Syllabus of Math 314: Discrete Mathematics

Textbook

List of material to be covered

In brief: Chapters 1-7 and 9 and a selection of topics from Chapters 8, 10, 12, 13.

Chapter 1: Yes, There are Proofs!

1. Compound Statements
2. Proofs in Mathematics
3. Truth Tables
4. The Algebra of Propositions
5. Logical Arguments

Chapter 2: Sets and Relations

1. Sets
2. Operations on Sets
3. Binary Relations
4. Equivalence Relations
5. Partial Orders

Chapter 3: Functions

1. Domain, Range, One-to-One, Onto
2. Inverses and Composition
3. One-to-One Correspondence and the Cardinality of a Set

Chapter 4: The Integers

1. The Division Algorithm
2. Divisibility and the Euclidean Algorithm
3. Prime Numbers
4. Congruence
5. Applications of Congruence

Chapter 5: Induction and Recursion

1. Mathematical Induction
2. Recursively Defined Sequences
3. Solving Recurrence Relations: The Characteristic Polynomial
4. Solving Recurrence Relations: Generating Functions

Chapter 6: Principles of Counting

1. The Principle of Inclusion-Exclusion
2. The Addition and Multiplication Rules
3. The Pigeon-Hole Principle

Chapter 7: Permutations and Combinations

1. Permutations
2. Combinations
3. Repetitions

Additional material to be decided.