# 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%) + Weekly homework problem sets (20%) + Midterm (30%) + Final Project + 15 min Presentation (40%).

## 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
9 May 2022: Final day to dropping a 4th course;
18 May 2022: Final day to withdraw a course.

## Syllabus

Tentative lecture plan which may be subject to further changes.

Week Lecture
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; Gamblerâ€™s Ruin; Diffusion Limit of Random Walks
Week 9 Reserved final paper presentations

## 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

## 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.