Recent Senior Projects in Mathematics
- "Hilbert Series and Free Resolutions"
- "Combinatorial Laplacians of Simplicial Complexes"
- "Hilbert Sequences of Monomial Ideals"
- "Forbidden Subgraphs for Edge Domination"
- "Geodesics on Types of Singular Surfaces"
- "On the Curvature of Polyhedra"
- "The Matching Model for Routing Permutations on Graphs"
- "SET® Theory"
Writing
a Senior Project in Mathematics
The
senior project at Bard, required of every students in the college, is
the culminating experience of four years of academic work at the college.
It will most likely be the longest and most complex piece of academic
work a student will have done. It will also be one of the most memorable
parts of a Bard education. During its writing, a project can also be
a source of frustration and anxiety, though it need not be with the
right approach.
What
is a Mathematics Senior Project?
A senior project in mathematics is a year-long investigation of
a particular topic or problem in mathematics. Such a topic may be in
pure or applied mathematics. It might involve areas that relate to mathematics
(e.g. physics or economics), and it might make use of computers, though
in either case the project must be solidly mathematical. A project will
involve both learning some new mathematics and writing an original exposition
of what you have learned, as well as an attempt to solve a problem to
which the student does not know the result. Unlike a doctorate, publishable
new results are not needed for a successful undergraduate project. Senior
projects in mathematics are evaluated according to three criteria: mathematical
content, exposition and effort. To get a feel for what a senior project
in mathematics might involve, please consult with the faculty members
of the Mathematics Program.
Project
Adviser
It is up to the student to choose a project adviser, as long as the
proposed adviser agrees. The project adviser need not be student's academic
adviser. A project adviser should be chosen before the end of the junior
year, prior to registration for the fall semester, since the project
adviser needs to sign the registration card when a student registers
for senior project. Prior to the end of the junior year, a student should
discuss with the project adviser what should be looked at over the summer.
During the senior year, a student will set up a regular schedule of
meetings with the project adviser, usually once per week.
Choosing
a Topic
The best project topic is one that can sustain the student's interest
for a whole year. Although the adviser will be glad to suggest topics,
it is best if the student has as much input as possible into the choice
of topic. If a student has a specific topic, the project adviser will
help evaluate its feasibility. If a student does not have a specific
topic, the project adviser will make suggestions of sources for topics.
A good place to start looking is to browse through the mathematics collection
in the library (which have Library of Congress letters QA). There are
also a number of journals in the library that are aimed at undergraduates,
such as "The American Mathematical Monthly" and "The Mathematical Intelligencer."
Events Along the Way
1. Prospectus Talk
During the first semester of the senior project, the student will give a 10 minute presentation to the students and faculty of the Natural Science and Mathematics Division about what she intends to do for the project. It is understood that anything said at this talk is tentative.2. Weekly Meetings
The student should schedule a regular meeting time with her project adviser.3. Handing in Drafts
The student should set up with the project adviser a schedule for handing in rough drafts. These drafts need to be handed in enough ahead of the project due date so that the project adviser will have sufficient time to read the drafts and make comments.4. The Final Draft
On the date senior projects are due, the student must have three copies of the project ready, one to be handed to each member of the project board (after the project is taken to the dean's office).5. Project Board
The project board will consist of the project adviser and two other faculty members to be assigned by the NS & M Division. Student preferences about the composition of the board are taken into account, though they are not always fulfilled. The board will meet with the student in the middle of the senior year for a midway review, and will meet with the student after the project is completed for a project review. The grade for the project is determined by the NS & M Division after hearing a recommendation from the board.6. Poster Session
After the senior project due date, all seniors in the NS & M Division participate in the divisional poster session, in which each student presents a poster explaining the results obtained during the course of the senior project.7. Project Talk
After the senior project due date, each mathematics senior presents her work as part of the Mathematics and Computer Science colloquium series at Bard.