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Last updated:

September 23, 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 (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.

Course Curriculum

  • 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

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