SUMR is an enhancement of the Honors Mathematics Track for undergraduates. It starts informally with the year long course, Honors Multivariable Calculus, Math 265-266, based on Apostol's Calculus, Volume II. This course is a part of the Honors Mathematics Track. It seeks to introduce the sophomore level student to higher mathematics. It makes heavy use of Linear Algebra, and is rigorous while trying to be geometric and attractive.
In April of the Sophomore year the formal program begins with a letter of invitation to join SUMR. This letter is sent to all sophomore Honors Track Math students who have performed well in the first two years (A's and A-'s in math courses). The letter emphasizes that the program seeks to prepare students for graduate work in one of the mathematical sciences. Students who join SUMR embark on a two year program of studies going beyond the Honors Mathematics track.
During the summer after Sophomore year, SUMR members follow a program of readings in General Topology. Sophomore SUMR students are also invited to participate in a seven week summer REU at Notre Dame (funded by a grant from the National Science Foundation). This is centered around two topics. For REU 2003, these will be: Topology and the Fundamental Group and The Theory of Modules over a Euclidean Domain. The REU also has an important independent research component, in which students work on a research problem tailored to their ability. See REU
During the Junior year each SUMR student takes a full year Abstract Algebra course (Groups, Fields, Rings, Modules) and a full year course in Real Analysis (Measure, Integration, PDE, etc.).
In addition to these, the SUMR student participates in the full year course, Math 499, a seminar which meets once per week, for two and 1/4 hours. This is the core of SUMR; all other parts are elaborations. This seminar has existed for 13 years. Each year the topic is different. It aims at being a topic which will be of great help during graduate work but one which is not usually offered to undergraduates. In six recent years the topics of Math 499 have been: Algebraic Number Theory; Lie Algebras and Lie Groups; Morse Theory; Riemannian Geometry; Geometric Complex Function Theory, Vector Bundles and Characteristic Classes.
During the Junior year SUMR students apply to at least two of the many REU's run by NSF, or NSA, and many SUMR students have been selected for these. All students are also encouraged to apply for the Goldwater Scholarship. Six SUMR students have won these.
Senior SUMR students generally take one graduate mathematics course each semester, along with elective math courses. SUMR students also attend the 2 1/4 hour weekly seminar, Math 499, with the Juniors. For this reason the seminar topic must change each year. Seniors then typically apply to graduate school in one of the mathematical sciences. Pure Mathematics is most popular, though some pursue Applied Math, Physics, or Electrical Engineering. The great majority of participants in SUMR decide to pursue graduate work in one of the mathematical sciences mentioned above (see Appendix A). Of these, virtually all who have applied have been accepted in one of the top 12 graduate programs with a fellowship or assistantship.
Finally each Senior SUMR student writes a Senior Thesis. It is hoped that it might help the student to develop a research direction for subsequent graduate work. Further details on this project can be found in the next section.
The morale of the group of SUMR students is quite high. They see themselves as a mathematical elite, which in fact, they certainly are. Currently there are 7 Notre Dame students in SUMR.
Updated on:
Thursday, May 24, 2007 9:28 AM
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