During their first year, students develop a strong background in pure and/or applied mathematics. Courses cover broad areas of pure mathematics (algebra; analysis; topology) and applied mathematics (e.g., numerical analysis, stochastic processes and uncertainty quantification, and analytic study of PDEs). There are also many opportunities for developing more specific interests. To name a few, courses have recently been offered in algebraic number theory, algebraic topology, arithmetic geometry, combinatorics, complex networks/systems, functional analysis, game theory, knot theory, logic, mathematical biology, numerical analysis, probability, Riemannian geometry, set theory, and signal processing.
Just before the beginning of the first summer (and optionally also in the first fall), students complete a preliminary exam in pure or applied mathematics.
Students in their second year (which begins with the summer term) continue to broaden their mathematical knowledge through coursework and research projects. Students form an Advancement Committee consisting of three faculty to guide them through their second year. Those in applied math will be involved in a summer research project, whose written summary and extension will be the basis of an Advancement Examination consisting of a presentation and oral exam. Students in pure mathematics arrange an individually-tailored Advancement Examination with their Advancement Committee.
In the second year, students also complete a seminar which provides training for how to become an effective communicator and classroom teacher. After advancing to PhD candidacy, students are appointed as faculty to teach one Dartmouth course independently in each of their third, fourth (and often fifth) years.
Most of our graduate students finish the work that comprises their thesis during the fifth year, the last year in which we offer financial support.