Syllabus Math 499


Math 499. Introduction to Graduate Mathematics

This course/seminar is required of all incoming graduate students. It meets throughout the academic year on Mondays at 4 p.m. in 245 Altgeld Hall. The course offers 1 hour of credit and has no formally assigned outside work.

Math 499 serves as a forum for first-year graduate students (and other interested parties) to get to know the research interests of the Mathematics Department faculty. The speakers are invited to participate by the Director of Graduate Studies (“DGS”).

The goal of Math 499 is to energize beginning students about current topics of research. This is normally accomplished by a skillful introduction to basic concepts that lead to a discussion of research opportunities.

Students enrolled in Math 499 are given the task of “critiquing” the speakers on the effectiveness of their talks. The DGS uses the initial meeting of Math 499 each academic year to discuss principles on which to base one’s critique.

The material covered in each seminar will include

  1. What the subject is about.
  2. Why the speaker is enthusiastic about the subject.
  3. How the subject relates to U of I courses/research interests and to the rest of mathematics
  4. What there is for students to do as thesis work.

The sessions are open to other interested graduate students and faculty members. Vigorous discussion will be encouraged and each hour will close with a question and answer period (e.g., do algebraic number theory and analytic number theory have anything to do with each other? What is the difference between algebraic topology and algebraic geometry?). Finally, Math 499 provides a format in which graduate students and faculty can meet each other.