# 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 215-217-300 sequence and the 216-218 sequence 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 at the 300- and 400-level or higher, including:

- one course in
**real analysis**(from the 320s or 420s or 200 or 300 or 385 or 520) - one course in
**complex analysis**(from the 330s) - one course in
**algebra**(from the 340s or 440s) - one course in
**geometry**or**topology**(from the 350s or 450s or 360s or 460s, or alternatively, one course in discrete mathematics from the 370s or 470s) - an additional four courses at the 300 level or higher.
- Up to three of the eight departmental courses may be cognate courses outside the Mathematics Department, with permission from the Junior or Senior Advisors or Director of Undergraduate Studies. (Courses from other departments that are cross-listed with MAT do not need permission and do not count toward the total of three allowed cognates.)

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.

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 a junior paper, one in each term of the junior year
*or*two junior seminars, one in each term of the junior year*and*a senior thesis in the final year.

Students who have particular interests may speak with faculty members about reading courses in those areas not covered in the regular curriculum. Reading courses are intended for students who have taken all the 300/400 level courses in their area of interest and would like to delve deeper into the material. Normally at most one course each term can be a reading course. At most two reading courses can count toward the basic "8 mathematics courses" requirement. Applications for approval of reading courses are available in 404 Morrison Hall or on the Registrar's website, and must be approved by the staff of the Office of the Dean of the College after departmental approvals are obtained. Permission to take graduate courses in mathematics (other than the bridge courses described below) is granted through a version of the reading course approval process. Because the process has so many stages, reading course applications are due in the department no later than the first Wednesday of the term.

In addition to undergraduate courses, the Mathematics Department offers some introductory graduate courses that are accessible to undergraduates with sufficient background. These are called "bridge" courses. In general, students interested in taking a graduate course should consult the instructor about the advisability of doing so. Many graduate courses 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. It is not possible for undergraduates to register for graduate courses online. For bridge courses and graduate courses in other departments, please go to https://registrar.princeton.edu/forms for the "Undergraduate Permission to Enroll in Graduate Courses Form". The form must be signed by three people---the instructor of the course, the Mathematics Director of Undergraduate Studies or Advisor, and your residential college dean---and then taken to the Registrar's office, since it is not possible for undergraduates to register for graduate courses on TigerHub. For more advanced Mathematics graduate courses, permission to enroll is accomplished via the "reading course" process -- contact the Undergraduate Administrator for more information.