## Section 2 An overview of the graduate program

The mathematics graduate program at Dartmouth College is a small, selective program that serves students who wish to complete a PhD. in pure or applied mathematics. The program is structured to serve both those who envision a career involving research and teaching as well as those who wish to continue their research in industry. The program at Dartmouth is a five-year program in which students are enrolled in each of the Summer, Fall, Winter, and Spring terms. Students admitted to the PhD program are offered support through a Dartmouth Fellowship or other grant for up to 5 years provided they continue to make satisfactory progress towards their degree.

During their first year, students develop a strong background in at least three research areas, selected from among algebra, analysis, topology, and two broad areas of applied mathematics which include numerical analysis, stochastic processes and uncertainty quantification, analytic study of PDEs, and general methods in applied mathematics. After their first spring, students choose three of those areas in which to complete a preliminary exam. During their second year the path followed by those in pure mathematics begins to diverge from those in applied mathematics. Students in applied math will be involved in a summer research project whose written summary and extension will be the basis of a presentation and oral exam. Students in pure mathematics form an Advancement Committee and craft an individually tailored Advancement Examination which can take a number of different forms. Students continue to broaden their mathematical knowledge through course work or research projects. By the end of the second year, a student will also complete a seminar which provides training for how to become an effective communicator and classroom teacher, secure an advancement committee consisting of a thesis advisor and two other faculty members, and advance to candidacy for the PhD. Graduate students are appointed as faculty to teach one Dartmouth course independently in each of their 3rd, 4th (and often 5th) years. Most of our graduate students finish the work that comprises their thesis during the 5th year, the last year in which the department offers financial support.

Areas which students have recently chosen for their dissertation research include algebraic number theory, algebraic topology, arithmetic geometry, combinatorics, complex networks/systems, functional analysis, knot theory, logic, mathematical biology, numerical analysis, Riemannian geometry, set theory, and signal processing. For our recent graduates, review their thesis abstracts and advisor and job information. Further online information is at math.dartmouth.edu/graduate-students.