Principles of Discrete Applied Mathematics
Massachusetts Institute of Technology via MIT OpenCourseWare
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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 {{% resource_link "8d257f11-e2b0-4925-8422-764c0519d33d" "CI-M" %}} (Communication Intensive in the Major) course and thus includes a writing component.
Syllabus
- Lecture 1: Pigeonhole Principle
- Lecture 2: Independence and Conditioning
- Lecture 3: Inclusion-Exclusion
- Lecture 4: Counting
- Lecture 5: More Counting and Generating Functions
- Lecture 6: More on Generating Functions
- Lecture 7: Generating Functions for Catalan Numbers
- Lecture 8: Tail Bounds
- Lecture 9: 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 & Shannon’s Noisy Coding Theorem
- Lecture 19: Error-Correcting Codes—Hamming Codes
- Lecture 20: Reed-Solomon Codes
Taught by
Prof. Ankur Moitra, Susan Ruff, and Prof. Peter Shor