CS 70: Discrete Mathematics and Probability Theory
CS 70: Discrete Mathematics and Probability Theory (Fall 2012, 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.
| Lecture 02 - Quantifiers, Proofs |
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Go to the Course Home or watch other lectures:
| Lecture 01 - Instruction, Propositions and Quantifiers |
| Lecture 02 - Quantifiers, Proofs |
| Lecture 03 - Proofs |
| Lecture 04 - Induction |
| Lecture 05 - Induction: Three Forms of Induction, Strengthening the Induction Hypothesis |
| Lecture 06 - The Stable Marriage Problem |
| Lecture 07 - Modular Arithmetic |
| Lecture 08 - Euclid's GCD Algorithm, Bijections |
| Lecture 09 - Fermat's Little Theorem, RSA Cryptosystem |
| Lecture 10 - Polynomials, Finite Fields |
| Lecture 11 - Secret Sharing, Finite Fields, Erasure Codes |
| Lecture 12 - Error Correcting Codes |
| Lecture 13 |
| Lecture 14 - Graphs and Induction |
| Lecture 15 - Counting |
| Lecture 16 - Probability |
| Lecture 17 - Birthday Paradox, Monty Hall Paradox |
| Lecture 18 |
| Lecture 19 - Independence, Unions, Random Variables |
| Lecture 20 - Expectation Variance |
| Lecture 21 - Variance, Markov's Inequality, Chebyshev's Inequality |
| Lecture 22 - Geometric, Poisson Distributions |
| Lecture 23 - Continuous Probability |
| Lecture 24 - Exponential Distribution, Gaussian Distribution, Kalman Filter |
| Lecture 25 - Inference, Kalman Filter, Midterm |
| Lecture 26 - Countable, Uncountable, Uncomputable |