Lecture 1: Pigeonhole Principle (18.200)
1:13:47Lecture 2: Independence and Conditioning (18.200)
1:10:58Lecture 3: Inclusion-Exclusion (18.200)
1:19:29Lecture 4: Counting (18.200)
1:18:26Lecture 5: More Counting and Generating Functions (18.200)
1:11:45Lecture 6: More on Generating Functions (18.200)
1:19:54Lecture 7: Generating Functions for Catalan Numbers (18.200)
1:11:49Lecture 8: Tail Bounds (18.200)
1:20:53Lecture 9: Chernoff Bounds (18.200)
55:18Lecture 10: Modular Arithmetic (18.200)
1:18:50Lecture 11: Basic Group Theory (18.200)
1:15:24Lecture 12: Introduction to Linear Programming (18.200)
1:14:04Lecture 13: Duality in Linear Programming (18.200)
1:16:12Lecture 14: Zero-Sum Games (18.200)
1:14:18Lecture 15: Max-Flow Min-Cut Theorem (18.200)
1:17:52Lecture 16: Data Compression and Shannon’s Noiseless Coding Theorem (18.200)
1:08:50Lecture 17: Huffman Coding (18.200)
1:17:59Lecture 18: Transmitting Information Reliably over a Noisy Channel & Shannon’s Noisy Coding Theorem (18.200)
1:12:21Lecture 19: Error-Correcting Codes—Hamming Codes (18.200)
1:18:31Lecture 20: Reed-Solomon Codes (18.200)
1:05:47Lecture 7: Generating Functions for Catalan Numbers (18.200)
This lecture focuses on deriving the generating function for Catalan numbers and subsequently using it to obtain their explicit formula, a key result in combinatorial mathematics.
MIT 18.200 Principles of Discrete Applied Mathematics, Spring 2024
Instructor: Peter Shor
View the complete course: https://ocw.mit.edu/courses/18-200-principles-of-discrete-applied-mathematics-spring-2024
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61p2fXeXjNCrfNHFwyW-bl0
Lecture 6: More on Generating Functions (18.200)
Next · Lecture 8Lecture 8: Tail Bounds (18.200)