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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 07 - Generating Functions for Catalan Numbers

We derive the formula for the generating functions of Catalan numbers, and we then use it to give the formula for Catalan numbers.

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