Class schedule - Fall 2026

Date Description Slides  Homework
Mon. 8/31 Introductions, class organization, motivating example Block 1  
Wed. 9/2 Probability spaces, conditional probability, independence Block 2a  
Mon. 9/7 Labor day - No class    
Wed. 9/9 Random variables, discrete and continuous, expectations   HW1 due
Mon. 9/14 Multiple RVs, joint distribution, expectations    
Wed. 9/16 Bounds, convergence notions and limit theorems Block 2b  
Mon. 9/21 Conditional probabilities, distributions and expectations   HW2 due
Wed. 9/23 Markov chains, examples, Chapman-Kolmogorov equations Block 3a  
Mon. 9/28 Traveling - No class    
Wed. 9/30 Gambler's ruin problem, discrete-time queuing models   HW3 due
Fri. 10/2 Classes of states, irreducible Markov chains    
Mon. 10/5 Limiting distributions Block 3b  
Wed. 10/7 Ergodicity   HW4 due
Mon. 10/12 Fall break - No class    
Wed. 10/14 Ranking of nodes in graphs, PageRank Block 3c  
Mon. 10/19 Exponential times, memoryless property, counting processes Block 4a  
Wed. 10/21 Poisson processes, interarrival times, definitions, examples   HW5 due
Fri. 10/23 Midterm review lecture    
Mon. 10/26 Traveling - No class    
Wed. 10/28 In-class midterm exam    
Fri. 10/30 Continuous-time Markov chains, birth and death processes Block 4b  
Mon. 11/2 Transition probability function, Kolmogorov's equations    
Wed. 11/4 Limiting distributions, ergodicity, balance equations   HW6 due
Mon. 11/9 Queuing theory, M/M/1, M/M/2, queue tandem Block 4c  
Wed. 11/11 Predator-prey population dynamics, Lotka-Volterra model Block 4d  
Mon. 11/16 Markov and Gaussian processes Block 5a  
Wed. 11/18 Brownian motion, geometric Brownian motion, white noise   HW7 due
Mon. 11/23 Arbitrages and risk neutral measure Block 5b  
Wed. 11/25 Thanksgiving recess - No class    
Mon. 11/30 Black-Scholes formula for options pricing    
Wed. 12/2 Stationary processes, implications, wide-sense stationarity Block 5c HW8 due
Mon. 12/7 Linear filtering of wide-sense stationary processes    
Wed. 12/9 Matched filter, Wiener filter    
Mon. 12/14 Principal component analysis   HW9 due
Sun. 12/20 In-class final exam