### 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 | 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

Appendix

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 |