Modules

This is the entire course content organized into modules.

Extension Policy
If you would like an extension for the HW, simply fill out the extension request form here; as per course policy, any extension requested before the due date is granted.

Important Dates for Fall 2025
Fall Break: October 9-13, 2025 🍂
Exam 1: Tuesday, October 14, 2025 (Sets, Relations, Functions, Counting)
Exam 2: Tuesday, November 25, 2025 (Probability, Logic, and Proofs)
Thanksgiving Break: November 27 - December 1, 2025 🦃
Last Day of Classes: December 4, 2025
Final Exam: Date and location TBA (during exam period Dec 15-20)
Will cover all topics (Final = Exam 1 + Exam 2)

Course Introduction

Aug 26

Class Lecture 0: Why Are You Here?: Slides , 🔊 Recording (Panopto, audio only), ⚙️ Transcript

Sets, Relations and Functions

Aug 28

Class Lecture 1: Sets, definition and notation: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§1), 🎥 Recording (Panopto), 📚 Davies §2.1–2.6 (pp. 7–16)

Aug 29

Recitation Recitation 0: Speed Networking and LaTeX Overview: Slides

Sep 2

Class Lecture 2: Set operations: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§1, continued), 🎥 Recording (Panopto), 📚 Davies §2.7-2.10 (pp. 16–25)

Sep 4

Class Lecture 3: Set operations (continued): 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§1, continued), 🎥 Recording (Panopto), 📚 Davies §2.7-2.10 (pp. 16–25)

Sep 5

Recitation Recitation 1: Exercises on Sets: Resource not found.

Sep 9

Class Lecture 4: Powersets and Cartesian Products: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§2), 🎥 Recording (Panopto), 📚 Davies §2.11-2.12 (pp. 25–28)

Sep 11

Class Lecture 5: Relations: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.1 (pp. 35–37)

Sep 12

Recitation Recitation 2: Exercises on Relations: Resource not found.

Homework Homework 1: Sets and Set Operations: Due Monday, September 22, 2025 at 11:59 PM, Online Part, Written Part

Sep 16

Class Lecture 6: Properties of Relations: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.5 (pp. 40–44)

Sep 18

Class Lecture 7: Functions: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.6 and §3.7 (pp. 45–52)

📝 Lectures below will be updated as the semester progresses, none of the dates below have been updated

Class Lecture 8: Properties of Functions (injection/surjection/bijection): 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.6 and §3.7 (pp. 45–52)

Counting: Introduction to Combinatorics

Sep 18

Class Lecture 7: Introduction to counting: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§4), 🎥 Recording (Panopto), 📚 Davies §6.1 (pp. 141–147)

Sep 19

Recitation Recitation 3: Exercises on Counting: Resource not found.

Homework Homework 2: Introduction to counting: Due ??, Online Part,
Resource not found.

Sep 23

Class Lecture 8: The bijection principle, permutations, combinations: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§5), 🎥 Recording (Panopto), 📚 Davies §6.2 (pp. 147–148)

Sep 25

Class Lecture 9: More advanced counting: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§6), 🎥 Recording (Panopto), 📚 Davies §6.2 (pp. 151-160)

Sep 26

Recitation Recitation 4: Exercises on Advanced Counting

Resource not found.

Sep 30

Class Lecture 10: Advanced Stars-and-Bars Examples: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§6), 🎥 Recording (Panopto), 📚 Davies §6.3 (pp. 160-165)

Oct 2

Class Lecture 11: Inclusion-Exclusion Principle: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§6), 🎥 Recording (Panopto), 📚 Davies §6.4 (pp. 165-170)

Oct 3

Recitation Recitation 5: Review for Exam 1: Resource not found.

Homework Homework 3: Advanced Counting: Due ??, Online Part,
Resource not found.

Discrete Probability

Oct 7

Class Lecture 12: Introduction to Discrete Probability: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§7), 🎥 Recording (Panopto), 📚 Davies §4.1 (pp. 59-61)

Oct 9-13

🍂 Fall Break 🍁 Take a break, recharge, and enjoy the autumn! 🎃✨

Oct 14

Exam Exam 1: Sets, Relations, Functions, Counting: 📝
Resource not found.

Oct 16

Class Lecture 13: Discrete Probability Continued: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§7), 🎥 Recording (Panopto), 📚 Davies §4.1 (pp. 59-61)

Oct 17

Recitation Recitation 6: Exercises on Probability: Resource not found.

Homework Homework 4: Introduction to Discrete Probability: Due ??, Online Part,
Resource not found.

Oct 21

Class Lecture 14: Rules of Probability: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§8) and (§9), 🎥 Recording (Panopto), 📚 Davies §4.2-4.3 (pp. 61-68)

Oct 23

Class Lecture 15: Independence & Random Variables: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§9) and (§10), 🎥 Recording (Panopto), 📚 Davies §4.4 (pp. 68-75)

Oct 24

Recitation Recitation 7: Exercises on Advanced Probability: Resource not found.

Logic

Oct 28

Class Lecture 16: Expectation, Indicator Variables & Bayes’ Theorem: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§10), 🎥 Recording (Panopto), 📚 Davies §4.4-4.5 (pp. 75-83)

Homework Homework 5: Advanced Probability: Due Mon Nov 4 at 11:59PM, Online Part,
Resource not found.

Oct 30

Class Lecture 17: Introduction to Logic - Propositional Logic: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§11), 🎥 Recording (Panopto), 📚 Davies §8.1-8.4 (pp. 231-241)

Oct 31

Recitation Recitation 8: Exercises on Logic: Resource not found.

Nov 4

Class Lecture 18: Boolean Algebra and Normal Forms: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§11), 🎥 Recording (Panopto), 📚 Davies §8.5-8.6 (pp. 241-249)

Nov 6

Class Lecture 19: Predicate Logic: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§12), 🎥 Recording (Panopto), 📚 Davies §8.7-8.9 (pp. 249-258)

Nov 7

Recitation Recitation 9: Exercises on Predicate Logic: Resource not found.

Homework Homework 6: Logic: Due ??, Online Part,
Resource not found.

Proof Methods

Nov 11

Class Lecture 20: Introduction to Proofs: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§13), 🎥 Recording (Panopto), 📚 Davies §9.1-9.3 (pp. 267-276)

Nov 13

Class Lecture 21: Direct Proofs and Proof by Contrapositive: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§13), 🎥 Recording (Panopto), 📚 Davies §9.4-9.5 (pp. 276-283)

Nov 14

Recitation Recitation 10: Exercises on Proofs: Resource not found.

Nov 18

Class Lecture 22: Proof by Contradiction: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§14), 🎥 Recording (Panopto), 📚 Davies §9.6 (pp. 283-287)

Homework Homework 7: Proofs: Due Mon Nov 25 at 11:59PM, Online Part,
Resource not found.

Nov 20

Class Lecture 23: Mathematical Induction (Weak Induction): 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§15), 🎥 Recording (Panopto), 📚 Davies §9.7 (pp. 287-295)

Nov 21

Recitation Recitation 11: Exam 2 Review

📝

Resource not found.

Nov 25

Exam Exam 2: Probability, Logic, and Proofs: 📝
Resource not found.

Nov 27 - Dec 1

🦃 Thanksgiving Break 🍂 Enjoy time with family and friends! Rest and recharge! 🍁🥧

Dec 1 (?)

Class Lecture 24: Strong Induction and Structural Induction: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§16), 🎥 Recording (Panopto), 📚 Davies §9.8 (pp. 295-301)

Introduction to Graphs

Dec 2

Class Lecture 25: Introduction to Graphs: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§17), 🎥 Recording (Panopto), 📚 Davies §5.1-5.3 (pp. 97-108)

Dec 4

Class Lecture 26: Trees and Graph Coloring: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§18), 🎥 Recording (Panopto), 📚 Davies §5.4-5.6 (pp. 108-120)

Dec 5

Recitation Recitation 12: Final Exam Review: Resource not found.

Homework Homework 8: Introduction to Graphs (Optional/Extra Credit): Due ??, Online Part,
Resource not found.

Final Exam

Dec 8-15

📚 Reading Days Review all course materials and prepare for the final exam

Dec 15-20

Final Exam Date and Location TBA: The final exam will be comprehensive, covering all topics from the semester:

Sets, Relations, and Functions
Counting and Combinatorics
Discrete Probability
Logic (Propositional and Predicate)
Proof Methods (Direct, Contrapositive, Contradiction, Induction)
Introduction to Graphs : 📝
Resource not found.
: 📚
Resource not found.