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 4: Counting (18.200)
This lecture explores combinatorial counting techniques, focusing on binomial coefficients, bijections, and dual counting methods, demonstrating how Catalan numbers enumerate Dyck paths and various tree structures.
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 3: Inclusion-Exclusion (18.200)
Next · Lecture 5Lecture 5: More Counting and Generating Functions (18.200)
Seminar notes & discussion
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