內容大鋼
《離散與組合數學手冊》出版的目的是為需要離散與組合數學信息的電腦科學家、工程師、數學家和學生、物理與社會科學家，以及相關的圖書管理員提供一本全方位的參考書。本書的第一版是以准參考資料的形式，為在工作或學習中用到與本書主題相關知識的人準備的展現這類信息的第一手資料，第二版是對第一版的重大修訂。它包括了大量的添加和更新，這些添加與更新在本書前言的後半部分進行了總結。本書的範圍包括通常被認為是離散數學的一部分的許多領域，集中於被認為在電腦科學、工程和其他學科的應用中至關重要的信息。本書是一部大型的工具書。本書呈現材料的方式可以讓讀者快速、輕鬆地找到和使用關鍵信息。每章都包含一個辭彙表，用來對該章節中最重要的術語提供簡潔的定義。單獨的主題包含在每章的各個部分和小節中，每個部分都是清晰可辨的：定義、事實和示例。
目錄
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/P?lya 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 Ru?
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 — Andr?s Gy?rf?s
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 - J?nos 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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