Course Videos

Week 01 - Propositions

• How to complete Homework 1 Overview (11:07)

• Homework 01 - Getting Started (2:37)

• Homework 01 - Entering Text Answers (10:09)

• Homework 01 - Entering LaTeX Answers (2:20)

• Homework 01 - Entering Python Answers (4:18)

Week 02 - Quantifiers

• Challenge 1.5.1 Help (2:41)

• Challenge 1.9.1 Help (2:56)

• Challenge 1.10.1 Help (5:05)

Week 03 - Sets

• Introduction to Sets (7:19)

• Using Python to work with Sets (6:30)

• What is Cartesian Product? (7:14)

Week 04 - Functions

• Functions Part 1 - Review Cartesian Product and Power Set (2:18)

• Functions Part 2 - Domain and Codomain (5:29)

• Functions Part 3 - Floor and Ceiling (1:11)

• Functions Part 4 - Classifying Functions (one-to-one and onto) (6:13)

• Functions Part 5 - Inverse of a Function (2:04)

Week 05 - Relations

• Relations Part 1 - Review (2:52)

• Relations Part 2 - Introduction to Relations (2:58)

• Relations Part 3 - Properties of Binary Relations (20:25)

• Relations Part 4 - Direct Graphs and Relations (3:06)

Week 06 - Graphs

• Handshaking Theorem (7:41)

• Finding an Euler Circuit (5:07)

• Finite State Machines Part 1 - Introduction (6:00)

• Finite State Machines Part 2 - Producing Output (12:23)

• Finite State Machines Part 3 - Recognizing a Language (10:07)

Week 07 - Trees

• Huffman (Prefix) Trees (20:46)

• Shorter Example of Huffman (Prefix) Encoding (6:44)

• Breadth-first and Depth-first Search (8:08)

• Prim's Algorithm (5:44)

• Python Implementation of Huffman Encoding (Optional for those interested) (9:33)

Week 08 - Sequences, Summations, Recursion

• Sequences in Python (8:39)

• Summations in Python (3:24)

• Recurrence Relations in Python (6:26)

Week 09 - Prime Numbers, Modular Arithmetic, GCD, Euclid's Algorithm

• Linear Combinations (5:19)

• Modular Arithmetic - Addition and Multiplication (7:09)

• Congruences and Equivalence Classes (3:59)

• Simplifying Computations Using Modular Arithmetic (8:57)

• Calculating Exponents with Modular Arithmetic (3:09)

• GCD and Euclid's GCD Algorithm (11:20)

• Modular Multiplicative Inverse or MMI (5:18)

• Extended Euclidean Algorithm example (11:44)

Week 10 - Fast Exponentiation, RSA Cryptography

• Extended Euclidean Algorithm Review (9:04)

• Converting between number bases (9:09)

• Fast Modular Exponentiation (8:13)

• Symmetric Encryption (7:41)

• RSA Algorithm Part I (12:42)

• RSA Algorithm Part II (8:30)

Week 11 - Counting

• Introduction to Counting, Sum and Product Rule (15:53)

• Counting Techniques - Permutations and Combinations (11:11)

• Simplifying Factorials (1:13)

• More Counting Techniques (12:00)

Week 12 - More Counting

• Generating Permutations (10:08)

• Binomial Coefficients (9:30)

• Pascal's Triangle (4:31)

• The Pigeonhole Principle (12:12)

Week 13 - Discrete Probability

• Introduction to Discrete Probability (10:39)

• Probability Distribution and Other Probability Examples (8:30)

• Using Python to Explore Probability (10:07)

• Conditional Probability (7:52)

• Bayes' Theorem Example (5:47)