SUMR at Notre Dame
The Senior Thesis

What is the Senior Thesis?

All Mathematics majors have the option of completing a Senior Thesis. This is intended to give a better sense of how mathematics is done than can be obtained in the classroom, and also to help develop the habit of learning mathematics in an independent setting. A senior thesis can be a very fulfilling experience, and a practically useful one for those who are planning graduate studies. As well as giving you first-hand experience of what mathematical research is about, doing a senior thesis shows graduate admissions committees that you are able to complete a prolonged and mostly self-motivated research project, while dealing with many other responsibilities at the same time.

In most cases, the senior thesis is expository, based on readings beyond the level of an undergraduate course, and representing an effort that goes well beyond what is found in such a course. At the end of senior year, there is an opportunity to present senior thesis work at the College of Science Joint Annual Meeting. All students who successfully complete a senior thesis receive the citation "Graduation with Senior Thesis" on their diplomas, and a copy of the thesis is deposited in the Mathematics library.

Writing a Senior Thesis

Begin by finding an advisor in the area of mathematics on which you wish to write a thesis. Any member of the department can serve as a senior thesis advisor. A list of faculty who have expressed particular interest in advising, along with some suggested topics, may be found here. You may also find it helpful to look at the list of recent senior theses topics found here. You can begin looking for an advisor towards the end of the fall semester, or during the spring semester, of your junior year.

Your advisor will propose a collection of appropriate readings to get the process started. You should then register for 2 credits of Undergraduate Research (MATH 48800) for the coming semester. To get registration permission you have to contact the Director of Undergraduate Studies (currently Matthew Dyer) telling him that you intend to complete a senior thesis, and telling him who your advisor is. (Don't forget to sign your email with your full name!) You should continue registering for 2 credits of MATH 48800 for each semester that you work on the thesis, until the final semester (spring of senior year) when you should instead register for 2 credits of Thesis (MATH 48900). Each registration period you will need to contact the DUS to get the necessary permissions; it would be helpful to him if each time you reminded him who your advisor is and what your topic is.

Writing a senior thesis is a major undertaking. It is never too early to begin planning and writing it. Although the details of your progress will vary depending on the specific plan you've worked out with your advisor, one possible timeline might be as follows. You might meet with your advisor for about an hour a week during fall semester of senior year (and maybe spring semester of junior year, if you started earlier), and in most cases you should aim to have most of the research and reading completed, and be able to give an outline of the thesis to your advisor, by the end of fall of senior year. You can then turn to writing, aiming to submit a draft of the thesis to your advisor by mid March, so that a final version can be ready by early April. Regular meetings with your advisor during the spring semester will help this process along. Usually your advisor will help you work out a more detailed plan of study, but there is a great deal of flexibility in this as the work progresses.

The length of your thesis will depend very much on the subject matter. Past theses have ranged from 15 to 60 pages, with most in the 30 to 50 page range. A good guideline is that the thesis should be long enough for you to convey enough details and explanations that a mathematics major would be able to follow it. Your advisor will help you with more precise guidelines specific to your chosen topic.

There are just a few deadlines to keep in mind throughout the process:

  • If you are an Honors student, then as soon as you know who your advisor is and what you topic will be, you should pass this information on to Liviu Nicolaescu (again, remembering to sign your email with your full name).
  • By January 24 of senior year you need to write to the DUS letting him know the following information: your full name, ND email address, the exact title of the thesis, your majors and minors, and your advisor's name. This information is required by the registrar.
  • By April 12 of senior year a hard copy of the thesis, with a cover page signed by your advisor, must be submitted to the DUS. He will then assign readers who will decide whether the thesis is acceptable. This decision will be made in time for the registrar to be informed, so that the appropriate citation can be put on your diploma.

Once your thesis has been approved, you should take the time to upload it to Curate ND so that it will be permanently available to future scholars. You should also consider giving a short talk about your thesis at the College of Science Joint Annual Meeting. Your advisor will help you figure out the deadline for this.

A note for Glynn Family Honors students: Your Glynn Family Honors Thesis can be submitted to the Department of Mathematics. You should follow the schedule described above, but note that there might also be additional requirements specific to the Glynn Family Honors program.

Some recent Senior Theses

Here are examples of some topics that students have written senior theses on. For more information on the 2013 theses, please see the College of Science page about seniors graduating with senior theses.

  • Matt Charnley (2013, Double major in Chemical and Biomolecular Engineering and Honors Mathematics): Thermal Detection of Inaccessible Corrosion (advisor: Nancy Stanton)
  • Sean Meehan (2013, Honors Mathematics): On the Topic of Ramsey Theory (advisor: David Galvin)
  • MurphyKate Montee (2013, Double major in Honors Mathematics and Music): On Characteristic Classes of Complex Vector Bundles (advisor: Frank Connolly)
  • Katherine Ritchey (2013, Honors Mathematics): Linear Error Correcting Codes (advisor: Dennis Snow)
  • Edward Sanchez (2013, Major in Mathematics, minor in Philosophy): Equivalent Formulations of the Cayley-Bacharach Theorem for Points in Projective Space (advisor: Claudia Polin)
  • Vikram Saraph (2013, Major in Computer Science Engineering, supplementary major in Honors Mathematics): Index Sets of Computable Groups (advisor: Julia Knight)
  • James Schmidt (2013, Triple major in Mathematics, Philosophy and Mechanical Engineering): Forcing in Algebra (E.C. Groups) (advisor: Cameron Hill)
  • Nick Seewald (2013, Double major in Honors Mathematics and Life Science): Entropy and Counting (advisor: David Galvin)
  • Edward Stivers (2013, Mathematics): Financial Applications of Partial Differential Equations (advisors: Alex Himonas and Tom Cosimano)


Updated on: Tuesday, May 20, 2014 3:00 PM
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