CS 70: Discrete Mathematics and Probability Theory (Spring 2015, UC Berkeley). Instructor: Professor Umesh Vazirani.
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September 26, 2023
English
English [CC]
Description
This course discusses the foundation for many algorithms, concepts, and techniques in the field of Electrical Engineering and Computer Science. Topics covered in this course include: Logic, infinity, and induction; applications include undecidability and stable marriage problem. Modular arithmetic and GCDs; applications include primality testing and cryptography. Polynomials; examples include error correcting codes and interpolation. Probability including sample spaces, independence, random variables, law of large numbers; examples include load balancing, existence arguments, Bayesian inference.
Course Curriculum
- Lecture 01 – Introduction, Propositions and Quantifiers Unlimited
- Lecture 02 – Proofs Unlimited
- Lecture 03 – Induction Unlimited
- Lecture 04 – Induction (continued) and Recursion Unlimited
- Lecture 05 – Stable Marriage Problem Unlimited
- Lecture 06 – Graphs, Eulerian Tour Unlimited
- Lecture 07 – Graphs: Trees and Hypercubes Unlimited
- Lecture 08 – Modular Arithmetic Unlimited
- Lecture 09 – Bijections, RSA Cryptosystem Unlimited
- Lecture 10 – Fermat’s Little Theorem and RSA, Polynomials Unlimited
- Lecture 11 – Polynomials, Secret Sharing, Erasure Codes Unlimited
- Lecture 12 – ECC (Error-Correcting Codes) Unlimited
- Lecture 13 – Infinity, Uncountability, Diagonalization Unlimited
- Lecture 14 – Self-reference, Quines and Godel Unlimited
- Lecture 15 – Probability: Counting Unlimited
- Lecture 16 – Probability: Sample Spaces, Events, Independence, Conditional Probability Unlimited
- Lecture 17 – Conditional Probability Unlimited
- Lecture 18 – Two Killer Applications: Hashing and Load Balancing Unlimited
- Lecture 19 – Random Variables and Expectation Unlimited
- Lecture 20 – Linearity of Expectation and Examples, Independence, Variance Unlimited
- Lecture 21 – Variance, Chebyshev Inequality Unlimited
- Lecture 22 – Some Important Distributions: Binomial, Geometric, and Poisson Distributions Unlimited
- Lecture 23 – Continuous Probability Unlimited
- Lecture 24 – Inference Unlimited
- Lecture 25 – Zipf’s Law and Power Law Distributions Unlimited
- Lecture 26 – How to Lie with Statistics Unlimited
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