### Overview

To complete your MS in Mathematics degree, you have a choice of writing a master's degree thesis or passing two comprehensive exams. Most students choose the comprehensive exam option because

- The prerequisite is lower. To do a thesis, you need a GPA of 3.5 or better. To attempt the comprehensive exams, a GPA of 3.0 suffices.
- It's faster. Writing a thesis can take several terms. Comprehensive exams can be passed in one term.
- It's cheaper. If you don't pass the comprehensive exams on the first attempt, subsequent attempts cost $10 each - assuming that you are not taking any courses.

Even so, if you have ambitions to do a PhD, or are just enthusiastic about mathematical research, you should consider doing a thesis. You should be aware of the Math Department's Thesis Policy, as well as those of the college and university:

It is expected that you will write the thesis in LaTeX, a mathematical typesetting language that anyone serious about publishing mathematics should know. To help meet the university's complicated and extensive formatting requirements, you should start with the Math Department's LaTeX Thesis Template.

### Math Department Thesis Policy

Students completing a master’s thesis will produce a written work (thesis) and give an oral presentation (defense) on a topic chosen with consultation of a thesis supervisor.

**Time:** A thesis typically takes at least two or three semesters of solid work.

**Length:** A thesis is typically 50 to 100 pages.

**Requirements:** A student is required to have a GPA of 3.5 or better on the MS degree program, EXCLUDING DIRECTED STUDY COURSES, and have completed at least 3 5000-level courses from his/her MS degree program when a faculty member agrees to be the thesis supervisor. The GPA must also be 3.5 or more when submitting the GS-12 and registering in Math 5990 (Thesis).

**Content and Presentation:** The thesis should contain an original research result or consist of an expository discussion of a topic, organized in an original way. If the thesis contains an original research result, it should also discuss the broad context in which the result occurs (e.g., other related results or conjectures in the field, historical development, etc.). The thesis must contain some content of theoretical significance, e.g., some theorems and their proofs. The writing should be grammatically correct and structurally sound, i.e., the presentation of the results and their context should follow a logical order. The introduction to the thesis should be readable by a person who has some mathematical knowledge, but is not necessarily an expert in the subject.

**Research:** The thesis must draw from multiple sources in the mathematical literature.

**Oral Defense:** The oral defense of a thesis is a public event. An announcement of an upcoming thesis defense should be posted in the Math Department at least a week in advance. A student’s defense presentation will typically last one hour, followed by questions from the thesis committee and other members of the audience.

**Prospectus and Committee:** At least one to two semesters before the planned thesis defense, the student, in consultation with the proposed thesis supervisor, will write a 1-2 page thesis prospectus, including a tentative title and a research plan. The prospectus will then be used to recruit a thesis committee, normally consisting of the thesis supervisor and two other math department faculty members able to evaluate the thesis and oral defense. Faculty members from other departments can serve on a thesis committee that is interdisciplinary in nature. At least two of the thesis committee members must be from the math department (typically the advisor and one other faculty member).

**Abstract:** One semester before the defense, the student, in consultation with the thesis supervisor, should choose a title for the thesis and write an abstract. The abstract and a GS-12 form are submitted to the College Associate Dean for approval.

Revised: September 2020

### LaTeX Thesis Template

You can download the Math Department LaTeX thesis template, edit as needed, then typeset and print out your completed thesis. The template takes care of the margins, pagination, the formats of the title page, copyright page, references, appendices, etc. Comments in the LaTeX files provide information on how to use the templates. Portable Document File (.pdf) versions of these files are also provided in case they are useful.

If you don't have LaTeX or don't know how to use LaTeX you might start at the Consolidated TeX Archive Network or at The LaTeX Project.

**Abstract**

The GS-12 form and a thesis abstract need to be sent to the Associate Dean of the college at least one semester before the thesis defense. The abstract accompanying the GS-12 does not actually need to be in the same, precisely specified, form as the abstract in the thesis, but why not make it the same.

▪ Abstract template in LaTeX form

▪ Abstract template in .pdf form

**Thesis Template**

In theory, you can take this LaTeX thesis template, insert your own title, abstract, chapters, graphics, committee member names, etc. and then not have to worry about the margins, pagination, the formats of the title page, copyright page, references, appendices, etc.

To typeset the template, you will need the cycloid graphic. This graphic serves only to demonstrate how such graphics can be included in a LaTeX document. If you don't care about that, you don't need the graphics file, and the first change you might make to the thesis template is to remove all the \includegraphics commands. This graphics file needs to be put somewhere your LaTeX application can find it - for example, it could be placed in the same folder as the thesis template itself.

▪ Thesis template in LaTeX form

▪ Thesis template in .pdf form

▪ Cycloid graphic in .pdf form

**Submission**

Details on the submission process, and submission deadlines are found in the University Thesis Guidelines. You upload your completed thesis in .pdf format (without signatures) to ProQuest. You must also obtain the signatures of all committee members and the department chair on the GS-13 Form. Submit the signed GS-13 Form with original ink signatures to your Thesis/Dissertation Reviewer. The department graduate advisor would also like a signed copy of this form.