# Honors in mathematics

Students desiring to graduate with honors must satisfy two requirements: they must have at least a 3.7 GPA in upper-division math courses (300-level and above) at the time of graduation, and they must write an honors thesis.

### Thesis:

Students must write a thesis under the direction of an advisor, covering an advanced topic in mathematics. The student must give an oral presentation of the thesis to a committee, who must give their final approval.

Writing a thesis involves learning about an advanced topic in mathematics. To prepare yourself to be able to do this, it is a good idea to take one or more 400-level courses during your junior year. This is not a requirement, but it is strongly recommended.

### Timeline and Suggestions

### Thesis Advisor and Topic:

Honors theses from past years are available for perusal in Hilbert Space (University 107-108). These will give you an idea of what students have done in the past, and they might even inspire ideas for what you would like to do.

If you decide to pursue honors, then near the end of your junior year you should investigate possible advisors. Occasionally students have an idea right away of what topic they want to write their thesis on, and then they have to search for an advisor who is capable and willing to supervise such a thesis. What happens more often is that students know a professor who they would like to work with, and the professor recommends a topic (in consultation with the student). In either scenario, spring of your junior year is a good time to shop around for possible advisors. Most professors are happy to talk with students about possibilities for a thesis. If all else fails, you can always talk to the head undergraduate advisor or the director of undergraduate affairs (see Useful Contacts in the sidebar of this page).

It is important to have chosen an advisor before you start your senior year. This means making the arrangements during the spring of your junior year, or at the very latest during the summer after your junior year. Your work on your thesis will take place during the fall and winter of your senior year, with much of the writing done during the spring. The “work” usually involves the student reading an advanced piece of mathematics and meeting weekly (sometimes biweekly) with his or her advisor for discussion.

** At the beginning of fall of your senior year, you should send an email to both the director of undergraduate studies and the head undergraduate advisor informing them that you will be working on an honors thesis, and naming your topic and your advisor.**

### Thesis Committee:

In addition to your advisor you must select a thesis committee; this will consist of your advisor together with two other professors (usually math professors, but this is not required). The thesis committee does not have to be chosen until the winter of your senior year, and usually your advisor will make suggestions of people who are familiar with the area of your thesis.

### Thesis Completion and Oral Presentation:

Once your written thesis is completed, you must give a copy to all the people on your committee and then schedule a thesis defense. The defense must be held by the end of week 9 of spring term, and your committee members must get a copy of the thesis at least two weeks before the defense. So the written thesis must be completed by the end of week 7 of spring term. Usually committee members will make suggestions for improvements, and so this is not necessarily the “final” form of the thesis, but it should be very close to the final form.

When a date and time for the oral defense has been decided, work with the Undergraduate Coordinator (in the main math office) to schedule a room and post public announcements of the defense around Fenton and University. Oral defenses are open to the public! Announcements should be posted at least a week ahead of time.

The exact nature of the oral defense is worked out in consultation with the thesis advisor. Usually it involves the student giving a 30-45 minute presentation of the work, followed by questions from the thesis committee. At the end of the defense everyone except the thesis committee leaves the room, and the committee determines whether or not the thesis meets expectations.

At the end of the year, submit the final version of your thesis to the Director of Undergraduate Studies. This will be bound and added to the library in Hilbert Space.

### Optional LaTeX style file for honors theses:

Thanks to Seth Temple for providing the file.

### Recent Honors Theses:

**2021-2022:**

Hannah (Qiaochu) Cui Using Information Theory to Understand Neural Representation in the Auditory Cortex

Jessica Taylor Lines and Conics in Quartic Surfaces An Algorithmic Approach

**2020-2021:**

Peter DeBello, Symmetric Functions & the Character Table of

Simon Venter, Lifting Automorphisms of

**2018-2019:**

Sierra Nicole Battan, *Orthogonal Structure on a Tripod*

**2017-2018:**

Ben Estevez, *Random *-Cosquare Matrices and Self-Inverse Polynomials*

Nathaniel B. Schieber, *A Computational Approach to Tangles*

Aleksander Shmakov, *Galois Representations in Étale Fundamental Groups and the Profinite Grothendieck-Teichmüller Group*

Seth David Temple, *The Tweedie Index Parameter and Its Estimator*

**2016-2017:**

Lianjie Jiang,* Higher Order Beliefs and Sequential Reciprocity*

Dongmin Roh, *Reflexive Polygons and Loops*

Graham Simon, *Hawkes Processes in Finance: A Review with Simulations*