Discrete Mathematics and Its Applications 8th Edition by Kenneth Rosen, ISBN-13: 978-1259676512

Discrete Mathematics and Its Applications 8th Edition by Kenneth Rosen, ISBN-13: 978-1259676512

[PDF eBook eTextbook]

• Publisher: ‎ McGraw Hill; 8th edition (July 9, 2018)
• Language: ‎ English
• 1120 pages
• ISBN-10: ‎ 125967651X
• ISBN-13: ‎ 978-1259676512

Rosen’s Discrete Mathematics and its Applications presents a precise, relevant, comprehensive approach to mathematical concepts. This world-renowned best-selling text was written to accommodate the needs across a variety of majors and departments, including mathematics, computer science, and engineering. As the market leader, the book is highly flexible, comprehensive and a proven pedagogical teaching tool for instructors. Digital is becoming increasingly important and gaining popularity, crowning Connect as the digital leader for this discipline.

Table of Contents:

About the Author vi
Preface vii
Online Resources xvi
To the Student xix
1 The Foundations: Logic and Proofs . . . . . 1
1.1 Propositional Logic . . . . . . . . . . . . . . . . . . . 1
1.2 Applications of Propositional Logic. . . . . . . . . . . . . .17
1.3 Propositional Equivalences . . . . . . . . . . . . . . . . . . . . . 26
1.4 Predicates and Quantifiers . . . . . . . . . . . . . . . . . . . . . . 40
1.5 Nested Quantifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.6 Rules of Inference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
1.7 Introduction to Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . 84
1.8 Proof Methods and Strategy . . . . . . . . . . . . . . . . . . . . . 96
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 115
2 Basic Structures: Sets, Functions, Sequences, Sums,
and Matrices . . . . . . . . . . . . . . . . . . . . . . . . 121
2.1 Sets . . . . . . . . . . 121
2.2 Set Operations .. . . . . . . . . .133
2.3 Functions . . . . . 147
2.4 Sequences and Summations . . . . . . . . . . . . . . . . . . . . 165
2.5 Cardinality of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
2.6 Matrices . . . . . . 188
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 195
3 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 201
3.1 Algorithms. . . .201
3.2 The Growth of Functions . . . . . . . . . . . . . . . . . . . . . . 216
3.3 Complexity of Algorithms . . . . . . . . . . . . . . . . . . . . . 231
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 244
4 Number Theory and Cryptography . . .251
4.1 Divisibility and Modular Arithmetic . . . . . . . . . . . . 251
4.2 Integer Representations and Algorithms . . . . . . . . . 260
4.3 Primes and Greatest Common Divisors . . . . . . . . . 271
4.4 Solving Congruences. . . . . . . . . . . . . . . . . . . . . . . . . .290
4.5 Applications of Congruences . . . . . . . . . . . . . . . . . . 303
4.6 Cryptography . . . . . . . . . . .310
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 324
5 Induction and Recursion . . . . . . . . . . . . . 331
5.1 Mathematical Induction . . . . . . . . . . . . . . . . . . . . . . . 331
5.2 Strong Induction and Well-Ordering . . . . . . . . . . . . 354
5.3 Recursive Definitions and Structural Induction . . . 365
5.4 Recursive Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 381
5.5 Program Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . 393
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 398
6 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
6.1 The Basics of Counting. . . . . . . . . . . . . . . . . . . . . . . .405
6.2 The Pigeonhole Principle . . . . . . . . . . . . . . . . . . . . . . 420
6.3 Permutations and Combinations . . . . . . . . . . . . . . . . 428
6.4 Binomial Coefficients and Identities . . . . . . . . . . . . 437
6.5 Generalized Permutations and Combinations . . . . 445
6.6 Generating Permutations and Combinations . . . . . 457
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 461
7 Discrete Probability . . . . . . . . . . . . . . . . . .469
7.1 An Introduction to Discrete Probability . . . . . . . . . 469
7.2 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
7.3 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
7.4 Expected Value and Variance . . . . . . . . . . . . . . . . . . 503
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 520
8 Advanced Counting Techniques . . . . . . 527
8.1 Applications of Recurrence Relations . . . . . . . . . . . 527
8.2 Solving Linear Recurrence Relations . . . . . . . . . . . 540
8.3 Divide-and-Conquer Algorithms and Recurrence Relations . . . . . . . . . 553
8.4 Generating Functions . . . . . . . . . . . . . . . . . . . . . . . . . 563
8.5 Inclusion–Exclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 579
8.6 Applications of Inclusion–Exclusion . . . . . . . . . . . . 585
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 592
9 Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
9.1 Relations and Their Properties . . . . . . . . . . . . . . . . . 599
9.2 n-ary Relations and Their Applications. . . . . . . . . .611
9.3 Representing Relations . . . . . . . . . . . . . . . . . . . . . . . . 621
9.4 Closures of Relations. . . . . . . . . . . . . . . . . . . . . . . . . .628
9.5 Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . . . 638
9.6 Partial Orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 665
10 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .673
10.1 Graphs and Graph Models . . . . . . . . . . . . . . . . . . . . . 673
10.2 Graph Terminology and Special Types of Graphs 685
10.3 Representing Graphs and Graph Isomorphism . . . 703
10.4 Connectivity . . 714
10.5 Euler and Hamilton Paths . . . . . . . . . . . . . . . . . . . . . .728
10.6 Shortest-Path Problems. . . . . . . . . . . . . . . . . . . . . . . .743
10.7 Planar Graphs . 753
10.8 Graph Coloring 762
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 771
11 Trees .781
11.1 Introduction to Trees . . . . . . . . . . . . . . . . . . . . . . . . . . 781
11.2 Applications of Trees . . . . . . . . . . . . . . . . . . . . . . . . . 793
11.3 Tree Traversal . 808
11.4 Spanning Trees 821
11.5 Minimum Spanning Trees . . . . . . . . . . . . . . . . . . . . . 835
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 841
12 Boolean Algebra . . . . . . . . . . . . . . . . . . . . . 847
12.1 Boolean Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847
12.2 Representing Boolean Functions . . . . . . . . . . . . . . . 855
12.3 Logic Gates . . .. . . . . . . . . . 858
12.4 Minimization of Circuits . . . . . . . . . . . . . . . . . . . . . . 864
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 879
13 Modeling Computation . . . . . . . . . . . . . . 885
13.1 Languages and Grammars . . . . . . . . . . . . . . . . . . . . . 885
13.2 Finite-State Machines with Output. . . . . . . . . . . . . .897
13.3 Finite-State Machines with No Output . . . . . . . . . . 904
13.4 Language Recognition . . . . . . . . . . . . . . . . . . . . . . . . 917
13.5 Turing Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .927
End-of-Chapter Material . . . . . . . . . . . . . . . . . . . . . . 938
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . .A-1
1 Axioms for the Real Numbers and the Positive Integers . . . . . . . . . .A-1
2 Exponential and Logarithmic Functions . . . . . . . . .A-7
3 Pseudocode . . A-11
Suggested Readings B-1
Answers to Odd-Numbered Exercises S-1
Index of Biographies I-1

Ken Rosen (Middletown, NJ) is a distinguished member of the technical staff at AT & T Labs.

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