Readings are assigned from the required textbook.
Ross, Sheldon. A First Course in Probability. 8th ed. Pearson Prentice Hall, 2009. ISBN: 9780136033134.
Additional readings are available in the links listed below.
| SES # | TOPICS | READINGS |
|---|---|---|
| 1 | Permutations and combinations | Sections 1.1–1.3 (also Pascal’s triangle—as studied (not invented) by Pascal, see also correspondence with Fermat: Fermat and Pascal on Probability (PDF)) |
| 2 | Multinomial coefficients and more counting | Sections 1.4–1.5 (see Pascal’s pyramid) |
| 3 | Sample spaces and set theory | Sections 2.1–2.2 |
| 4 | Axioms of probability | Sections 2.3–2.4 |
| 5 | Probability and equal likelihood | Sections 2.5–2.7 (and a bit more history) |
| 6 | Conditional probabilities | Sections 3.1–3.2 (and Conditional risk) |
| 7 | Bayes’ formula and independent events | Sections 3.3–3.5 |
| 8 | Discrete random variables | Sections 4.1–4.2 |
| 9 | Expectations of discrete random variables | Sections 4.3–4.4 (and, for non-discrete setting, examples of non-measurable sets, as in the Vitali construction) |
| 10 | Variance | Section 4.5 |
| 11 | Binomial random variables, repeated trials and the so-called Modern Portfolio Theory | Section 4.6 (and the so-called Modern Portfolio Theory) |
| 12 | Poisson random variables | Section 4.7 |
| 13 | Poisson processes | Section 9.1 |
| 14 | More discrete random variables | Sections 4.8–4.9 |
| 15 | Continuous random variables | Sections 5.1–5.2 |
| 16 | Review for Midterm Exam 1 | No Readings |
| 17 | Midterm Exam 1 | No Readings |
| 18 | Uniform random variables | Section 5.3 |
| 19 | Normal random variables | Section 5.4 |
| 20 | Exponential random variables | Section 5.5 |
| 21 | More continuous random variables | Sections 5.6–5.7 |
| 22 | Joint distribution functions | Sections 6.1–6.2 |
| 23 | Sums of independent random variables | Sections 6.3–6.5 |
| 24 | Expectation of sums | Sections 7.1-7.2 |
| 25 | Covariance | Sections 7.3–7.4 |
| 26 | Conditional expectation | Sections 7.5–7.6 |
| 27 | Moment generating distributions | Sections 7.7–7.8 |
| 28 | Review for Midterm Exam 2 | No Readings |
| 29 | Midterm Exam 2 | No Readings |
| 30 | Weak law of large numbers | Sections 8.1–8.2 |
| 31 | Central limit theorem | Section 8.3 |
| 32 | Strong law of large numbers and Jensen’s inequality | Sections 8.4–8.5 (see also the truncation-based proof on Terry Tao’s blog and the characteristic function proof of the weak law) and Jensen’s inequality |
| 33 | Markov chains | Section 9.2 |
| 34 | Entropy | Sections 9.3–9.4 |
| 35 | Martingales and the Optional Stopping Time Theorem | Martingales and the Optional Stopping Time Theorem |
| 36 | Risk Neutral Probability and Black-Scholes | Black-Scholes (look up options quotes at the Chicago Board Options Exchange) |
| 37 | Review for Final Exam | No Readings |
| 38 | Review for Final Exam (cont.) | No Readings |
| 39 | Review for Final Exam (cont.) | No Readings |
| 40 | Final Exam | No Readings |
