MATH 2305 - Discrete Mathematics (Fall 2024) |
Dallas College - Brookhaven Campus |
Instructor: Dr. Janak Joshi |
Course Description |
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.
Textbook |
Discrete Mathematics and Its Applications 8th Edition (Rosen) - Chapters 1-11
Textbook Link| Full Discrete Mathematics Notes |
Notes by Unit |
| 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 |
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