Lecture 1: Set Theory and Linear Algebra Basics, August 24, 2026.

Lecture 2: Probability Basics, August 26, 2026.

Lecture 3: Stochastic Matrices and Discrete Time Markov Chains, August 28, 2026.

Lecture 4: Properties of Markov Chains and Hitting Times, August 31, 2026.

Lecture 5: Stopping Time, Strong Markov Property and Generating Functions, September 2, 2026.

Lecture 6: Martingales and the Optional Stopping Theorem, September 4, 2026.

Lecture 7: Martingale characterization of Markov Chains, September 9, 2026.

Lecture 8: Class Structure, September 11, 2026.

Lecture 9: Recurrence and Transience, September 14, 2026.

Lecture 10: Class Properties of Recurrence and Transience, September 16, 2026.

Lecture 11: Invariant distributions, September 18, 2026.

Lecture 12: Positive recurrence and invariant distributions, September 21, 2026.

Lecture 13: Time Reversal and Detailed Balance, September 23, 2026.

Lecture 14: Aperiodicity and Convergence to Invariant Distribution, September 25, 2026.