Program Overview

MATH 106: Stochastic Processes with Applications

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.
• Programming skills are 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

The grading formula consists of:

• Homework Problem Sets (30%)
• Midterm (30%)
• Final (40%)

Course Details

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: 10 block MWF 10:10-11:15 (x-hour Thu 12:15pm-1:05pm) at 201 Kemeny Hall
• Office: 210 Kemeny Hall

Important Dates

• Homework problem sets are due weekly
• Midterm: To Be Determined
• Final: To Be Determined

Syllabus

Tentative Lecture Plan

The tentative lecture plan is subject to further changes and includes:

• 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 during closed-book exams and quizzes are strictly prohibited. Any form of plagiarism is not allowed in the final project.

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.

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, and our terms are intensive. There are a number of resources available to you on campus to support your wellness.

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.