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Last updated:

September 26, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

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.

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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