# Program Overview

**Prerequisites:**

To major in mathematics students need a strong foundation in linear algebra and analysis, in both one and several variables, as well as experience in understanding and writing rigorous mathematical proofs. Generally, prospective majors with a very strong background in calculus are strongly recommended to start in 215, followed by 217 and 300. Prospective majors with extensive prior experience with calculus and rigorous proofs can start in 216, followed by 218. Students with an interest in rigorous proofs may start in 210 or 214 and then continue to the 215-217-300 sequence.

Generally, either 215-217-300 or 216-218 or 203-204-215 are strongly recommended for admission to the department. Some math majors start in the 103-104-201 sequence and then transition to the more proof-based courses a bit later. Prospective mathematics majors should consult the department early and plan a program that includes as much of the 215-217-300 or 216-218 sequence as possible. Most majors begin taking courses at the 300-level by the second semester of the sophomore year, in preparation for their junior independent work. Majors who have not satisfied the multivariable prerequisite with MAT203 or MAT218 (or equivalent) should take MAT300 (offered fall only) in their junior year.

Degree requirements include completion of eight upper-division courses: four core courses, one from each of real analysis, complex analysis, algebra and geometry/topology/discrete math; and four additional courses which can be chosen to create an appropriate program of study for particular fields of pure and applied mathematics such as numerical analysis, discrete mathematics, optimization, physics, the biological sciences, probability and statistics, finance, economics, or computer science. For students interested in these areas, a coherent program containing up to three courses in a cognate field may be approved. (Note that no more than three cognate courses can be counted towards these degree requirements.)

All departmental students engage in independent work, supervised by a member of the department chosen in consultation with a departmental adviser. The independent work in the junior year generally consists of participating actively in a junior seminar in both the fall and the spring semesters. Alternatively, a student may opt to replace **one** junior seminar with supervised reading in a special subject and then writing a paper based on that reading. The independent work in the senior year centers on writing a senior thesis. Each senior takes an oral examination based on the senior thesis and the broader subfield to which it contributes. A departmental committee conducts the examination in May.