Discrete Mathematics with Applications, 7th Edition

Discrete Mathematics with Applications, 7th Edition Discrete Mathematics with Applications, 7th ...

ISBN: 9780073383095 / 0073383090

Table of Contents

Chapter 1

The Foundations: Logic And Proofs

1.1 Propositional Logic Exercises p.12
1.2 Applications of Propositional Logic Exercises p.22
1.3 Propositional Equivalences Exercises p.34
1.4 Predicates and Quantifiers Exercises p.53
1.5 Nested Quantifiers Exercises p.64
1.6 Rules of Inference Exercises p.78
1.7 Introduction to Proofs Exercises p.91
1.8 Proof Methods and Strategy Exercises p.108
Review Questions p.111
Supplementary Exercises p.111

Chapter 2

Basic Structures: Sets, Functions, Sequences, Sums, And ...

2.1 Sets Exercises p.125
2.2 Set Operations Exercises p.136
2.3 Functions Exercises p.152
2.4 Sequences and Summations Exercises p.167
2.5 Cardinality of Sets Exercises p.176
2.6 Matrices Exercises p.183
Review Questions p.186
Supplementary Exercises p.187

Chapter 3


3.1 Algorithms Exercises p.202
3.2 The Growth of Functions Exercises p.216
3.3 Complexity of Algorithms Exercises p.229
Review Questions p.232
Supplementary Exercises p.233

Chapter 4

Number Theory And Cryptography

4.1 Divisibility and Modular Arithmetic Exercises p.244
4.2 Integer Representations and Algorithms Exercises p.255
4.3 Primes and Greatest Common Divisors Exercises p.272
4.4 Solving Congruences Exercises p.284
4.5 Applications of Congruences Exercises p.292
4.6 Cryptography Exercises p.304
Review Questions p.307
Supplementary Exercises p.307

Chapter 5

Induction And Recursion

5.1 Mathematical Induction Exercises p.329
5.2 Strong Induction and Well-Ordering Exercises p.341
5.3 Recursive Definitions and Structural Induction Exercises p.357
5.4 Recursive Algorithms Exercises p.370
5.5 Program Correctness Exercises p.377
Review Questions p.378
Supplementary Exercises p.379

Chapter 6


6.1 The Basics of Counting Exercises p.396
6.2 The Pigeonhole Principle Exercises p.405
6.3 Permutations and Combinations Exercises p.413
6.4 Binomial Coefficients and Identities Exercises p.421
6.5 Generalized Permutations and Combinations Exercises p.432
6.6 Generating Permutations and Combinations Exercises p.438
Review Questions p.439
Supplementary Exercises p.440

Chapter 7

Discrete Probability

7.1 An Introduction to Discrete Probability Exercises p.451
7.2 Probability Theory Exercises p.466
7.3 Bayes' Theorem Exercises p.475
7.4 Expected Value and Variance Exercises p.492
Review Questions p.495
Supplementary Exercises p.496

Chapter 8

Advanced Counting Techniques

8.1 Applications of Recurrence Relations Exercises p.510
8.2 Solving Linear Recurrence Relations Exercises p.524
8.3 Divide-and-Conquer Algorithms and Recurrence Relations Exercises p.535
8.4 Generating Functions Exercises p.549
8.5 Inclusion-Exclusion Exercises p.557
8.6 Applications of Inclusion-Exclusion Exercises p.564
Review Questions p.566
Supplementary Exercises p.567

Chapter 9


9.1 Relations and Their Properties Exercises p.581
9.2 n-ary Relations and Their Applications Exercises p.589
9.3 Representing Relations Exercises p.596
9.4 Closures of Relations Exercises p.606
9.5 Equivalence Relations Exercises p.615
9.6 Partial Orderings Exercises p.630
Review Questions p.634
Supplementary Exercises p.635

Chapter 10


10.1 Graphs and Graph Models Exercises p.649
10.2 Graph Terminology and Special Types of Graphs Exercises p.665
10.3 Representing Graphs and Graph Isomorphism Exercises p.675
10.4 Connectivity Exercises p.689
10.5 Euler and Hamilton Paths Exercises p.703
10.6 Shortest-Path Problems Exercises p.716
10.7 Planar Graphs Exercises p.725
10.8 Graph Coloring Exercises p.732
Review Questions p.737
Supplementary Exercises p.738

Chapter 11


11.1 Introduction to Trees Exercises p.755
11.2 Applications of Trees Exercises p.769
11.3 Tree Traversal Exercises p.783
11.4 Spanning Trees Exercises p.795
11.5 Minimum Spanning Trees Exercises p.802
Review Questions p.804
Supplementary Exercises p.805

Chapter 12

Boolean Algebra

12.1 Boolean Functions Exercises p.818
12.2 Representing Boolean Functions Exercises p.822
12.3 Logic Gates Exercises p.827
12.4 Minimization of Circuits Exercises p.841
Review Questions p.844
Supplementary Exercises p.844

Chapter 13

Modeling Computation

13.1 Languages and Grammar Exercises p.856
13.2 Finite-State Machines with Output Exercises p.863
13.3 Finite-State Machines with No Output Exercises p.875
13.4 Language Recognition Exercises p.887
13.5 Turing Machines Exercises p.897
Review Questions p.900
Supplementary Exercises p.901

Chapter A


A3 Pseudocode Exercises p.A-16
A2 Exponential and Logarithmic Functions Exercises p.A-9
A1 Axioms for the Real Numbers and the Positive Integers Exercises p.A-6
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