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 5: More Counting and Generating Functions (18.200)
The Cayley tree theorem is proved through double counting. The lecture then introduces generating functions, detailing their basic structure and methods for combination, such as addition and multiplication.
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 4: Counting (18.200)
Next · Lecture 6Lecture 6: More on Generating Functions (18.200)