**ORC Course Description:** This course is a more theoretical introduction to probability theory than Math 20.
In addition to the basic content of Math 20, the course will include other topics
such as continuous probability distributions 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%) + Midterm (40%) + Final Project + 15 min Presentation (50%).

There will be suggested homework problem sets (optional, non-graded).

- Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
- Course Time: MWF 11:15-12:20 (x-hour Tu 12:00-12:50) at 008 Kemeny Hall
- Office Hours: Monday 3:00pm-5:00pm, Friday 3:00pm-5pm, and by appointment.
- Office: 210 Kemeny Hall
- Email: feng.fu@dartmouth.edu

- Final project proposal due on: Friday 22 April 2016
- Midterm exam: Tuesday 3 May 2016 at 6-9pm, Moore Hall Room B03
- Final project presentations: in the week of 23rd May (week 9)
- Final project report (written in a research paper form) due on: Monday 30 May
- Course withdrawal deadlines:

6 May 2016: Final day to drop a 4th course;

17 May 2016: Final day to withdraw a course.

Tentative lecture plan which may be subject to further changes.

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

28 March 2016 | Course Overview & Basic Concepts of Discrete Probability | 1.2: 7, 9, 10, 12, 15, 16, 23, 27, 31 |

30 March 2016 | Continuous Probability Densities | Ch. 2.2: 2, 6, 8(b), 14, 16, 21 |

1 April 2016 | Permutations | Ch. 3.1: 3, 7, 19, 23, 24 |

4 April 2016 | Combinations | Ch. 3.2: 8, 16, 22, 32, 33, 35 |

6 April 2016 | Discrete Conditional Probability | Ch. 4.1: 7, 16, 26, 37, 38, 40 |

8 April 2016 | Continuous Conditional Probability | Ch. 4.2: 3, 4, 5(c), 6, 10 |

11 April 2016 | Important Distributions & Densities | Ch. 5.1: 11, 32, 39; 5.2: 2, 10, 31, 34, 37 |

13 April 2016 | Expected Value & Variance | Ch. 6.1 7, 25, 26, 28; 6.2: 15, 17, 18, 20, 22, 24 |

15 April 2016 | Expected Value & Variance of Continuous Random Variables | Ch. 6.3: 3, 8, 10, 12, 26, 28 |

18 April 2016 | Sums of Independent Random Variables | Ch. 7.2: 5, 7, 8, 11, 14 |

20 April 2016 | Review of Functions of Random Variables | |

22 April 2016 | Weak Law of Large Numbers | Ch. 8.1: 7, 9, 8.2: 2, 6, 8, 18 |

22 April 2016 | Course project proposal due | |

25 April 2016 | Generating Functions for Discrete Random Variables | Ch. 10.1: 1, 3, 6, 8 |

27 April 2016 | Generating Functions for Continuous Densities | Ch. 10. 3: 1, 7, 8 |

29 April 2016 | Central Limit Theorem | Ch. 9.3: 1, 2, 14 |

2 May 2016 | Theory of Branching Processes I | Ch. 10.2: 2, 8 |

3 May 2016 | Midterm | 6-9pm @ Moore Hall Room B03 |

4 May 2016 | Theory of Branching Processes II | Ch. 10.2: 2, 8 |

6 May 2016 | Markov Chains | Ch. 11.1: 1, 7; 11.2: 6, 11, 21, 22; 11.3: 3, 6 |

6 May 2016 | Final day for dropping a 4th course | |

9 May 2016 | Fundamental Limit Theorem | |

11 May 2016 | Mean First Passage Time | |

13 May 2016 | Markov Process in Continuous Time (Poisson Process) | |

16 May 2016 | Random Walks | |

17 May 2016 | Final day to withdraw from a course | |

18 May 2016 | Gambler’s Ruin | |

20 May 2016 | Diffusion Limit of Random Walks | |

23 May 2016 | Applications of Probability Theory I | |

24 May 2016 | X-Hour | TBD |

25 May 2016 | Applications of Probability Theory II | |

27 May 2016 | Applications of Probability Theory III | |

30 May 2016 | Final project report due |

Course projects are listed in the alphabetical order of student names, and will be updated once more progresses are made by the students.

Name | Project Title |
---|---|

Herbert Chang | Music and Market Prediction with Information Theoretic LSTM Recurrent Neutral Networks |

Jon Chu | Earnings Release Trading: Developing Strategies Based on Probabilities of Events |

James Detweiler & Jonathan Meng | Optimal Leveraging Strategy for Investing in a Cryptocurrency Casino |

Gwendolyn Howard | Modeling and Predicting Crude Oil Prices Using Markov Chain Approach |

James Keefe | Exploring the Black-Sholes Model |

Michael Li | Evolutionary Dynamics of Positive Interactions |

Anwita Mahajan | Optimal Strategies in Rock-Paper-Scissors Games |

Dan Salas & Ryan Schiller | Does Antibiotic Resistance Influence Pharmaceutical Patent and R&D Incentives? |

Shikhin Sethi | Caches and Jumps |

Eric Sun | Risk Analysis of Car Accidents |

Josh Ufland | Utility of Trading for Draft Picks in the NFL |

Eva Wang | Understanding Bidding Behavior in Two-Item Auctions by Combining Experiments with Modeling |

Ran Zhuo | Spatial Epidemiological Modeling of Disease Transmission and Intervention Strategies |