Discrete mathematical structures = 离散数学结构 / 6th ed.
副标题：无
作 者：Bernard Kolman, Robert C. Busby, Sharon Cutler Ross.
分类号：O158
ISBN：9787040310450
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简介
discrete mathematical structures, sixth edition. offers a clear and concise presentation of the fundamental concepts of discrete mathematics. ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field. this book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.
features
the focus on computer science prepares students for future computer science careers.
the emphasis on proof lays the foundation for mathematical thinking.
clear organization of topics prevents students from being overwhelmed. the authors treat relations and digraphs as two aspects of the same fundamental ideawhich is then used as the basis of virtually all the concepts introduced in the book.
vignettes of mathematical history open each chapter, providing students with a practical background of how these ideas were developed.
additional number theory coverage provides more information on the properties of integers, including base n representations, and gives more contexts for isomorphism.
cryptology is explored throughout the book, introducing students to this exciting field.
coverage of coding provides students with a full picture of all of its aspects, including efficiency, effectiveness, and security. a set of coding exercises for each chapter is also included in appendix c.
exercises emphasize multiple representations of concepts, and provide practice on reading and writing mathematical proofs.
experiments provide opportunities for in-depth exploration and discovery, as well as for writing and for working in groups. topics include weighted voting systems, petri nets, catalan numbers, and others.
end-of-chapter material includes tips for proofs, a summary of key ideas, and a self-test, which contains a set of conceptual review questions to help students identify and synthesize the main ideas of each chapter.
目录
preface xvii
a word to students xxi
fundamentals 1
1.1 sets and subsets 2
1.2 operations on sets 5
1.3 sequences 131.4 properties of 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 68
2.5 mathematical statements 75
2.6 logic and problem solving 78
3 counting 91
3.1 permutations 92
3.2 combinations 96
3.3 pigeonhole principle 100
3.4 elements of probability 104
.3.5 recurrence relations 112
4 relations and digraphs 122
4.1 product sets and partitions 123
4.2 relations and digraphs 127
4.3 paths in relations and digraphs 135
4.4 properties of relations 141
4.5 equivalence relations 148
4.6 data structures for relations and digraphs 152
4.7 operations on relations 159
4.8 transitive closure and warshall's algorithm 169
5 functions 180
5.1 functions 181
5.2 functions for computer science 190
5.3 growth of functions 200
5.4 permutation functions 205
6 order relations and structures 217
6.1 partially ordered sets 218
6.2 extremal elements of partially ordered sets 228
6.3 lattices 233
6.4 finite boolean algebras 243
6.5 functions on boolean algebras 250
6.6 circuit design 254
7 trees 270
7.1 trees 271
7.2 labeled trees 275
7.3 tree searching 280
7.4 undirected trees 288
7.5 minimal spanning trees 295
8 topics in graph theory 305
8.1 graphs 306
8.2 euler paths and circuits 311
8.3 hamiltonian paths and circuits 318
8.4 transport networks 321
8.5 matching problems 329
8.6 coloring graphs 334
9 semigroups and groups 344
9.1 binary operations revisited 345
9.2 semigroups 349
9.3 products and quotients of semigroups 356
9.4 groups 362
9.5 products and quotients of groups 372
9.6 other mathematical structures 377
10 languages and finite-state machines 386
10.1 languages 387
10.2 representations of special grammars and languages 394
10.3 finite-state machines 403
10.4 monoids, machines, and languages 409
10.5 machines and regular languages 414
10.6 simplification of machines 420
11 groups and coding 429
11.1 coding of binary information and error detection 430
11.2 decoding and error correction 440
11.3 public key cryptology 449
appendix a: algorithms and pseudocode 455
appendix b: additional experiments in discrete mathematics 467
appendix c: coding exercises 473
answers to odd-numbered exercises 477
answers to chapter self-tests 515
glossary g-1
index i-1
photo credits p- 1
a word to students xxi
fundamentals 1
1.1 sets and subsets 2
1.2 operations on sets 5
1.3 sequences 131.4 properties of 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 68
2.5 mathematical statements 75
2.6 logic and problem solving 78
3 counting 91
3.1 permutations 92
3.2 combinations 96
3.3 pigeonhole principle 100
3.4 elements of probability 104
.3.5 recurrence relations 112
4 relations and digraphs 122
4.1 product sets and partitions 123
4.2 relations and digraphs 127
4.3 paths in relations and digraphs 135
4.4 properties of relations 141
4.5 equivalence relations 148
4.6 data structures for relations and digraphs 152
4.7 operations on relations 159
4.8 transitive closure and warshall's algorithm 169
5 functions 180
5.1 functions 181
5.2 functions for computer science 190
5.3 growth of functions 200
5.4 permutation functions 205
6 order relations and structures 217
6.1 partially ordered sets 218
6.2 extremal elements of partially ordered sets 228
6.3 lattices 233
6.4 finite boolean algebras 243
6.5 functions on boolean algebras 250
6.6 circuit design 254
7 trees 270
7.1 trees 271
7.2 labeled trees 275
7.3 tree searching 280
7.4 undirected trees 288
7.5 minimal spanning trees 295
8 topics in graph theory 305
8.1 graphs 306
8.2 euler paths and circuits 311
8.3 hamiltonian paths and circuits 318
8.4 transport networks 321
8.5 matching problems 329
8.6 coloring graphs 334
9 semigroups and groups 344
9.1 binary operations revisited 345
9.2 semigroups 349
9.3 products and quotients of semigroups 356
9.4 groups 362
9.5 products and quotients of groups 372
9.6 other mathematical structures 377
10 languages and finite-state machines 386
10.1 languages 387
10.2 representations of special grammars and languages 394
10.3 finite-state machines 403
10.4 monoids, machines, and languages 409
10.5 machines and regular languages 414
10.6 simplification of machines 420
11 groups and coding 429
11.1 coding of binary information and error detection 430
11.2 decoding and error correction 440
11.3 public key cryptology 449
appendix a: algorithms and pseudocode 455
appendix b: additional experiments in discrete mathematics 467
appendix c: coding exercises 473
answers to odd-numbered exercises 477
answers to chapter self-tests 515
glossary g-1
index i-1
photo credits p- 1
Discrete mathematical structures = 离散数学结构 / 6th ed.
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