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 (see Paulos' NYT article and a famous hat problem) |

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 |