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.

Teaching Format:

• The class is lecture-based, and electronic lecture notes that are prepared by the instructor will be distributed to facilitate learning.

• Virtual instruction via Canvas and Zoom available for remote participation.

Grading Formula: (i) Homework Problem Sets (30%) + (ii) Midterm (30%) + (iii) Final (40%).

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: 9L MWF 8:50am-9:55pm (x-hour Thu 9:05am-9:55am) at 004 Kemeny Hall
• Office Hours: Tue 3:30pm-5:00pm & Thu 3:30pm-5:00pm and 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.

Student Accessibility and Accommodations

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see the instructor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office in Carson Hall 125 or by phone: (603) 646-9900 or email: Student.Accessibility.Services@Dartmouth.edu. Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to the instructor. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Student Religious Observances

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

Mental Health and Wellness

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean, Counseling and Human Development, and the Student Wellness Center. The instructor would like to encourage you to use these resources to take care of yourself throughout the term, and to come speak to the instructor if you experience any difficulties.

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.