Tentative Schedule and Learning Goals¶
You should aim to complete all assigned readings in advance of the corresponding classroom sessions. This will facilitate a much deeper understanding of the material as we work through additional examples in class and it will also help you complete the assigned homework. Please follow the links (as they become available) in the Due column below to see all assigned exercises.
| Class | Topics | Readings | Due |
|---|---|---|---|
| 9/4 | Preliminaries; Propositional Logic | 1; 2.1 | |
| 9/9 | Logic: Statements; Arguments | 2.2–2.3 | |
| 9/11 | Application: Digital Circuits | 2.4–2.5 | Hw1 |
| 9/16 | Quantified Statements | 3.1–3.2 | |
| 9/18 | Logical arguments with quantifiers | 3.3–3.4 | Hw2 |
| 9/23 | Direct Proofs | 4.1–4.4 | |
| 9/25 | Indirect Proofs | 4.5–4.7 | Hw3 |
| 9/30 | Sequences | 5.1 | |
| 10/2 | Induction | 5.2–5.3 | Hw4 |
| 10/7 | Strong Induction | 5.4 | |
| 10/9 | Application: The GCD Algorithm | 4.8; 5.5 | Midterm 1 |
| Fall Break | |||
| Oct 12–20 | |||
| 10/21 | Recursive definitions of sequences | 5.6 | |
| 10/23 | Solving Recurrences | 5.7–5.8 | Hw5 |
| 10/28 | Recursion & Induction | 5.9 | |
| 10/30 | Set theory | 6 (all sections) | Hw6 |
| 11/4 | Functions | 7.1–7.3 | |
| 11/6 | Relations | 8.1–8.3 | Hw7 |
| 11/11 | Application: Modular Arithmetic | 8.4 | |
| 11/13 | Counting: Product/Sum Rules | 9.1–9.3 | Hw8 |
| 11/18 | Pigeonhole principle | 9.4 | |
| 11/20 | Combinations | 9.5–9.6 | Midterm 2 |
| 11/25 | Binomial Theorem | 9.7 | |
| 11/27 | Probability basics | 9.8 | Hw9 |
| Thanksgiving Break: Nov 27 (after classes) - Dec 1 | |||
| 12/2 | Conditional Probability | 9.9 | |
| 12/4 | Graphs: Trails, Paths, Circuits | 10.1–10.2 | Hw10 |
| 12/9 | Trees | 10.5–10.6 | |
| 12/11 | Application: Coloring Graphs | Instructor Notes | Hw11 |
| Review Period: Dec 13-14; Exam Period: Dec 15-20 | |||
Learning Outcomes¶
By the end of this course, students will be able to:
- construct logical statements from natural language descriptions, and vice versa.
- develop proofs for mathematical statements and the correctness of simple computational procedures.
- perform combinatorial and probability calculations by using techniques for counting.
- reason about fundamental concepts and properties of discrete combinatorial structures like graphs and trees
- develop basic computational thinking skills and an appreciation for the critical role played by discrete mathematics in computational applications.