Class schedule - Fall 2024
| Date | Description | Slides | Homework | |
| Mon. 8/26 | Introductions, class organization, motivating example | Block 1 | ||
| Wed. 8/28 | Probability spaces, conditional probability, independence | Block 2a | ||
| Mon. 9/2 | Labor day - No class | |||
| Wed. 9/4 | Random variables, discrete and continuous, expectations | HW1 due | ||
| Mon. 9/9 | Multiple RVs, joint distribution, expectations | |||
| Wed. 9/11 | Bounds, convergence notions and limit theorems | Block 2b | ||
| Mon. 9/16 | Conditional probabilities, distributions and expectations | HW2 due | ||
| Wed. 9/18 | Markov chains, examples, Chapman-Kolmogorov equations | Block 3a | ||
| Mon. 9/23 | Gambler's ruin problem, discrete-time queuing models | |||
| Wed. 9/25 | Classes of states, irreducible Markov chains | HW3 due | ||
| Mon. 9/30 | Limiting distributions | Block 3b | ||
| Wed. 10/2 | Ergodicity | HW4 due | ||
| Mon. 10/7 | Ranking of nodes in graphs, PageRank | Block 3c | ||
| Wed. 10/9 | Exponential times, memoryless property, counting processes | Block 4a | ||
| Mon. 10/14 | Fall break - No class | |||
| Wed. 10/16 | Poisson processes, interarrival times, definitions, examples | HW5 due | ||
| Mon. 10/21 | Continuous-time Markov chains, birth and death processes | Block 4b | ||
| Wed. 10/23 | Transition probability function, Kolmogorov's equations | HW6 due | ||
| Fri. 10/25 | Midterm review lecture | |||
| Mon. 10/28 | Traveling to Asilomar 2024 - No class | |||
| Wed. 10/30 | In-class midterm exam | |||
| Fri. 11/1 | Limiting distributions, ergodicity, balance equations | |||
| Mon. 11/4 | Queuing theory, M/M/1, M/M/2, queue tandem | Block 4c | ||
| Wed. 11/6 | Predator-prey population dynamics, Lotka-Volterra model | Block 4d | ||
| Mon. 11/11 | Markov and Gaussian processes | Block 5a | HW7 due | |
| Wed. 11/13 | Brownian motion, geometric Brownian motion, white noise | |||
| Mon. 11/18 | Arbitrages and risk neutral measure | Block 5b | ||
| Wed. 11/20 | Black-Scholes formula for options pricing | HW8 due | ||
| Mon. 11/25 | Stationary processes, implications, wide-sense stationarity | Block 5c | ||
| Wed. 11/27 | Thanksgiving recess - No class | |||
| Mon. 12/2 | Linear filtering of wide-sense stationary processes | HW9 due | ||
| Wed. 12/4 | Matched filter, Wiener filter | |||
| Mon. 12/9 | Principal component analysis | HW10 due |