CSS.207.1: Probability

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In Fall 2022, I am offering a graduate-level course on Probability Theory and its applications. This course will tentatively cover the following topics.

A. Probability Measures

  • Measure Spaces, Sigma-Algebras, Probability measures
  • Expectation, Convergence Theorems, Product Measures
  • Conditional Expectation

B. Random Variables and Stochastic Processes

  • Distribution functions, Moment Generating functions
  • Multivariate Normal Distribution and its properties
  • Basic Concentration Inequalities
  • Convergence of random variables, Law of Large Numbers, Martingale Convergence Theorems
  • Basics of Markov Chains

C. Application to Learning Theory

  • Generalization bounds, symmetrization, and concentration
  • Basics of High Dimensional Probability


Undergraduate-level probability, basic mathematical analysis


Problem-solving will be our primary vehicle for learning the material. We will have bi-weekly problem sets, a mid-term and a final exam. The final grade will be a weighted average of these three components as detailed below:
  • Problem Sets (50%)
  • Mid-term (20%)
  • Final Exam (30%)


  • Schedule: Monday (4 - 5:30 pm) and Thursday (4 - 5:30 pm)
  • Venue: A-201


We will not follow any one particular source, in general. However, the following references will be useful