An edition of Discrete and combinatorial mathematics (1985)

Discrete and combinatorial mathematics

an applied introduction

2nd ed.

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Cover of: Discrete and combinatorial mathematics by Ralph P. Grimaldi, Ralph P. Grimaldi
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  • ★★★★ 4.3 (3 ratings)
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  • 2 Currently reading
  • 3 Have read
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Last edited by Drini
September 14, 2025 | History
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An edition of Discrete and combinatorial mathematics (1985)

Discrete and combinatorial mathematics

an applied introduction

2nd ed.

by

  • ★★★★ 4.3 (3 ratings)
  • 36 Want to read
  • 2 Currently reading
  • 3 Have read

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Publish Date
Publisher
Addison-Wesley
Language
English

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Subjects

Mathematics, Computer science, Combinatorial analysis, Algebra, Electronic data processing, Mathématiques, Computer science, mathematics, Discrete groups, Computer science--mathematics, Qa39.2 .g748 1994, 510, Qa39.2 .g748 2004, Analyse combinatoire, Informatique

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1961-

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Cover of: Discrete and combinatorial mathematics
Discrete and combinatorial mathematics: an applied introduction
2004, Pearson Addison Wesley
in English - 5th ed.
Cover of: Discrete and combinatorial mathematics
Discrete and combinatorial mathematics: an applied introduction
1999, Addison-Wesley Longman
in English - 4th ed.
Cover of: Discrete and combinatorial mathematics
Discrete and combinatorial mathematics: an applied introduction
1994, Addison-Wesley
in English - 3rd ed.
Cover of: Discrete and combinatorial mathematics
Discrete and combinatorial mathematics: an applied introduction
1989, Addison-Wesley
in English - 2nd ed.

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Book Details

Table of Contents

Chapter 1. Fundamental Principles of Counting
1.1. The Rules of Sum and Product
Page 1
1.2. Permutations
Page 4
1.3. Combinations: The Binomial Theorem
Page 14
1.4. Combinations with Repetition: Distributions
Page 23
1.5. An Application in the Physical Sciences (Optional)
Page 32
1.6. Summary and Historical Review
Page 32
Chapter 2. Fundamentals of Logic
2.1. Basic Connectives and Truth Tables
Page 41
2.2. Logical Equivalence: The Laws of Logic
Page 49
2.3. Logical Implication: Methods of Proof
Page 60
2.4. The Use of Quantifiers
Page 77
2.5. Summary and Historical Review
Page 91
Chapter 3. Set Theory
3.1. Sets and Subsets
Page 97
3.2. Set Operations and the Laws of Set Theory
Page 106
3.3. Counting and Venn Diagrams
Page 117
3.4. A Word on Probability
Page 120
3.5. Summary and Historical Review
Page 123
Chapter 4. Properties of the Integers: Mathematical Induction
4.1. The Well-Ordering Principle: Mathematical Induction
Page 129
4.2. The Division Algorithm: Prime Numbers
Page 145
4.3. The Greatest Common Divisor: The Euclidean Algorithm
Page 153
4.4. The Fundamental Theorem of Arithmetic
Page 159
4.5. Summary and Historical Review
Page 161
Chapter 5. Relations and Functions
5.1. Cartesian Products and Relations
Page 166
5.2. Functions: Plain and One-to-One
Page 170
5.3. Onto Functions: Stirling Numbers of the Second Kind
Page 175
5.4. Special Functions
Page 180
5.5. The Pigeonhole Principle
Page 186
5.6. Function Composition and Inverse Functions
Page 190
5.7. Computational Complexity
Page 199
5.8. Analysis of Algorithms
Page 204
5.9. Summary and Historical Review
Page 212
Chapter 6. Languages: Finite State Machines
6.1. Language: The Set Theory of Strings
Page 220
6.2. Finite State Machines: A First Encounter
Page 228
6.3. Finite State Machines: A Second Encounter
Page 236
6.4. Summary and Historical Review
Page 243
Chapter 7. Relations: The Second Time Around
7.1. Relations Revisited: Properties of Relations
Page 249
7.2. Computer Recognition: Zero-One Matrices and Directed Graphs
Page 255
7.3. Partial Orders: Hasse Diagrams
Page 266
7.4. Equivalence Relations and Partitions
Page 276
7.5. Finite State Machines: The Minimization Process
Page 281
7.6. Summary and Historical Review
Page 287
Chapter 8. The Principle of Inclusion and Exclusion
8.1. The Principle of Inclusion and Exclusion
Page 295
8.2. Generalizations of the Principle
Page 305
8.3. Derangements: Nothing Is in Its Right Place
Page 309
8.4. Rook Polynomials
Page 311
8.5. Arrangements with Forbidden Positions
Page 315
8.6. Summary and Historical Review
Page 319
Chapter 9. Generating Functions
9.1. Introductory Examples
Page 323
9.2. Definition and Examples: Calculational Techniques
Page 327
9.3. Partitions of Integers
Page 336
9.4. The Exponential Generating Function
Page 339
9.5. The Summation Operator
Page 344
9.6. Summary and Historical Review
Page 345
Chapter 10. Recurrence Relations
10.1. The First-Order Linear Recurrence Relation
Page 351
10.2. The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients
Page 361
10.3. The Nonhomogeneous Recurrence Relation
Page 371
10.4. The Method of Generating Functions
Page 377
10.5. A Special Kind of Nonlinear Recurrence Relation (Optional)
Page 382
10.6. Divide-and-Conquer Algorithms (Optional)
Page 388
10.7. Summary and Historical Review
Page 399
Chapter 11. An Introduction to Graph Theory
11.1. Definitions and Examples
Page 405
11.2. Subgraphs, Complements, and Graph Isomorphism
Page 413
11.3. Vertex Degree: Euler Trails and Circuits
Page 424
11.4. Planar Graphs
Page 433
11.5. Hamilton Paths and Cycles
Page 448
11.6. Graph Coloring and Chromatic Polynomials
Page 457
11.7. Summary and Historical Review
Page 466
Chapter 12. Trees
12.1. Definitions, Properties and Examples
Page 475
12.2. Rooted Trees
Page 482
12.3. Trees and Sorting Algorithms
Page 501
12.4. Weighted Trees and Prefix Codes
Page 506
12.5. Biconnected Components and Articulation Points
Page 511
12.6. Summary and Historical Review
Page 517
Chapter 13. Optimization and Matching
13.1. Dijkstra's Shortest-Path Algorithm
Page 523
13.2. Minimal Spanning Trees: The Algorithms of Kruskal and Prim
Page 531
13.3. Transport Networks: The Max-Flow Min-Cut Theorem
Page 538
13.4. Matching Theory
Page 549
13.5. Summary and Historical Review
Page 558
Chapter 14. Rings and Modular Arithmetic
14.1. The Ring Structure: Definition and Examples
Page 563
14.2. Ring Properties and Substructures
Page 568
14.3. The Integers Modulo n
Page 575
14.4. Ring Homomorphisms and Isomorphisms
Page 580
14.5. Summary and Historical Review
Page 587
Chapter 15. Boolean Algebra and Switching Functions
15.1. Switching Functions: Disjunctive and Conjunctive Normal Forms
Page 591
15.2. Gating Networks: Minimal Sums of Products: Karnaugh Maps
Page 600
15.3. Further Applications: Don't-Care Conditions
Page 609
15.4. The Structure of a Boolean Algebra (Optional)
Page 615
15.5. Summary and Historical Review
Page 624
Chapter 16. Groups, Coding Theory, and Polya's Method of Enumeration
16.1. Definition, Examples, and Elementary Properties
Page 629
16.2. Homomorphisms, Isomorphisms, and Cyclic Groups
Page 635
16.3. Cosets and Lagrange's Theorem
Page 639
16.4. Elements of Coding Theory
Page 642
16.5. The Hamming Metric
Page 647
16.6. The Parity-Check and Generator Matrices
Page 649
16.7. Group Codes: Decoding with Coset Leaders
Page 654
16.8. Hamming Matrices
Page 658
16.9. Counting and Equivalence: Burnside's Theorem
Page 661
16.10. The Cycle Index
Page 669
16.11. The Pattern Inventory: Polya's Method of Enumeration
Page 673
16.12. Summary and Historical Review
Page 679
Chapter 17. Finite Fields and Combinatorial Designs
17.1. Polynomial Rings
Page 685
17.2. Irreducible Polynomials: Finite Fields
Page 693
17.3. Latin Squares
Page 700
17.4. Finite Geometries and Affine Planes
Page 707
17.5. Block Designs and Projective Planes
Page 713
17.6. Summary and Historical Review
Page 718
Answers
Page A-1
Index
Page I-1

Edition Notes

Includes index.

Published in
Reading, Mass

Classifications

Dewey Decimal Class
510
Library of Congress
QA39.2 .G7478 1989, QA39.2.G7478 1989

The Physical Object

Pagination
p. cm.

Edition Identifiers

Open Library
OL2038956M
ISBN 10
0201119544
LCCN
88015398
LibraryThing
354863

Work Identifiers

Work ID
OL1901959W

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History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
September 14, 2025 Edited by Drini Add TOC from Tocky
July 17, 2022 Edited by ImportBot import existing book
March 13, 2020 Edited by Drini Added new cover
January 9, 2018 Edited by ImportBot import new book
April 1, 2008 Created by an anonymous user Imported from Scriblio MARC record