Modules

A list of all our modules.

Here is a summary of all the modules offered.

ℹ️ 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. ℹ️

The final exam is scheduled for Monday, December 16, 2024, from 6:00 PM to 8:00 PM in David Rittenhouse Lab A8, see listing on Courses @ Penn.
You can read more information and see photos of the exam room on the Schedule page.
If you have a conflict or are unable to attend the exam due to illness or other reasons, please let us know as soon as possible by submitting this form. Provide as much availability as possible, and we will work with you to arrange an alternative.

Course Introduction

Aug 27

Class Why Are You Here?, Administrivia: Slides , No recording

Aug 29

❌ Class cancelled

Aug 30

Recitation Recitation 0: Networking and Math Puzzlers: Slides

Sets, Relations and Functions

Sep 3

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

Sep 5

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

Sep 6

Recitation Recitation 1: Exercises on Sets: Slides

Sep 10

Class Lecture 3: Powersets and Cartesian Products: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§2), 🎥 Recording (Panopto), 📚 Davies §2.11-2.12 (pp. 25–28)

Sep 12

Homework Homework 1: Sets and Set Operations: Due Mon Sep 16 at 11:59PM, Online Part, Written Part , LaTeX template on Overleaf, Gradescope Submission

Class Lecture 4: Relations and functions: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.1 (pp. 35–37)

Sep 13

Recitation Recitation 2: Exercises on Relations: Slides

Sep 16

Homework Homework 2: Introduction to counting: Due Mon Sep 23 at 11:59PM, Online Part (only available starting Thursday Sept 19 at 12:01AM), Written Part , LaTeX template on Overleaf, Gradescope Submission

Sep 17

Class Lecture 5: Functions and their properties (injection/surjection/bijection): 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§3), 🎥 Recording (Panopto), 📚 Davies §3.6 and §3.7 (pp. 45–52)

Counting: Introduction to Combinatorics

Sep 19

Class Lecture 6: Introduction to counting: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§4), 🎥 Recording (Panopto), 📚 Davies §6.1 (pp. 141–147)

Sep 20

Recitation Recitation 3: Exercises on Countings: Slides

Sep 23

Homework Homework 3: Advanced Counting: Due Mon Sep 30 at 11:59PM, Online Part, Written Part , LaTeX template on Overleaf, Gradescope Submission (TBA)

Sep 24

Class Lecture 7: The bijection principle, permutations, combinations: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§5), 🎥 Recording (Panopto), 📚 Davies §6.2 (pp. 147–148)

Sep 26

Class Lecture 8: More advanced counting: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§6), 🎥 Recording (Panopto), 📚 Davies §6.2 (pp. 151-160)

Sep 27

Recitation Recitation 4: Exercises on Advanced Countings: Handout , Slides

Oct 1

Class Lecture 9A: Advanced Stars-and-Bars Examples: 👨‍🏫 Tablet Notes , 🎥 Recording (Panopto)

Discrete Probability

Oct 1

Class Lecture 9B: Introduction to Discrete Probability: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§7), 🎥 Recording (Panopto) [starting at 1 hour], 📚 Davies §4.1 (pp. 59-61)

Oct 3-6

🍂 Fall Break 🌿 Take a break, recharge, and enjoy! ✨

Oct 8

Class Lecture 10: Discrete Probability Continued: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§7), 🎥 Recording (Panopto), 📚 Davies §4.1 (pp. 59-61)

Oct 9

Homework Homework 4: Introduction to Discrete Probability: Due Mon Sep 30 at 11:59PM, Online Part, Written Part , LaTeX template on Overleaf, Gradescope Submission (TBA)

Oct 10

Class Lecture 11: Rules of Probability: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§8) and (§9), 🎥 Recording (Panopto), 📚 Davies §4.1 (pp. 59-61)

Oct 11

Recitation Recitation 5: Exam 1 Review: 📝 Sample Exam (Fall 2023 Exam 1) , Slides

Oct 15

Exam Exam 1: Sets, Relations, Functions, Counting: 📣 Announcement, 📝 Sample Exam (Fall 2023 Exam 1) , 🧩 Slido Polls from Lectures 00-10

Oct 17

Class Lecture 12: Independence & Random Variables: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§9) and (§10), 🎥 Recording (Panopto), 📚 Davies §4.4 (pp. 68)

Oct 18

Recitation Recitation 6: Exercises on Probability: Slides

Oct 22

Class Lecture 13: Expectation, Indicator Variables & Bayes’ Theorem: 👨‍🏫 Tablet Notes , (§10), 🎥 Recording (audio), 📚 Davies §4.4 (pp. 75)

Oct 24

Class Lecture 14: Continuing Expectation, Indicator Variables: 👨‍🏫 Tablet Notes , (§10), 📚 Davies §4.4 (pp. 75)

Oct 25

Recitation Recitation 7: Exercises on Advanced Probability: Slides

Logic

Oct 29

Class Lecture 15: Introduction to Logic: 🎥 Recording (Panopto), 📝 Lecture Notes (§11)

Oct 31

Class Lecture 16: More Logic: 🎥 Recording (Panopto)

Nov 1

Recitation Recitation 8: Exercises on Logic: Slides

Proof Methods

Nov 5

❌ Class cancelled

Nov 7

Class Lecture 18: Introduction on proof: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§13), 📚 Davies §4.1 (pp. 223-244), 🪄 Scheinermann's Proof Templates , 📚 Scheinermann Proof Chapter Part 1 , 📚 Scheinermann Proof Chapter Part 2

Nov 8

Recitation Recitation 9: Exercises on Proof: Slides

Nov 12

❌ Class cancelled

Nov 14

Class Lecture 19: Introduction to Induction: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§15), 📚 Davies §4.1 (pp. 231-240)

Nov 15

Recitation Recitation 10: Exercises on Induction: Slides

Nov 15

Homework Homework 5: Expectation and Logic: Due Mon Nov 25 at 11:59PM, Online Part, Written Part , LaTeX template on Overleaf, Gradescope Submission (TBA)

Nov 19

Class Lecture 20: Introduction to Strong Induction: 👨‍🏫 Tablet Notes , 📝 Lecture Notes (§16), 🎥 Recording (Passcode: Qs7ea&vS), 📚 Davies §4.1 (pp. 240-243)

Nov 21

Class Lecture 21: Introduction to Strong Induction: 👨‍🏫 Tablet Notes , Hand-Out

Nov 22

Recitation Recitation 11: Exercises on Strong Induction: Slides

Nov 22

Homework Homework 6: Proof: Due Mon Dec 2 at 11:59PM, Online Part, Written Part , LaTeX template on Overleaf, Gradescope Submission (TBA)

Introduction to Graphs

Nov 26

Class Lecture 22: Introduction to Graphs: 👨‍🏫 Tablet Notes , 🎥 Recording (Passcode:2B+isA!!)

Dec 3

Class Lecture 23: Questions on Graphs: 👨‍🏫 Tablet Notes , 🎥 Recording (Panopto)

Dec 5

Class Lecture 24: Induction and Proofs on Graphs: 👨‍🏫 Tablet Notes , 🎥 Recording (Panopto)

Dec 6

Recitation Recitation 12: Exercises on Graph: Slides

Final Exam

Dec 12

Review Session: 👨‍🏫 Tablet Notes , 🎥 Recording (Panopto), 👨‍🏫 Tablet Notes from Fall 2023 Recap , 📚 Tablet Notes from Fall 2023 Lectures

Dec 16

FINAL EXAM date confirmed on Oct 9, 2024, see announcement at top of page: 📣 Announcement, 📝 Sample Exam (Fall 2023 Final) , 🧩 Slido Polls from Lectures 11-24 , 📖 Review Session on Thur. Dec. 12th at 5:15PM (password to be posted on Ed)