MATH 106: Stochastic Processes with Applications

ORC Course Description: Stochastic models are central to the study of many problems in physics, engineering, finance, evolutionary biology, and medicine. This course introduces concepts and techniques in probability theory and key methods for stochastic processes, along with their applications to evolutionary games, cancer dynamics, and infectious diseases.

Prerequisites: The student should be familiar with basic concepts in differential equations, probability and complex variable theory. Programing skills highly recommended, but not required.

Textbooks:

• Karlin, S., & Taylor, H. E. (1975). A first course in stochastic processes. Academic Press.
• Bailey, N. T. (1964). The elements of stochastic processes; with applications to the natural sciences. John Wiley & Sons Inc.
• Ewens, W. J. (2012). Mathematical population genetics 1: theoretical introduction (Vol. 27). Springer Science & Business Media.

Grading Formula: (i) Homework Problem Sets (30%) + (ii) Paper Presentation (10%) + (iii) Midterm (30%) + (iv) Final (30%).

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: 10A TuThu 10:10am-12:00pm (x-hour Wed 3:30pm-4:20pm) at 004 Kemeny Hall
• Office Hours: Wed 3:30pm-4:20pm & by appointment.
• Office: 210 Kemeny Hall
• Email: feng.fu@dartmouth.edu

Important Dates

• Homework problem sets due weekly
• Midterm TBD
• Final TBD

Syllabus

Tentative lecture plan which may be subject to further changes. Download

Week	Lecture
Week 1	Basic concepts of probability & generating function approach
Week 2	Applications of generating function approach
Week 3	Markov chains
Week 4	Random walks
Week 5	Continuous time Markov processes
Week 6	Diffusion theory
Week 7	Birth and death processes
Week 8	Branching processes
Week 9	Reserved for review sections & paper presentations

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.