dynamic Graph Algorithms - Joan Feigenbaum and Sampath Kannan
19. DATA MINING
19.1 Data Mining Fundamentals - Richard Scherl
19.2 Frequent Itemset Mining and Association Rules - Richard Scherl
19.3 Classification Methods - Richard Scherl
19.4 Clustering - Daniel Aloise and Pierre Hansen
19.5 Outlier Detection - Richard Scherl
20. DISCRETE BIOMATHEMATICS
20.1 Sequence Alignment - Stephen F. Altschul and Mihai Pop
20.2 Phylogenetics - Joseph Rusinko
20.3 Discrete-Time Dynamical Systems - Elena Dimitrova
20.4 Genome Assembly - Andy Jenkins and Matthew Macauley
20.5 RNA Folding - Qijun He, Matthew Macauley, and Svetlana Poznanovic
20.6 Combinatorial Neural Codes — Carina Curto and Vladimir ltskov
20.7 Food Webs and Graphs - Margaret Cozzens
BIOGRAPHIES - Victor J. Katz
INDEX
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