Program Overview

Math 60: Probability Theory (Honors)

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).

Grading Formula

• Participation & in-class quizzes (10%)
• Weekly homework problem sets (20%)
• Midterm (30%)
• Final Project + 15 min Presentation (40%)

Instructor and Course Details

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: 10A; Tue/Thu 10:10am-12:00pm, X-HR Friday 3:30pm-4:20pm (reserved only for moving classes, not regularly used)
• Classroom: TBD

Important Dates

• Final project proposal (one-pager) due on: Tuesday 19 April 2022
• Midterm exam: TBD
• Final project presentations: in the week of 23rd May (Week 9)
• Final project report (written in a research paper form) due on: Thursday 2 June 2022
• Course withdrawal deadlines:
  • 9 May 2022: Final day to drop a 4th course
  • 18 May 2022: Final day to withdraw a course

Syllabus

Tentative lecture plan which may be subject to further changes.

• Week 1: Course Overview & Basic Concepts of Discrete Probability; Continuous Probability Densities; Permutations
• Week 2: Combinations; Discrete Conditional Probability; Continuous Conditional Probability
• Week 3: Important Distributions & Densities; Expected Value & Variance; Expected Value & Variance of Continuous Random Variables
• Week 4: Sums of Independent Random Variables; Review of Functions of Random Variables; Weak Law of Large Numbers
• Week 5: Generating Functions for Discrete Random Variables; Generating Functions for Continuous Densities; Central Limit Theorem
• Week 6: Theory of Branching Processes; Markov Chains
• Week 7: Fundamental Limit Theorem; Mean First Passage Time; Markov Process in Continuous Time (Poisson Process)
• Week 8: Random Walks; Gambler’s Ruin; Diffusion Limit of Random Walks
• Week 9: Reserved final paper presentations

Course Projects

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

• Name: Project Title

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.

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 the instructor before the end of the second week of the term.

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 the 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.