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Discrete Mathematics and Its Applications, 7th Edition Discrete Mathematics and Its Applications, 7th Edition
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
Algorithms
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
Counting
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
Relations
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
Graphs
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
Trees
11.1 | Introduction to Trees | Exercises | p.755 |
11.2 |
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