Topics covered in each lecture will be listed below, with relevant chapter in the book. Many other books and lecture notes on probability are available, and may be helpful. These can be found in the library or online.

Date | Chapter | Notes | Topics |
---|---|---|---|

01-09 | N/A | Counting | |

01-11 | Ch. 1 | probability definition | |

01-13 | Ch. 1 | Birthday asymptotics, properties of probability | |

01-16 | Ch. 1 | Conditional probability, Independent events | |

01-18 | Ch. 1 | Law of total probability, Bayes formula | |

01-20 | Ch. 2 | Random Variables | |

01-23 | Ch. 2 | More Random Variables, expectation | |

01-25 | Ch. 2 | Expectation of discrete RVs, continuous RVs definition, exponential | |

01-27 | Ch. 2 | Normal distribution, expectation of continuous RVs | |

01-30 | Ch. 2 | Expectation, moments | |

02-01 | Ch. 2 | Joint distribution, Marginals | |

02-03 | Ch. 2 | Covariance | |

02-13 | Ch. 2.7 | Law of Large Numbers | |

02-15 | Ch. 2.7 | Central limit theorem | |

02-17 | N/A | midterm | |

02-27 | Ch. 2.7 | some statistics | |

02-27 | Ch. 2.7 | some statistics | |

03-01 | Ch. 2.7 | hypothesis testing, confidence intervals | |

03-03 | Ch. 3 | Conditional distribution and expectation | |

03-06 | Ch. 4 | Gambler's ruin, transience and recurrence | |

03-08 | Ch. 4 | random walks in dim d | |

03-10 | Ch. 4 | Random walks | |

03-13 | Ch. 4 | general Markov chains basics | |

03-15 | Ch. 4 | general Markov chains - cont. | |

03-17 | Ch. 4 | general Markov chains - classification of states | |

03-20 | Ch. 4 | general Markov chains - recurrence, stationary dist. | |

03-22 | Ch. 4 | time reversal and reversibility | |

03-24 | Ch. 4 | Reversibility | |

03-27 | Reversibility | ||

03-29 | Ch. 4 | Reversibility applications | |

03-31 | Ch. 4 | First step analysis | |

04-03 | Ch. 4 | First step analysis, branchnig processes | |

04-03 | Ch. 4 | branching processes, Markov Chain Monte Carlo |