A course designed to prepare math, computer science, and engineering majors for a background in abstraction, notation, and critical thinking for the mathematics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, combinatorics, discrete probability, recursion, sequence and recurrence, elementary number theory, graph theory, and mathematical proof techniques.
Discrete Mathematics and Its Applications 8th Edition (Rosen) - Chapters 1-11
Textbook Link| Full Discrete Mathematics Notes |
| Chapter 1 - Logic and Proofs (8/25/24 - 9/15/24) |
Propositional Logic Propositional Equivalences Predicates and Quantifiers Nested Quantifiers Rules of Inference Introduction to Proofs Proof Methods and Strategy |
Notes |
| Chapter 2 - Sets, Functions, Sequences, Sums, and Matrices (9/16/24 - 9/30/24) |
Sets Set Operations Functions Sequences and Summations |
Notes |
| Chapter 3 - Algorithms (9/30/24 - 10/2/24) | Algorithms | Notes |
| Chapter 4 - Number Theory and Cryptography (10/2/24 - 10/18/24) |
Divisibility and Modular Arithmetic Integer Representation and Algorithms Primes and Greatest Common Divisors Solving Congruences |
Notes |
| Chapter 5 - Induction and Recursion (10/19/24 - 11/3/24) |
Mathematical Induction Strong Induction and Well-Ordering Recursive Definitions and Structural Induction Recursive Algorithms |
Notes |
| Chapter 6 - Counting (11/4/24 - 11/22/24) |
The Basics of Counting The Pigeonhole Principle Permutations and Combinations Binomial Coefficients and Identities Generalized Permutations and Combinations |
Notes |
| Chapter 7 - Discrete Probability (11/23/24 - 11/27/24) | An Introduction to Discrete Probability | Notes |
| Chapter 8 - Advanced Counting Techniques (11/28/24 - 12/3/24) |
Applications of Recurrence Relations Inclusion-Exclusion |
Notes |
| Chapter 9 - Relations (12/4/24 - 12/5/24) | Relations and the Properties | Notes |
| Chapter 10 - Graphs (12/6/24 - 12/7/24) |
Graphs and Graph Models Graph Terminology and Special Types of Graphs |
Notes |
| Chapter 11 - Trees (12/8/24 - 12/10/24) | Introduction to Trees | Notes |