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Instructor: Nianqiao Phyllis Ju
Time and location: 2A, Tuesday & Thursday 2:25-4:15pm, Kemeny 007. 2AX, Wednesday 5:30-6:20pm.
Office hours and tutorials: Monday 10-11am, Wednesday 9-10am & by appointment; Kemeny 331. Tuesday, Thursday 7-9pm, Haldeman 028.
Textbook: Pick one you like or read both!
- Grinstead and Snell's Introduction to Probability by Charles Miller Grinstead and James Laurie Snell. Available for free online at https://math.dartmouth.edu/~prob/prob/prob.pdf and print copies available at AMS bookstore and Amazon.
- (main textbook) Introduction to Probability, by Joseph K. Blitzstein and Jessica Hwang. Available for free online at https://probabilitybook.net/ and print copies available at CRC Press and Amazon.
Format: Weekly lectures, homework assignments ((8-2)*20 = 120pts) , two midterms(2*30 = 60pts)and one final exam (60pts; scheduled by the registrar).
Tentative schedule See Math 20, Fall 2025 website for a sample schedule.
| Week | Dates | Lectures | Homework |
|---|---|---|---|
| 1 | 9/15, 17 | Counting, axioms of probability, inclusion-exclusion | H0 & H1 out |
| 2 | 9/22, 24 | Conditional probability, independence, law of total probabilty. | H1 due, H2 out |
| 3 | 9/29, 10/1 | Midterm 1 review and problem solving (positions of Aces, Monty Hall, Gambler's ruin). Random variables, named distributions (Bernoulli, Binomial, Geometric), PMF, expectation. | H2 due, H3 out |
| 4 | 10/6, 8 | CDF, lotus, linearity of expectation, variance. Joint (discrete) distribution, covariance. | H3 due, H4 out |
| 10/7 | Midterm 1 (2AX slot) | ||
| 5 | 10/13, 10/15 | independence, Central Limit Theorem. Gaussian distribution. Continuous random variables, PDF. | H4 due, H5 out |
| 6 | 10/20, 10/22 | Exponential & Poisson. Change of variables. Joint continuous distributions. | H5 due, H6 out |
| 7 | 10/27, 10/29 | Midterm 2 review and problems (coupon collector, birthday problem). Conditional expectation, law of total expectation. | H6 due, H7 out |
| 8 | 11/3 | No class on 11/3. | H7 due, H8 out |
| 11/4 | Midterm 2 (2AX slot) | ||
| 11/5 | Inequalities and Law of Large Numbers (w/ proof). Moment generating functions. Proof of CLT. | ||
| 9 | 11/10, 11/12 | Review for finals and new problems: secretary problem, order statistics, buffon's needle, CLT for median, etc. | H8 due, H9 out |
| 10 | 11/17 | Markov Chains and random walk. | - |