# Requirements

Mathematics majors are expected to have a background knowledge of calculus in one and several variables and of linear algebra and to have had at least some experience with rigorous proofs and formal mathematical arguments before entering the department. The standard calculus sequence 103-104-203-204 covers the basic background material. The honors sequence 215-217 and the accelerated honors sequence 216-218 cover calculus and linear algebra more thoroughly and theoretically and serve as an introduction to some mathematical techniques and results that are a background for further work in analysis. Any of the courses 214-215-216-217-218 will serve as introductions to rigorous proofs and formal mathematical arguments. It is not necessary for students who have had equivalent courses elsewhere to take these specific courses. For any questions please see the Advisors for Mathematics Majors or the Placement Officer.

Mathematics majors must of course meet the general University requirements for graduation. These include a writing seminar, which must be taken during the freshman year, some proficiency in a foreign language, and ten courses in the various distribution areas as described in the undergraduate announcement. It is wise to get these requirements out of the way as early in your undergraduate years as possible, to leave freedom in the junior and senior years for courses in mathematics and other topics in which you are seriously interested. Mathematics majors are required to successfully complete a minimum of 31 courses for graduation, of which a minimum of 19 must be outside the Mathematics Department. Of these 19 courses, two can be from the list of 200-level prerequisite courses for the department.

Please Note: Students who take more than 12 courses at any level in the Mathematics Department, in addition to two prerequisite courses, must take more than the usual number of courses altogether in order to have at least 19 courses outside the department.

Mathematics majors are required to take at least **eight departmental courses** in mathematics:

Students must complete **four core requirements**:

- one course in
**real analysis**(e.g. 320 or 325 or 425 or 385) - one course in
**complex analysis**(e.g. 330 or 335) - one course in
**algebra**(e.g. 340 or 345) - one course in
**geometry**or**topology**(e.g. 350 or 355 or 365 or 560)

It is recommended that students complete some of these core requirements by the end of the sophomore year. Completing these core courses early will give you more options for junior and senior independent work.

Note: One course in **discrete mathematics** (e.g. 375, 377 or 378) can replace the geometry/topology core requirement, if desired.

**In addition to the four core requirements**, students must complete an additional four courses at the 300 level or higher, up to three of which may be cognate courses outside the mathematics department, with permission from the junior or senior advisers or departmental representative.

The final choice of departmental courses is settled in consultation with the Advisors for Mathematics Majors during the spring term of the senior year.

The formal independent work requirements in the mathematics department consist of a junior seminar and/or junior paper during each term of the junior year, and a senior thesis in the final year.

Students who have particular interests are encouraged to talk to faculty members about possible topics they would like to have offered; the Mathematics Department attempts to meet the demands for special courses to the extent possible within staffing limits if there is sufficient student interest. Students who have particular topics in mind sometimes take reading courses in those areas not covered in the regular curriculum; normally at most one course each term can be a reading course. Applications for approval of reading courses are available in 404 West College and must be approved by the staff of the Office of the Dean of the College.

In addition to undergraduate courses the Mathematics Department usually offers some introductory graduate courses that are accessible to undergraduates with sufficient background. Lists of graduate courses with instructors and times are usually posted outside the Common Room. Students interested in taking a graduate course should consult the instructor first. Many graduate course are quite specialized, and are directed towards graduate students and visitors who are working in a particular area. They do not provide a broad enough overview of the field to be of interest to most undergraduates. Forms for registering to take a graduate course can be obtained from the Registrar's web pages. These forms must be signed by the instructor of the course, the mathematics Departmental Representative or Advisor and your residential college dean, then taken to the Registrar's office, since it is not possible for undergraduates to register for graduate courses on SCORE.