- STATS 412: Introduction to Probability and Statistics, Fall 2005, Winter 2006 and Winter 2007.This course provides a first look at probability and statistics for undergraduate students in the engineering and computer science fields. It assumes moderate calculus background and covers equal amounts of probability and statisitcs.
- STATS 425: Introduction to Probability, Winter 2010 and Fall 2012.Calculus-based introduction to basic probability for undergraduate students interested in statistics, mathematics, actuarial science, engineering, or other quantitative fields.
- STATS 621: Probability Theory, Winter 2011.This course provides a rigorous introduction to Probability Theory. The required measure theoretic background is developed from scratch. Then the concepts of independence, integration, and expectation are introduced. Special attention is payed on various modes of convergence that are ubiquitous in Probability and Statistics. The laws of large numbers and the central limit theorem are proved. The course concludes with a careful treatment of conditional expectation via the Radon-Nikodym Theorem and basic results on martingales.
- STATS 520: Mathematical Methods in Statistics, Falls of 2006 – 2009.The course provides background on topics from advanced linear algebra, real analysis, and measure theory, indispensable for the graduate studies in statistics.
- STATS 810: Literature Proseminar, Fall 2008.
- STATS 711: Topics of Theoretical Statistics II: Long-range dependence, self-similarity, and heavy tails, Winter 2006.Special topics course for graduate students reviewing recent advances on theory and applications involving dependent data with emphasis on Internet traffic modeling.
Simulation of the Brownian motion: Paul Levy’s midpoint displacement technique.
The MATLAB code generating the above GIF animation can be found here. The top plot shows successive refinements over a dyadic grid, which converge almost surely and uniformly to a single continuous path of the Brownian motion. The bottom plot shows the conventional technique of taking cumulative sums of iid normal random variables, which does not have the “refinement property”. That is, it yields different paths each time one wants to refine the grid.