MATH 418+544 - Honours and Graduate Probability

Lectures: Mon Wed Fri 10:00 - 10:50
Math 202
Instructor: Omer Angel
angel at math dt ubc dt ca
Office hours: Mon 14:00-15:00, Fri after class or by appointment
Math Annex 1210
Exam: some time in december.
Discussion board: On Piazza
Course Outline: Together with 419/545 in term 2, these courses form a comprehensive introduction to probability theory. No prior background in probability is required, but some analysis and a general mathematical maturity will be assumed.
You can find a course syllabus here. Topics will roughly include chapters 1-4 of Durrett, and include the following.
  1. Probability spaces: random variables, expectation, independence
  2. modes of convergence, Laws of Large Numbers,
  3. Borel-Cantelli lemma, Kolmogorov and Hewitt-Savage 0-1 Laws.
  4. Characteristic functions, weak convergence, Central Limit Theorem, Poisson convergence.
  5. Random walks, stopping times,
  6. conditional expectation, Martingales.
  7. Applications.
Evaluation: 70% assignments, 30% final exam in december, date, time and place TBA.