— Probability Theory

Prerequisites & course information

This version has ended; see updated course, below. Course Description: Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. Learning Activities: Lecture 3 hour(s), Term Paper/Discussion 1 hour(s). Cross Listing: STA 235C . Grade Mode: Letter. MAT 235C — Probability Theory (4 units) Course Description: Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. Prerequisite(s): MAT 235B or STA 235B ; or consent of instructor. Learning Activities: Lecture 3 hour(s), Term Paper/Discussion 1 hour(s). Enrollment Restriction(s): Open to graduate students; open to undergraduate students with consent of instructor. Cross Listing: STA 235C . Grade Mode: Letter. This course version is effective from, and including: Winter Quarter 2027. Learning Activities: Lecture 3 hour(s), Term Paper/Discussion 1 hour(s). Cross Listing: STA 235C . Grade Mode: Letter. MAT 235C — Probability Theory (4 units) Course Description: Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory. Prerequisite(s): MAT 235B or STA 235B ; or consent of instructor. Learning Activities: Lecture 3 hour(s), Term Paper/Discussion 1 hour(s). Enrollment Restriction(s): Open to graduate students; open to undergraduate students with consent of instructor. Cross Listing: STA 235C . Grade Mode: Letter. This course version is effective from, and including: Winter Quarter 2027.