1 | Permutations and combinations | Sec. 1.1-1.3 (also Pascal's triangle — as studied (not invented) by Pascal, see also correspondence with Fermat) |

2 | Multinomial coefficients and more counting | Sec. 1.4-1.5 |

3 | Sample spaces and set theory | Sec. 2.1-2.2 |

4 | Axioms of probability | Sec. 2.3-2.4 (see Paulos' NYT article and a famous hat problem) |

5 | Probability and equal likelihood | Sec. 2.5-2.7 (and a bit more history) |

6 | Conditional probabilities | Sec. 3.1-3.2 |

7 | Bayes' formula and independent events | Sec. 3.3-3.5 |

8 | Discrete random variables | Sec. 4.1-4.2 |

9 | Expectations of discrete random variables | Sec. 4.3-4.4 (and, for non-discrete setting, examples of non-measurable sets, as in the Vitali construction) |

10 | Variance | Sec. 4.5 |

11 | Binomial random variables, repeated trials and the so-called Modern Portfolio Theory | Sec. 4.6 (and the so-called Modern Portfolio Theory) |

12 | Poisson random variables | Sec. 4.7 |

13 | Poisson processes | Sec. 9.1 |

14 | More discrete random variables | Sec. 4.8-4.9 |

15 | Continuous random variables | Sec. 5.1-5.2 |

16 | Review for Midterm Exam 1 | [No Readings] |

17 | Midterm Exam 1 | [No Readings] |

18 | Uniform random variables | Sec. 5.3 |

19 | Normal random variables | Sec. 5.4 |

20 | Exponential random variables | Sec. 5.5 |

21 | More continuous random variables | Sec. 5.6-5.7 |

22 | Joint distribution functions | Sec. 6.1-6.2 |

23 | Sums of independent random variables | Sec. 6.3-6.5 |

24 | Expectation of sums | Sec. 7.1-7.2 |

25 | Covariance | Sec. 7.3-7.4 |

26 | Conditional expectation | Sec. 7.5-7.6 |

27 | Moment generating distributions | Sec. 7.7-7.8 |

28 | Review for Midterm Exam 2 | [No Readings] |

29 | Midterm Exam 2 | [No Readings] |

30 | Weak law of large numbers | Sec. 8.1-8.2 |

31 | Central limit theorem | Sec. 8.3 |

32 | Strong law of large numbers and Jensen's inequality | Sec. 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 | Sec. 9.2 |

34 | Entropy | Sec. 9.3-9.4 |

35 | Martingales and the Optional Stopping Time Theorem | Martingales and the Optional Stopping Time Theorem (see also prediction market plots) |

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 | [No Readings] |

39 | Review for Final Exam | [No Readings] |

40 | Review for Final Exam | [No Readings] |