Instructor: Alexander Dunlap, Ph.D. (he/him; alexander decimal dunlap at duke decimal edu). Office: Physics 297. Office hours: Tuesdays 9:45am–11:00am, Wednesdays 3:30pm–4:45pm (subject to change), or by appointment. Please use email only for administrative issues. If you have questions about course content, please come to office hours or use our Ed Discussions site (accessible via Canvas). I will check emails and Ed Discussions at least once each workday; please do not expect immediate responses (e.g. on weekends or right before the homework is due).
Meetings: Tuesdays (T) and Thursdays (Θ), 8:30am–9:45am, Physics 235.
Textbooks: We will mostly follow [M], with some supplementary material (and a slightly more advanced perspective) from [GS].
Course description: This is a first course in probability with more rigor and depth than the standard probability course Math 230. We will cover discrete and continuous random variables, independence, joint and conditional distributions, generating functions, Bayes' formula, and Markov chains. We will rigorously study the classical limit theorems of probability (Law of Large Numbers, Central Limit Theorem, and Poisson limit theorem).
Course requirements: There will be homework assignments every week or two; you will have at least a week to complete each assignment. Homework assignments will be submitted on Gradescope. A (possibly proper) subset of the problems will be graded. There will two in-class midterm exams (Tuesdays, February 10 and March 24) and a final exam (as scheduled by the registrar, currently listed as Tuesday, April 28, 9am–12pm). Exam problems will be similar to those on the homework.
Grading: The final grade will be computed as a combination of 10% homework, 25% each midterm, and 40% final exam. The lowest two homework assignment scores will be dropped.
(very much subject to change, but I will try to keep this table up-to-date)
| Meetings | Topic | Textbook sections |
|---|---|---|
| Θ 1/8 | Probability spaces, experiments, outcomes, events, counting, some properties of probability measures. | [M], §1.1–3 |
| T 1/13–Θ 1/15 | Properties of probability measures, conditional probability, independence. | [M], §1.4–1.5 |
| T 1/20 | Law of large numbers v0. | [M], §1.6 |
| Θ 1/22 | Random variables, independent random variables. | [M], §2.1–2 |
| T 1/29–Θ 1/31 | Expectation and variance. Random vectors, conditional distributions and expectation. | [M], §2.3–4 |