Cover image for Handbook of discrete and combinatorial mathematics
Title:
Handbook of discrete and combinatorial mathematics
Author:
Rosen, Kenneth H.
Publication Information:
Boca Raton : CRC Press, [2000]

©2000
Physical Description:
1232 pages : illustrations ; 26 cm
Language:
English
Contents:
Foundations -- Counting methods -- Sequences -- Number theory -- Algebraic structures -- Linear algebra -- Discrete probability -- Graph theory -- Trees -- Networks and flows -- Partially ordered sets -- Combinatorial designs -- Discrete and computational geometry -- Coding theory and cryptology -- Discrete optimization -- Theoretical computer science -- Information structures.
ISBN:
9780849301490
Format :
Book

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Library
Call Number
Material Type
Home Location
Status
Central Library QA164 .H36 2000 Adult Non-Fiction Non-Fiction Area-Reference
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Summary

Summary

The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Editionpresents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.


Reviews 1

Choice Review

Rosen is a researcher at AT&T Laboratories, well known for his textbooks in discrete mathematics and number theory (Discrete Mathematics and Its Applications (4th ed., 1998; Elementary Number Theory and Its Applications, 1st ed., CH, Jan'85; 3rd ed., 1992). Together with dozens of contributors, Rosen has assembled essays on a wide range of topics in discrete mathematics, including enumerative combinatorics, number theory, linear and abstract algebra, discrete probability, graph theory, optimization, coding theory, and data structures. The book is organized into 17 chapters, each on a major area of this part of mathematics. Within each chapter there are essays on particular topics within the area, a glossary, a list of references, and a list of Internet resources. Many of the articles contain algorithms and tables of important formulas. A 60-page index makes it easy to locate particular terms. Although many areas covered by this book are discussed in other reference works, no other book covers such a wide range of topics in discrete mathematics. A very useful resource for upper-division undergraduate and graduate students, faculty, researchers, and professionals. B. Borchers; New Mexico Institute of Mining and Technology


Table of Contents

Jerrold W. GrossmanJerrold W. GrossmanJerrold W. GrossmanJohn G. MichaelsSusanna S. EppDavid RileyMukesh DalalJohn G. MichaelsJay YellenEdward W. PackelRobert G. RieperGeorge E. AndrewsAlan C. TuckerEdward A. BenderBruce E. SaganThomas A. Dowling and Douglas R. ShierRalph P. GrimaldiRalph P. GrimaldiJay YellenVictor S. MillerEdward A. BenderKenneth H. RosenKenneth H. RosenKenneth H. RosenKenneth H. RosenJon F. Grantham and Carl PomeranceJon F. Grantham and Carl PomeranceKenneth H. RosenKenneth H. RosenBart E. GoddardJeff ShalitKenneth H. RosenJohn G. MichaelsJoel V. BrawleyJoel V. BrawleyPeter R. TurnerBarry Peyton and Esmond NgR. B. BapatR. B. BapatJoseph R. BarrJoseph R. BarrJoseph R. BarrPeter R. TurnerPatrick JailletDouglas R. ShierVidyadhar G. KulkarniVidyadhar G. KulkarniLawrence M. LeemisLowell W. BeinekeJonathan L. GrossStephen B. MaurerEdward R. ScheinermanBennett ManvelArthur T. WhiteJonathan L. GrossJonathan L. GrossPaul K. StockmeyerMichael DoobStefan A. BurrAndreas GyarfasLisa CarboneUri PeledPaul StockmeyerJ. B. Orlin and Ravindra K. AhujaDouglas R. ShierJ. B. Orlin and Ravindra K. AhujaJ. B. Orlin and Ravindra K. AhujaJ. B. Orlin and Ravindra K. AhujaDavid Simchi-Levi and Sunil ChopraBruce L. Golden and Bharat K. KakuDouglas R. ShierGraham Brightwell and Douglas B. WestGraham Brightwell and Douglas B. WestCharles J. Colbourn and Jeffrey H. DinitzCharles J. Colbourn and Jeffrey H. DinitzCharles J. Colbourn and Jeffrey H. DinitzJames G. OxleyIleana StreinuKaroly BezdekJanos PachTamal K. DeyJianer ChenDina KravetsNancy M. AmatoW. Randolph FranklinAlfred J. Menezes and Paul C. van OorschotBeth NovickS. Louis HakimiSunil Chopra and David Simchi-LeviS. E. ElmaghrabyMichael Mesterton-GibbonsJoseph R. BarrJonathan L. GrossWilliam GasarchAarto SalomaaThomas CormenLane HemaspaandraMilena MihailCharles H. GoldbergJonathan L. GrossJianer ChenViera Krnanova ProulxJoan Feigenbaum and Sampath KannanVictor J. Katz
1. Foundationsp. 1
1.1 Propositional and Predicate Logicp. 12
1.2 Set Theoryp. 21
1.3 Functionsp. 31
1.4 Relationsp. 40
1.5 Proof Techniquesp. 50
1.6 Axiomatic Program Verificationp. 61
1.7 Logic-Based Computer Programming Paradigmsp. 67
2. Counting Methodsp. 81
2.1 Summary of Counting Problemsp. 84
2.2 Basic Counting Techniquesp. 90
2.3 Permutations and Combinationsp. 96
2.4 Inclusion/Exclusionp. 107
2.5 Partitionsp. 113
2.6 Burnside/Polya Counting Formulap. 120
2.7 Mobius Inversion Countingp. 127
2.8 Young Tableauxp. 129
3. Sequencesp. 135
3.1 Special Sequencesp. 138
3.2 Generating Functionsp. 171
3.3 Recurrence Relationsp. 178
3.4 Finite Differencesp. 189
3.5 Finite Sums and Summationp. 195
3.6 Asymptotics of Sequencesp. 201
3.7 Mechanical Summation Proceduresp. 204
4. Number Theoryp. 213
4.1 Basic Conceptsp. 219
4.2 Greatest Common Divisorsp. 226
4.3 Congruencesp. 231
4.4 Prime Numbersp. 236
4.5 Factorizationp. 255
4.6 Arithmetic Functionsp. 259
4.7 Primitive Roots and Quadratic Residuesp. 268
4.8 Diophantine Equationsp. 281
4.9 Diophantine Approximationp. 289
4.10 Quadratic Fieldsp. 295
5. Algebraic Structuresp. 299
5.1 Algebraic Modelsp. 305
5.2 Groupsp. 307
5.3 Permutation Groupsp. 319
5.4 Ringsp. 323
5.5 Polynomial Ringsp. 329
5.6 Fieldsp. 331
5.7 Latticesp. 341
5.8 Boolean Algebrasp. 344
6. Linear Algebrap. 355
6.1 Vector Spacesp. 361
6.2 Linear Transformationsp. 371
6.3 Matrix Algebrap. 377
6.4 Linear Systemsp. 392
6.5 Eigenanalysisp. 405
6.6 Combinatorial Matrix Theoryp. 417
7. Discrete Probabilityp. 427
7.1 Fundamental Conceptsp. 432
7.2 Independence and Dependencep. 435
7.3 Random Variablesp. 441
7.4 Discrete Probability Computationsp. 448
7.5 Random Walksp. 452
7.6 System Reliabilityp. 459
7.7 Discrete-Time Markov Chainsp. 468
7.8 Queueing Theoryp. 477
7.9 Simulationp. 484
8. Graph Theoryp. 495
8.1 Introduction to Graphsp. 509
8.2 Graph Modelsp. 525
8.3 Directed Graphsp. 526
8.4 Distance, Connectivity, Traversabilityp. 539
8.5 Graph Invariants and Isomorphism Typesp. 549
8.6 Graph and Map Coloringp. 557
8.7 Planar Drawingsp. 567
8.8 Topological Graph Theoryp. 574
8.9 Enumerating Graphsp. 580
8.10 Algebraic Graph Theoryp. 586
8.11 Analytic Graph Theoryp. 590
8.12 Hypergraphsp. 595
9. Treesp. 603
9.1 Characterizations and Types of Treesp. 607
9.2 Spanning Treesp. 616
9.3 Enumerating Treesp. 622
10. Networks and Flowsp. 629
10.1 Minimum Spanning Treesp. 633
10.2 Matchingsp. 641
10.3 Shortest Pathsp. 652
10.4 Maximum Flowsp. 663
10.5 Minimum Cost Flowsp. 673
10.6 Communication Networksp. 683
10.7 Difficult Routing and Assignment Problemsp. 692
10.8 Network Representations and Data Structuresp. 706
11. Partially Ordered Setsp. 717
11.1 Basic Poset Conceptsp. 724
11.2 Poset Propertiesp. 738
12. Combinatorial Designsp. 753
12.1 Block Designsp. 759
12.2 Symmetric Designs and Finite Geometriesp. 770
12.3 Latin Squares and Orthogonal Arraysp. 778
12.4 Matroidsp. 786
13. Discrete and Computational Geometryp. 797
13.1 Arrangements of Geometric Objectsp. 805
13.2 Space Fillingp. 824
13.3 Combinatorial Geometryp. 830
13.4 Polyhedrap. 839
13.5 Algorithms and Complexity in Computational Geometryp. 844
13.6 Geometric Data Structures and Searchingp. 853
13.7 Computational Techniquesp. 861
13.8 Applications of Geometryp. 867
14. Coding Theory and Cryptologyp. 889
14.1 Communication Systems and Information Theoryp. 896
14.2 Basics of Coding Theoryp. 900
14.3 Linear Codesp. 903
14.4 Bounds for Codesp. 915
14.5 Nonlinear Codesp. 917
14.6 Convolutional Codesp. 918
14.7 Basics of Cryptographyp. 923
14.8 Symmetric-Key Systemsp. 927
14.9 Public-Key Systemsp. 935
15. Discrete Optimizationp. 955
15.1 Linear Programmingp. 959
15.2 Location Theoryp. 986
15.3 Packing and Coveringp. 996
15.4 Activity Netsp. 1006
15.5 Game Theoryp. 1016
15.6 Sperner's Lemma and Fixed Pointsp. 1027
16. Theoretical Computer Sciencep. 1039
16.1 Computational Modelsp. 1048
16.2 Computabilityp. 1062
16.3 Languages and Grammarsp. 1066
16.4 Algorithmic Complexityp. 1077
16.5 Complexity Classesp. 1085
16.6 Randomized Algorithmsp. 1091
17. Information Structuresp. 1101
17.1 Abstract Datatypesp. 1108
17.2 Concrete Data Structuresp. 1117
17.3 Sorting and Searchingp. 1125
17.4 Hashingp. 1139
17.5 Dynamic Graph Algorithmsp. 1142
Biographiesp. 1153
Indexp. 1173

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