Debapratim Banerjee

Debapratim Banerjee
  • PhD Student

Contact Information

  • office Address:

    450 Jon M. Huntsman Hall, 3730 Walnut Street,
    Philadelphia, PA 19104

Research

Teaching

Past Courses

  • MATH546 - ADVANCED PROBABILITY

    The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). After a summary of the necessary results from measure theory, we will learn the probabist's lexicon (random variables, independence, etc.). We will then develop the necessary techniques (Borel Cantelli lemmas, estimates on sums of independent random variables and truncation techniques) to prove the classical laws of large numbers. Next come Fourier techniques and the Central Limit Theorem, followed by combinatorial techniques and the study of random walks.

  • STAT930 - PROBABILITY

    Measure theory and foundations of Probability theory. Zero-one Laws. Probability inequalities. Weak and strong laws of large numbers. Central limit theorems and the use of characteristic functions. Rates of convergence. Introduction to Martingales and random walk.