The University of Arizona

Graduate Courses in Mathematics

This page explains the various types of graduate courses in mathematics at the University of Arizona.

Core courses and regular courses

The core courses (511AB—Algebra, 523AB—Real Analysis, and 534AB—Topology-Geometry) constitute the foundation on which the rest of the program is built. These courses are normally taken in the first year and cover the material to be mastered for the qualifying exams.

“Regular courses” are by definition the more advanced courses taught for the most part in the traditional lecture format. These courses serve to take the student from the foundation provided by the core courses to more specialized knowledge required for dissertation research.


“Research Tutorial Groups” introduce graduate students to mathematical research at the end of the first year and beginning of the second year, typically well in advance of formal dissertation research. In the spring of the first year, students listen to short lecture series on topics of current interest (usually three or four series of three or four lectures, one hour per week). In the following fall, students choose one of the topics and work on a research problem with the sponsoring faculty member and a small group of fellow students. The spring lecture series is one credit hour while the fall research group is three credit hours.

Co-convened courses

“Co-convened” courses are advanced undergraduate courses (400 level) which are also given a 500 level number. (E.g., Symbolic Logic is both Math 401A and Math 501A.) The point is that graduate students may take these courses for graduate credit. They are mainly populated by senior level undergraduates and graduate students from other departments, but mathematics graduates students sometimes take these courses to fill in missing background or in Masters level coursework. A limited number of dual-numbered credits are applicable to the PhD.

Topics courses, seminar courses, and independent studies

Special topics courses are offered each term by faculty, usually in areas of particular expertise (although sometimes the inspiration is that the subject is hot and the faculty member wants to learn about it as well). They are typically one time only offerings and may lead to dissertation problems.

Independent studies are arranged between faculty and students at the discretion of the faculty member. In a typical such course, the student would study a book or paper and meet weekly with the faculty member to discuss the work and related problems.

Outside department courses

The spirit of this requirement is that students should learn to communicate with and appreciate the perspectives of users and producers of mathematics in other disciplines.  The requirement may be satisfied by either taking two courses (6 units) outside the Mathematics Department or by doing an internship. We maintain a list of a priori acceptable courses.