In 1999 the department
decided that all students in the Honors Mathematics Track would have the
option to write a senior thesis in mathematics. At that time the Senior
Thesis became a requirement for all students in the SUMR program. This
project is intended to give the student a better sense of how mathematics
is done and to develop in the student the habit of learning mathematics
in an independent setting. This work is expected in most cases, to be
expository, but based on graduate level readings.
During the final
three semesters at Notre Dame, the student works closely with a faculty
advisor on a program of readings in preparation for the thesis. The thesis
work of the student is recognized with a formal citation on the transcript
and on the diploma.
Earlier this program had been available to some students in the department, but most who wrote Senior Theses were from SUMR. In the accompanying table are the titles of all Senior Theses directed by department members in recent years. As can be seen the topics are typically quite impressive ones for undergraduates. This has proved to be a very rewarding experience for SUMR students.
There is a strong tendency for students who do a senior thesis to continue with graduate work in one of the mathematical sciences. For example 14 of the 21 students in the accompanying table subsequently pursued a Ph.D. in some area of mathematics, statistics, physics, or engineering (For SUMR students it is 12 of 13).
| Student | Advisor | Thesis Title |
| Hurtubise, D. (SUMR) | F. Connolly | Gromov's proof of Bieberbach's Theorems |
| Mohlenkamp, M. (SUMR) | F. Connolly | Classification of Simple Lie Algebras |
| Cecil, T. | A. Sommese | Polynnomial Continuation in C++ |
| Christophersen C. | A. Himonas | Differential Equations and Fouier Analysis |
| Hardgrove, M. | M. Alber | Chaos and Fractals |
| Luense, B. | J. Knight | Decidability and Control of Systems |
| O'Donnell, K. | J. Rosenthal | Methods of Ranking Tournament Teams |
| Powell, D. (SUMR) | F. Connolly | Spin^c -structures on Four Manifolds |
| Ponisciak, S. | M. Dyer | Reflection Groups and Coxeter Groups |
| Beh, J. (SUMR) | J. Rosenthal | Linear Systems and Shift Invariant Codes |
| Gries, K. | M. Dyer | Representations of the Symmetric Group |
| Couture, A. (SUMR) | F. Connolly | What is a Connection? |
| Dean, B. (SUMR) | F. Connolly | On the h-Cobordism Theorem |
| Schaffrin, H. (SUMR) | F. Connolly | Hyperelliptic Riemann Surfaces |
| Hatfield, E. (SUMR) | B. Smyth | Time Travel and Causality Violation |
| Siefring, R. (SUMR) | F. Connolly | Chern Classes of Complex Vector Bundles |
| Swinarski, D. (SUMR) | F. Connolly | The Abel-Jacobi Map for Riemann Surfaces |
| Assaf, S. (SUMR) | Cholak, Evens | Zeta Function of Imaginary Quadratic Fields |
| Ponto, K. (SUMR) | F. Connolly | Manifolds Homeomorphis to Spheres |
| Mapes, S. (SUMR) | D. Snow | Complex Simple Lie Algebras |
| Nerlinger, A. (SUMR) | F. Xavier | Dynamical Systems |
| McFeron, D. (SUMR) | F. Connolly | Connections and Characteristic Classes |
Updated on:
Thursday, May 24, 2007 9:28 AM
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© 2003 University of Notre Dame