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CS 70: Discrete Mathematics and Probability Theory (Spring 2015, UC Berkeley). Instructor: Professor Umesh Vazirani.
FREE
This course includes
Hours of videos
722 years, 1 month
Units & Quizzes
26
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
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 Currilcum
- 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
