ICTS Course no.: MTH 124.4

Venue: Online

Class timings: Tue/Th 11:00-12:30

First meeting: Jan 11, 2022

Course description:

  1. Review of discrete Probability
  2. Review of Measure theoretic facts (distribution of a random variable, expectation, product measures, Fubini’s theorem)
  3. Laws of Large numbers: independence, sums of an independent random variable, weak law of large numbers, Borel-Cantelli theorems, strong law of large numbers, random series
  4. Central limit theorems: weak convergence of probability measures, characteristic functions,  central limit theorem, infinitely divisible distributions
  5. Conditional expectation, Martingales (uniform integrability, Doob's up crossing lemma, martingale convergence and related topics)
  6. Introduction to Brownian motion
  7. Additional topics (if time permits): Random walks, Markov chains, ergodic theory.

Course Evaluation: The final grade will be based on the following three components:

  1. Final exam: The final exam will count towards 40% of the final grade.
  2. Homework: There will be four homework assignments throughout the semester and they will count towards 40% of the final grade.
  3. Class performance: The students will be required to make short (~30-45 min) in-class presentations approximately once every two weeks on pre-specified topics. These will count towards 20% of the final grade.