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18.200 Principles of Discrete Applied Mathematics

18.200 Principles of Discrete Applied Mathematics (Spring 2024, MIT OCW). Instructors: Prof. Ankur Moitra, Prof. Peter Shor, and Susan Ruff. This course will teach you illustrative topics in discrete applied mathematics, including counting, generating functions, probability, linear optimization, algebraic structures, basic number theory, information theory, and coding theory. It is a CI-M (Communication Intensive in the Major) course and thus includes a writing component. (from ocw.mit.edu)

Lecture 05 - More Counting and Generating Functions

We prove the Cayley tree theorem by counting in two ways. We then explain the basics of generating functions - what is a generating function, and how we combine two generating functions (e.g. adding them and multiplying them).


Go to the Course Home or watch other lectures:

Lecture 01 - Pigeonhole Principle
Lecture 02 - Independence and Conditioning
Lecture 03 - Inclusion-Exclusion
Lecture 04 - Counting
Lecture 05 - More Counting and Generating Functions
Lecture 06 - More on Generating Functions
Lecture 07 - Generating Functions for Catalan Numbers
Lecture 08 - Tail Bounds
Lecture 09 - Chernoff Bounds
Lecture 10 - Modular Arithmetic
Lecture 11 - Basic Group Theory
Lecture 12 - Introduction to Linear Programming
Lecture 13 - Duality in Linear Programming
Lecture 14 - Zero-Sum Games
Lecture 15 - Max-Flow Min-Cut Theorem
Lecture 16 - Data Compression and Shannon's Noiseless Coding Theorem
Lecture 17 - Huffman Coding
Lecture 18 - Transmitting Information Reliably over a Noisy Channel and Shannon's Noisy Coding Theorem
Lecture 19 - Error-Correcting Codes - Hamming Codes
Lecture 20 - Reed-Solomon Codes