Math 390 Individual Study Opportunities
A.J. Hildebrand

About Math 390

Sample Topics

• Game Theory: "The Iterated Prisoners Dilemma"
• Statistics: "Distinguishing Cause and Effect"
• Applied Mathematics: "Brownian Motion and PDEs"
• Pure Mathematics: "Master Class on Selected Topics in Combinatorics, Analysis, and Probability"
• Math Contest Training: "Putnam Master Class"

Text/course materials. For some topics there exists a single suitable textbook, but more typically no such text is available. In those cases we will use material from a variety of sources, such as chapters in textbooks, original articles, and lecture notes. Usually, these materials are available in electronic form, so there is no need to purchase texts.

Details

• Format. Math 390 is a "guided individual study" course: Instead of having formal lectures, students enrolled in Math 390 study appropriate materials on their own, with guidance by the instructor. My recent Math 390 courses have all been carried out in mini-groups of 2-4 students. I typically meet with the group once or twice a week for 1-2 hours each, depending on the number of credit hours that the students have registered for. At these meetings, we will go over the material the students have studied since the last last meeting, discuss any questions that have come up, and assign new readings and exercises to be completed by the next meeting.
• Credit: Math 390 can be taken for up to 3 hours of credit per course, and there is a maximum of 8 hours of Math 390 credit a student can earn altogether. The number of credit hours should correspond to the workload you plan to put into the course: 3 credit hours of Math 390 class should require a time investment equivalent to a regular 3 credit hour course; 1 credit hour should require about one third of the time investment of a 3 hour regular course.
• Prerequisites. While there are no absolute prerequisites, Math 390 is aimed at students who already have a strong record in math courses and are interested in learning topics beyond regular courses. For example, a student interested in taking Math 390 on a probability/statistics topic should, at a minimum, have taken Math 461 (or an equivalent course) with a grade of A or A+.
• Grading: Math 390 can be taken on a satisfactory/unsatisfactory basis or graded by letter grade. Grading will be based on successful completion of the readings and assignments.
• Math 390 versus regular classes. Aside from the different formats (individual study versus lecture style classes), the main difference to a regular class is in the nature of the topic covered, which should be an "advanced topic not covered in regular classes." In particular, Math 390 is not a substitute for taking regular classes.
• Math 390 (Individual Study) versus Math 492 (Undergraduate Research in Math). These two courses are closely related and targeted at similar audiences: students who have a strong record of math courses (typically including honors courses) and who may be considering graduate school in mathematics or a related field such as mathematical finance, economics, statistics, computer science, etc. Math 390 can lead to a Math 492 undergraduate research project, but can also be taken independently of any Math 492 plans, and it is not a prerequisite for Math 492. For more about Math 492 projects see my Math 492 Page and my Undergraduate Research Page.

How to apply

Once I have assembled a mini group of interested and qualified students, I will submit the Math 390 proposal to the Director of Undergraduate Studies for approval; once the approval is granted, you can register for the course. Note that the usual registration deadlines apply; in particular, a course cannot be added once the "Add" deadline has passed (usually during the second week of the semester).