# Math 60: Probability Theory (Honors)

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

## Important Dates

• 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
6 May 2016: Final day to drop a 4th course;
17 May 2016: Final day to withdraw a course.

## Syllabus

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 and Presentation Schedule (TBA)

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

## Course Policies

### Honor Principle

Collaborations (giving and receiving assistance) during closed-book exams and quizzes are strictly prohibited. Any form of plagiarism is not allowed in the final project. If you have questions, please ask the instructor before doing and should always refer to Academic Honor Principle.

### Accessibility Policy

Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see your instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested. At such a meeting please provide your instructor with a copy of a disability registration form, which lists the accommodations recommended for the student by Student Accessibility Services within the Academic Skills Center. The person you might want to contact at the Academic Skills center is Ward Newmeyer, Director of Student Accessibility Services 205 Collis Center - (603) 646-9900.

### Student Religious Observances

Some students may wish to take part in religious observances that fall during this academic term. Should you have a religious observance that conflicts with your participation in the course, please come speak with your instructor before the end of the second week of the term to discuss appropriate accommodations.

### Late Policy

By "deadline" we really mean it. On the condition of accepting the penalty for turning in the final project report late (that is, 5% each additional day), however, an extension of maximum 4 days will be granted on a case-by-case basis. In exceptional circumstances, students with disabilities should inform the instructor of their accommodation requests well in advance, so that the instructor will have sufficient time to work with Student Accessibility Services to provide appropriate accommodations.