**ORC Course Description:** This course gives a foundational introduction to probability theory. Topics covered include (discrete and continuous) random variables, multivariate distributions, expectations, independence, conditioning, conditional distributions and expectations, law of large numbers and the central limit theorem, random walks, Markov chains and their applications.

**Textbook:** Introduction to Probability (2nd Rev Ed), Charles M. Grinstead & J. Laurie Snell, American Mathematical Society (1997).
By courtesy of the authors, this book is freely available on the internet (here).

**Grading Formula:**
Participation & in-class quizzes (10%) + Weekly homework problem sets (20%) + Midterm 1 (20%) + Midterm 2 (20%) + Final (30%).

- Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
- Course Time: MWF 11:30-12:35 (x-hour Tu 12:15-1:05) at 006 Kemeny Hall
- Office Hours: Mon 2:00pm-3:00pm, Wed 2:00pm-3pm, and by appointment.
- Office: 210 Kemeny Hall
- Email: feng.fu@dartmouth.edu

- Homework due weekly on Friday
- Midterm 1: 24 July 2019, 6:30pm-8:30pm @ Kemeny Hall 006
- Midterm 2: 12 August 2019, 6:30pm-8:30pm @ Kemeny Hall 006
- Final Exam: Saturday, August 24, 2019 at 8:00am
- Course withdrawal deadlines:

31 July 2019: Final day to drop a 4th course;

7 August 2019: Final day to withdraw a course.

Tentative lecture plan which may be subject to further changes.

Date | Lecture | Homework |
---|---|---|

21 June 2019 | Course Overview & Basic Concepts of Discrete Probability | Ch.1.2: 6, 7, 13, 14, 23 |

24 June 2019 | Guest lecture by Xingru Chen: Continuous Probability Densities | suggested reading: Ch. 2 |

26 June 2019 | No class (makeup class on x-hr) | suggested reading: Ch. 3 |

28 June 2019 | No class (makeup class on x-hr) | HW: Ch. 2.2: 6, 8(a),(b),(c),(d),(e),(h) |

1 July 2019 | Permutations | Ch. 3.2: 7, 8, 9, 16, 22, 23, 32 |

2 July 2019 | X-HR: Combinations | Reading: Ch. 4.1 & 4.2 |

3 July 2019 | Discrete Conditional Probability | |

5 July 2019 | Continuous Conditional Probability | Ch. 4.1: 14, 17, 26, 36; 4.2: 3, 5(c)(d) |

8 July 2019 | Important Distributions & Densities | Ch. 5.1: 11, 32, 39; 5.2: 2, 10, 31, 34, 37 |

9 July 2019 | X-HR: Expected Value & Variance | Ch. 6.1 7, 13; 6.2: 15, 18, 20, 22, 27 |

10 July 2019 | Expected Value & Variance of Continuous Random Variables | Ch. 6.3: 3, 8, 10, 12, 17, 26, 28 |

12 July 2019 | Sums of Independent Random Variables | |

15 July 2019 | Review of Functions of Random Variables | |

17 July 2019 | Weak Law of Large Numbers | |

19 July 2019 | Generating Functions for Discrete Random Variables | |

22 July 2019 | Generating Functions for Continuous Densities | |

24 July 2019 | Midterm 1 | |

26 July 2019 | Central Limit Theorem | |

29 July 2019 | Theory of Branching Processes I | |

31 July 2019 | Theory of Branching Processes II | |

31 July 2019 | Last day to drop a 4th class | |

2 August 2019 | Markov Chains | |

5 August 2019 | Fundamental Limit Theorem | |

7 August 2019 | Mean First Passage Time | |

7 August 2019 | Final day for withdrawing a course | |

9 August 2019 | Markov Process in Continuous Time (Poisson Process) | |

12 August 2019 | Random Walks | |

12 August 2019 | Midterm 2 | |

14 August 2019 | Gambler’s Ruin | |

16 August 2019 | Diffusion Limit of Random Walks | |

19 August 2019 | Applications of Probability Theory | |

21 August 2019 | Last day of class: Review of finals | |

24 August 2019 | Final Exam at 8:00am |