Master the fundamentals of discrete mathematics and proof-writing with MATHEMATICS: A DISCRETE INTRODUCTION With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is presented from a mathematician's perspective, you will learn the importance of discrete mathematics in the fields of computer science, engineering, probability, statistics, operations research, and other areas of applied mathematics. Tools such hints and proof templates prepare you to succeed in this course.
Author(s): Edward R. Scheinerman
Edition: 3rd
Publisher: Cengage Learning
Year: 2012
Language: English
Pages: 470
Cover
......Page 1
Title Page
......Page 5
Copyright
......Page 6
Contents......Page 9
To the Student......Page 19
To the Instructor......Page 21
What's New in This Third Edition......Page 25
Acknowledgments......Page 27
1 Joy......Page 31
2 Speaking (and Writing) of Mathematics......Page 32
3 Definition......Page 34
4 Theorem......Page 38
5 Proof......Page 45
6 Counterexample......Page 53
7 Boolean Algebra......Page 55
Chapter 1 Self Test......Page 60
8 Lists......Page 63
9 Factorial......Page 70
10 Sets I: Introduction, Subsets......Page 73
11 Quantifiers......Page 81
12 Sets II: Operations......Page 86
13 Combinatorial Proof: Two Examples......Page 96
Chapter 2 Self Test......Page 100
14 Relations......Page 103
15 Equivalence Relations......Page 108
16 Partitions......Page 115
17 Binomial Coefficients......Page 120
18 Counting Multisets......Page 131
19 Inclusion-Exclusion......Page 139
Chapter 3 Self Test......Page 147
20 Contradiction......Page 149
21 Smallest Counterexample......Page 155
22 Induction......Page 165
23 Recurrence Relations......Page 179
Chapter 4 Self Test......Page 195
24 Functions......Page 197
25 The Pigeonhole Principle......Page 208
26 Composition......Page 213
27 Permutations......Page 218
28 Symmetry......Page 230
29 Assorted Notation......Page 234
Chapter 5 Self Test......Page 240
30 Sample Space......Page 243
31 Events......Page 247
32 Conditional Probability and Independence......Page 253
33 Random Variables......Page 261
34 Expectation......Page 265
Chapter 6 Self Test......Page 280
35 Dividing......Page 283
36 Greatest Common Divisor......Page 288
37 Modular Arithmetic......Page 296
38 The Chinese Remainder Theorem......Page 305
39 Factoring......Page 309
Chapter 7 Self Test......Page 317
40 Groups......Page 319
41 Group Isomorphism......Page 327
42 Subgroups......Page 332
43 Fermat's Little Theorem......Page 339
44 Public Key Cryptography I: Introduction......Page 346
45 Public Key Cryptography II: Rabin's Method......Page 349
46 Public Key Cryptography III: RSA......Page 355
Chapter 8 Self Test......Page 359
47 Fundamentals of Graph Theory......Page 361
48 Subgraphs......Page 369
49 Connection......Page 374
50 Trees......Page 380
51 Eulerian Graphs......Page 386
52 Coloring......Page 391
53 Planar Graphs......Page 397
Chapter 9 Self Test......Page 405
54 Fundamentals of Partially Ordered Sets......Page 409
55 Max and Min......Page 414
56 Linear Orders......Page 416
57 Linear Extensions......Page 419
58 Dimension......Page 424
59 Lattices......Page 430
Chapter 10 Self Test......Page 435
Appendix A: Lots of Hints and Comments; Some Answers......Page 439
Appendix B: Solutions to Self Tests......Page 465
Appendix C: Glossary......Page 486
Appendix D: Fundamentals......Page 492
Index......Page 495
