Probability is one of the most important ideas in human knowledge. This is a crash course to introduce the concept of probability formally; and exhibit its applications in computer science, combinatorics, and algorithms. The course will be different from a typical mathematics course in the coverage and focus of examples. After finishing this course a student will have a good understanding of both theory and practice of probability in diverse areas.INTENDED AUDIENCE : Computer Science & Engineering, Mathematics, Electronics, Physics, Statistics, & similar disciplines.PREREQUISITES : NilINDUSTRY SUPPORT : Machine Learning, Data Streaming, Discrete Optimization, Cryptography, Coding theory, Computer Algebra, Cyber
Week 1: Introductory examples. Probability for finite space.
Week 2: Sigma algebra. Conditional probability
Week 3: Expectation. Famous random variables.
Week 4: Concentration inequalities. Boosting by Chernoff.
Week 5: Stochastic process.
Week 6: Stationary distribution examples.
Week 7: Probabilistic method examples.
Week 8: Streaming algorithms.