Duke University 2003-2004 - Office of the Registrar - Duke University

Research Professors Degeratu, Haase, Hwang, Patashnick, Roudenko, and Zharkov;
VIGRE Postdoctoral Fellows Matthews, Rider, Romeo, Smolka, Topaz, and
Washington; Lecturing Fellow Berman; Associate Professors of the Practise Blake and
Bookman; Adjunct Professors Howard, Shearer and Wahl; Professors Emeriti Scoville,
Smith, Warner, and Weisfeld.
Graduate work in the Department of Mathematics is offered leading to the Ph.D.
degree. Admission to this program is based on the applicant's undergraduate academic
record, level of preparation for graduate study, the Graduate Record Examination
general and subject tests, and letters of recommendation.
The department offers research training in both pure and applied mathematics.
Major areas of research specialization include algebra and algebraic geometry,
analysis and partial differential equations, applied mathematics and scientific
computing, differential geometry, geometry and physics, mathematical biology,
probability and stochastic processes, and topology. Interdisciplinary programs with
connections to the department include the Center for Geometric Computing, the
Center for Hydrologic Science, the Center for Mathematics and Computation in the
Life Sciences and Medicine, the Center for Multi-Scale Modeling and Distributed
Computing, and the Center for Nonlinear and Complex Systems.
All Ph.D. students are required to pass a qualifying examination; most students
take this examination shortly after completing their first year of graduate study. While
students are normally admitted only to the Ph.D. program, the A.M. degree with a
major in mathematics is awarded upon completion of 30 units of graded course work
and passing the qualifying examination. Candidacy for the Ph.D. is established by
passing an oral preliminary examination. The preliminary examination is normally
taken during the third year. By this time the student should have chosen a thesis
advisor and demonstrated any computer skills or reading skills in a foreign language
judged to be necessary for work in the chosen area. The original research which begins
after successful completion of the preliminary examination should culminate in the
writing and defense of a dissertation. The dissertation is the most important
requirement for the Ph.D. degree.
Further details concerning the department, the graduate program, admissions,
facilities, the faculty and their research, and financial support may be obtained from
our web site http://www.math.duke.edu/. For inquiries, send e-mail to the director
of graduate studies at dgs-math@math.duke.edu.
For Seniors and Graduates
200. Introduction to Algebraic Structures I. Groups: symmetry, normal subgroups,
quotient groups, group actions. Rings: homomorphisms, ideals, principal ideal
domains, the Euclidean algorithm, unique factorization. Not open to students who have
had Mathematics 121. Prerequisite: Mathematics 104 or equivalent. Instructor: Staff. 3
units.
201. Introduction to Algebraic Structures II. Fields and field extensions, modules over
rings, further topics in groups, rings, fields, and their applications. Prerequisite:
Mathematics 200, or 121 and consent of instructor. Instructor: Staff. 3 units.
203. Basic Analysis I. Topology of Rn, continuous functions, uniform convergence,
compactness, infinite series, theory of differentiation, and integration. Not open to
students who have had Mathematics 139. Prerequisite: Mathematics 104. Instructor:
Staff. 3 units.
204. Basic Analysis II. Differential and integral calculus in Rn. Inverse and implicit
function theorems. Further topics in multivariable analysis. Prerequisite: Mathematics
104; Mathematics 203, or 139 and consent of instructor. Instructor: Staff. 3 units.
205. Topology. Elementary topology, surfaces, covering spaces, Euler characteristic,
fundamental group, homology theory, exact sequences. Prerequisite: Mathematics 104.
192 Courses and Academic Programs