Fall 2025
Konstantin Matveev
Subtitle:
Introduction to Probability using Measure Theory
Course Description:
We will study Probability by taking a journey from Combinatorics to Measure Theory and back. The topics will include probability spaces and random variables from the measure theoretic framework, laws of large numbers and the Central limit theorem, zero-one laws, martingales, Markov chains and Brownian motion. Time permitting, we will touch on examples from modern research areas, such as statistical physics and random matrix theory.
Text:
Probability with martingales by David Williams
Prerequisites:
Real Analysis (640:501 or equivalent) and an undergraduate probability course at the level of Ross’s text
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Fall 2023
Konstantin Matveev
Subtitle:
Introduction to Probability using Measure Theory
Course Description:
We will study Probability by taking a journey from Combinatorics to Measure Theory and back. The topics will include probability spaces and random variables from the measure theoretic framework, laws of large numbers and the Central limit theorem, zero-one laws, martingales, Markov chains and Brownian motion. Time permitting, we will touch on examples from modern research areas, such as statistical physics and random matrix theory.
Text:
Williams, Probability with martingales.
Prerequisites:
Real Analysis (640:501 or equivalent) and an undergraduate probability course at the level of Ross's text A first course in probability.
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Spring 2023
Kimberly Weston
Subtitle:
Introduction to Probability using Measure Theory
Course Description:
This course will be an introduction to the issues and techniques of probability theory, at the graduate level. The topics covered will include: (i) The measure theoretic framework of modern probability theory; probability spaces and random variables; (ii) Independence and zero-one laws; (iii) Laws of large numbers and Kolmogorov's three series theorem; (iv) Convergence in distribution and the Central Limit Theorem; (v) Conditional Expectation; (vi) An introduction to martingales in discrete-time and applications to Markov chains. Time permitting, we will try to give brief introduction to large deviations and Brownian motion.
Text:
not decided yet
Prerequisites:
Real Analysis (640:501 or an equivalent) and an undergraduate course at the level of Ross's text, A First Course in Probability.
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Fall 2020
Kimberly Weston
Subtitle:
Introduction to Probability using Measure Theory
Course Description:
This course will be an introduction to the issues and techniques of probability theory, at the graduate level. The topics covered will include: (i) The measure theoretic framework of modern probability theory; probability spaces and random variables; (ii) Independence and zero-one laws; (iii) Laws of large numbers and Kolmogorov's three series theorem; (iv) Convergence in distribution and the Central Limit Theorem; (v) Conditional Expectation; (vi) An introduction to martingales in discrete-time and applications to Markov chains. Time permitting, we will try to give brief introduction to large deviations and Brownian motion.
Text:
Probability with martingales by David Williams
Prerequisites:
Real Analysis (640:501 or an equivalent) and an undergraduate course at the level of Ross's text, A First Course in Probability.
Schedule of Sections:
Previous Semesters:
- Fall 2020 Prof. Weston
- Spring 2018 Prof. Larsen
- Spring 2017 Prof. Kontorovich
- Spring 2015 Prof. Ocone