## Table of contents for Discrete mathematical structures / Bernard Kolman, Robert C. Busby, Sharon Cutler Ross.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.

```Contents
Preface viii A Word to Students xii
1 Fundamentals 1
1.1 Sets and Subsets 2
1.2 Operations on Sets 5
1.3 Sequences 13
1.4 Division in the Integers 20
1.5 Matrices 32
1.6 Mathematical Structures 41
2 Logic 50
2.1 Propositions and Logical Operations 51
2.2 Conditional Statements 57
2.3 Methods of Proof 62
2.4 Mathematical Induction 67
3 Counting 78
3.1 Permutations 79
3.2 Combinations 83
3.3 Pigeonhole Principle 88
3.4 Elements of Probability 91
3.5 Recurrence Relations 100
4 Relations and Digraphs 110
4.1 Product Sets and Partitions 111
4.2 Relations and Digraphs 115
4.3 Paths in Relations and Digraphs 123
4.4 Properties of Relations 129
4.5 Equivalence Relations 136
4.6 Computer Representation of Relations and Digraphs 140
4.7 Operations on Relations 147
4.8 Transitive Closure and Warshall's Algorithm 157
5 Functions 168
5.1 Functions 169
5.2 Functions for Computer Science 178
5.3 Growth of Functions 183
5.4 Permutation Functions 188
6 Order Relations and Structures 200
6.1 Partially Ordered Sets 201
6.2 Extremal Elements of Partially Ordered Sets 211
6.3 Lattices 216
6.4 Finite Boolean Algebras 226
6.5 Functions on Boolean Algebras 233
6.6 Circuit Design 237
7 Trees 254
7.1 Trees 254
7.2 Labeled Trees 259
7.3 Tree Searching 264
7.4 Undirected Trees 273
7.5 Minimal Spanning Trees 280
8 Topics in Graph Theory 290
8.1 Graphs 291
8.2 Euler Paths and Circuits 296
8.3 Hamiltonian Paths and Circuits 304
8.4 Transport Networks 307
8.5 Matching Problems 315
8.6 Coloring Graphs 320
9 Semigroups and Groups 329
9.1 Binary Operations Revisited 330
9.2 Semigroups 334
9.3 Products and Quotients of Semigroups 341
9.4 Groups 347
9.5 Products and Quotients of Groups 358
9.6 Other Mathematical Structures 363
10 Languages and Finite-State Machines 372
10.1 Languages 373
10.2 Representations of Special Grammars and Languages 381
10.3 Finite-State Machines 390
10.4 Monoids, Machines, and Languages 396
10.5 Machines and Regular Languages 401
10.6 Simplification of Machines 407
11 Groups and Coding 416
11.1 Coding of Binary Information and Error Detection 417
11.2 Decoding and Error Correction 428
11.3 Public Key Cryptology 436
Appendix A: Algorithms and Pseudocode 443
Appendix B: Additional Experiments in Discrete Mathematics 454