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CS 70: Discrete Mathematics and Probability Theory (Fall 2012, UC Berkeley). Instructor: Professor Umesh Vazirani.
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English [CC]
FREE
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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.
Course content
- Lecture 01 – Instruction, Propositions and Quantifiers Unlimited
- Lecture 02 – Quantifiers, Proofs Unlimited
- Lecture 03 – Proofs Unlimited
- Lecture 04 – Induction Unlimited
- Lecture 05 – Induction: Three Forms of Induction, Strengthening the Induction Hypothesis Unlimited
- Lecture 06 – The Stable Marriage Problem Unlimited
- Lecture 07 – Modular Arithmetic Unlimited
- Lecture 08 – Euclid’s GCD Algorithm, Bijections Unlimited
- Lecture 09 – Fermat’s Little Theorem, RSA Cryptosystem Unlimited
- Lecture 10 – Polynomials, Finite Fields Unlimited
- Lecture 11 – Secret Sharing, Finite Fields, Erasure Codes Unlimited
- Lecture 12 – Error Correcting Codes Unlimited
- Lecture 14 – Graphs and Induction Unlimited
- Lecture 15 – Counting Unlimited
- Lecture 16 – Probability Unlimited
- Lecture 17 – Birthday Paradox, Monty Hall Paradox Unlimited
- Lecture 19 – Independence, Unions, Random Variables Unlimited
- Lecture 20 – Expectation Variance Unlimited
- Lecture 21 – Variance, Markov’s Inequality, Chebyshev’s Inequality Unlimited
- Lecture 22 – Geometric, Poisson Distributions Unlimited
- Lecture 23 – Continuous Probability Unlimited
- Lecture 24 – Exponential Distribution, Gaussian Distribution, Kalman Filter Unlimited
- Lecture 25 – Inference, Kalman Filter, Midterm Unlimited
- Lecture 26 – Countable, Uncountable, Uncomputable Unlimited
Instructor
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