Pigeonhole Principle
1:13:47Independence and Conditioning
1:10:58Inclusion-Exclusion
1:19:29Counting
1:18:26More Counting and Generating Functions
1:11:45More on Generating Functions
1:19:54Generating Functions for Catalan Numbers
1:11:49Tail Bounds
1:20:53Chernoff Bounds
55:18Modular Arithmetic
1:18:50Basic Group Theory
1:15:24Introduction to Linear Programming
1:14:04Duality in Linear Programming
1:16:12Zero-Sum Games
1:14:18Max-Flow Min-Cut Theorem
1:17:52Data Compression and Shannon’s Noiseless Coding Theorem
1:08:50Huffman Coding
1:17:59Transmitting Information Reliably over a Noisy Channel & Shannon’s Noisy Coding Theorem
1:12:21Error-Correcting Codes—Hamming Codes
1:18:31Reed-Solomon Codes
1:05:47Transmitting Information Reliably over a Noisy Channel & Shannon’s Noisy Coding Theorem
This lecture explores reliable information transmission over noisy channels, beginning with repetition codes, and proves Shannon's noisy coding theorem for the binary symmetric channel.
MIT 18.200 Principles of Discrete Applied Mathematics, Spring 2024