CS 70: Discrete Mathematics and Probability Theory
CS 70: Discrete Mathematics and Probability Theory (Spring 2015, UC Berkeley). Instructor: Professor Umesh Vazirani. 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.
| Lecture 25 - Zipf's Law and Power Law Distributions |
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Go to the Course Home or watch other lectures:
| Lecture 01 - Introduction, Propositions and Quantifiers |
| Lecture 02 - Proofs |
| Lecture 03 - Induction |
| Lecture 04 - Induction (continued) and Recursion |
| Lecture 05 - Stable Marriage Problem |
| Lecture 06 - Graphs, Eulerian Tour |
| Lecture 07 - Graphs: Trees and Hypercubes |
| Lecture 08 - Modular Arithmetic |
| Lecture 09 - Bijections, RSA Cryptosystem |
| Lecture 10 - Fermat's Little Theorem and RSA, Polynomials |
| Lecture 11 - Polynomials, Secret Sharing, Erasure Codes |
| Lecture 12 - ECC (Error-Correcting Codes) |
| Lecture 13 - Infinity, Uncountability, Diagonalization |
| Lecture 14 - Self-reference, Quines and Godel |
| Lecture 15 - Probability: Counting |
| Lecture 16 - Probability: Sample Spaces, Events, Independence, Conditional Probability |
| Lecture 17 - Conditional Probability |
| Lecture 18 - Two Killer Applications: Hashing and Load Balancing |
| Lecture 19 - Random Variables and Expectation |
| Lecture 20 - Linearity of Expectation and Examples, Independence, Variance |
| Lecture 21 - Variance, Chebyshev Inequality |
| Lecture 22 - Some Important Distributions: Binomial, Geometric, and Poisson Distributions |
| Lecture 23 - Continuous Probability |
| Lecture 24 - Inference |
| Lecture 25 - Zipf's Law and Power Law Distributions |
| Lecture 26 - How to Lie with Statistics |