Class schedule - Fall 2025
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| Date | Description | Slides | Homework | |
| Mon. 8/25 | Introductions, class organization, motivating example | Block 1 | ||
| Wed. 8/26 | Probability spaces, conditional probability, independence | Block 2a | ||
| Mon. 9/1 | Labor day - No class | |||
| Wed. 9/3 | Random variables, discrete and continuous, expectations | HW1 due | ||
| Mon. 9/8 | Traveling to EUSIPCO 2025 - No class | |||
| Wed. 9/10 | Traveling to EUSIPCO 2025 - No class | |||
| Mon. 9/15 | Multiple RVs, joint distribution, expectations | |||
| Wed. 9/17 | Bounds, convergence notions and limit theorems | Block 2b | ||
| Fri. 9/19 | Conditional probabilities, distributions and expectations | HW2 due | ||
| Mon. 9/22 | Markov chains, examples, Chapman-Kolmogorov equations | Block 3a | ||
| Wed. 9/24 | Gambler's ruin problem, discrete-time queuing models | |||
| Mon. 9/29 | Classes of states, irreducible Markov chains | HW3 due | ||
| Wed. 10/1 | Limiting distributions | Block 3b | ||
| Fri. 10/3 | Ergodicity | HW4 due | ||
| Mon. 10/6 | Ranking of nodes in graphs, PageRank | Block 3c | ||
| Wed. 10/8 | Exponential times, memoryless property, counting processes | Block 4a | ||
| Mon. 10/13 | Fall break - No class | |||
| Wed. 10/15 | Poisson processes, interarrival times, definitions, examples | HW5 due | ||
| Mon. 10/20 | Continuous-time Markov chains, birth and death processes | Block 4b | ||
| Wed. 10/22 | Transition probability function, Kolmogorov's equations | HW6 due | ||
| Fri. 10/24 | Midterm review lecture | |||
| Mon. 10/27 | Traveling to Asilomar 2025 - No class | |||
| Wed. 10/29 | In-class midterm exam | |||
| Fri. 10/31 | Limiting distributions, ergodicity, balance equations | |||
| Mon. 11/3 | Queuing theory, M/M/1, M/M/2, queue tandem | Block 4c | HW7 due | |
| Wed. 11/5 | Predator-prey population dynamics, Lotka-Volterra model | Block 4d | ||
| Mon. 11/10 | Markov and Gaussian processes | Block 5a | ||
| Wed. 11/12 | Brownian motion, geometric Brownian motion, white noise | HW8 due | ||
| Mon. 11/17 | Arbitrages and risk neutral measure | Block 5b | ||
| Wed. 11/19 | Black-Scholes formula for options pricing | |||
| Mon. 11/24 | Stationary processes, implications, wide-sense stationarity | Block 5c | HW9 due | |
| Wed. 11/26 | Thanksgiving recess - No class | |||
| Mon. 12/1 | Linear filtering of wide-sense stationary processes | |||
| Wed. 12/3 | Matched filter, Wiener filter | HW10 due | ||
| Mon. 12/8 | Principal component analysis |