Honors Thesis

Key Information for Students

MTH492H Honors Thesis is a one semester, writing-intensive course that will satisfy both the University Tier-II writing requirement and the Math Department Capstone requirement. It is meant to be the concluding part of a multi-semester project. By design, MTH492H provides students with a first-hand look at facets of academic research, and mirrors many of the activities that would be expected for graduate studies in mathematics. While original research sometimes forms the basis of MTH492H projects, it is not strictly required. Students interested in completing an Honors Thesis should find a thesis supervisor at least two semesters prior to the semester in which the thesis is to be written, to arrange for the completion of requisite coursework and preliminary training.

Example: students who wish to enroll in MTH492H in the Spring semester should choose a thesis supervisor by the preceding Summer, and complete preparatory coursework and training during the Fall semester.

Enrollment in MTH492H is subject to departmental approval. Applications (see instructions below) should be submitted after the students have completed the preparatory coursework and training, and before the start of the semester when the student will enroll in MTH492H. A student may enroll in MTH492H multiple times (up to four), each requiring separate application; each instance of MTH429H will require the submission of an original thesis and the delivery of an oral presentation.

Recommended Timeline

• Two semesters prior to the semester in which MTH492H will be taken:
  • First half of the semester: The student should speak to faculty members to discuss the possibility of a thesis project. It is recommended that students meet with multiple faculty members to find a best fit.
  • Midpoint of the semester: The student should reach tentative agreement with a faculty supervisor (or multiple faculty co-supervisors) on the subject, scope, and format of the thesis project. The faculty supervisor(s) should recommend preparatory activities to be completed during the semester to follow. These are typically (a) directed study (MTH490) or supervised research under the guidance of the faculty supervisor(s); or (b) completion of relevant advanced coursework.
• The semester prior to the semester in which MTH492H will be taken:
  • During the semester: The student should complete the preparatory training. Frequently students also get a head start on the thesis research, though it is not required.
  • At the end of the semester: The student and the faculty supervisor should complete the Application form and submit it for departmental approval.
• The semester during which MTH492H is taken:
  • Weeks 1 through 5: The student should continue the thesis-research activities.
  • Week 6: The student should begin writing the thesis.
  • Weeks 7 through 14: The student should continue to write, getting regular feedback on the written thesis from the faculty supervisor.
    • A complete first draft should be available no later than Week 12.
  • Weeks 12 through 15: The student should prepare and deliver their oral presentation.
  • At the end of semester: submit to the department (a) the written thesis; (b) copy of the Oral Presentation Feedback Form; and optionally (c) FERPA/Copyright release form.

Expectations of an Honors Thesis

The main expectations of a successful Honors Thesis are:

• Communications: reading. Students should carry out independent study or directed reading of primary literature, typically in the form of research articles or monographs. This portion can be done in collaboration with other students.
• Communications: writing. Students must independently write a thesis.
• Communications: presenting.
  • Students should hold regularly scheduled discussions with the faculty supervisor(s) and deliver progress reports.
  • Students must independently deliver an oral presentation before the end of semester.
• Intellectual Ownership. Students must independently carry out activities that develop deep understanding of the material. Some combination of the following is typical:
  • Performing original research.
  • Hands-on engagement with the material, e.g. applying techniques to specific problems, formalization of a mathematical proof in Lean, or concrete implementation of a theoretical algorithm.
  • Synthesis and evaluation of material from multiple sources, e.g. comparing and contrasting different approaches and techniques for solving the same problem, writing an expository summary on historical progress toward an open or long-standing problem.

Writing an undergraduate thesis is a time-consuming exercise, with continual revisions based on feedback from the supervising faculty. We recommend that students start writing by Week 6 of the semester. The research activities leading to the thesis may be carried out prior to the semester in which the student enrolls in MTH492H, provided that the Deliverables (see below) represent original work completed specifically for MTH492H.

To best ensure successful completion of the Honors Thesis requirements, we require students to demonstrate sufficient preparation before starting the honors thesis. Typically this can be satisfied by one of the following:

• Prior research experience under the supervision of the proposed faculty supervisor.
• Prior independent study / directed reading (MTH490) with the proposed faculty supervisor.
• Completion of relevant advanced coursework.

Policy

Application and Approval (Prior to enrolling in MTH492H)

The Honors Thesis Application Form must be completed and signed by both student and advisor, and submitted to both the Director of Undergraduate Studies and the Advanced Track Director for approval.

Information that will be requested on the Application Form include:

• Anticipated title of the honors thesis.
• Brief description of the thesis topic.
• A list of reference material that the student is expected to read (or have read) as part of the thesis research.
  • We will be checking for whether the assignment may be reasonably completed within the semester. So please clearly indicate when a student has already read some material (or some parts of it) as part of their prior preparation, and when a student is only expected to read certain chapters/sections of a book or paper.
• Description of student's prior preparation (see Expectations section).

Description of the activities that the student will undertake to meet the "Intellectual Ownership" expectations described in the Expectations section.

Deliverables (at completion of MTH492H)

To receive a passing grade in MTH492H, the student must:

1. Write an original undergraduate thesis.
   1. The document should be typeset to professional standards. (The student may use document preparation software of their choice. Students using LaTeX should use the msutermpaper class and template provided here.)
   2. The document must follow general academic standards on attributions and citations.
   3. The length of the body text (excluding figures, tables, code samples, but including mathematical formulae) should be at least 15 pages.
2. Deliver an oral presentation in front of a faculty panel consisting of at least two faculty members.
   1. The presentation should be at least 20 minutes in length.
   2. This can be done as part of the Student Math Conference organized by the Math Department, or as a separately arranged "oral defense" prior to the end of the semester.
   3. The student should provide the faculty panel with a copy of the "Oral Presentation Feedback Form"; the faculty panel will provide written feedback and sign the form.

Grade assignment for MTH492H rests strictly with the faculty advisor(s). The final grade may be based on the written thesis, the oral presentation, as well as student performance during the regular in-semester meetings. Students are encouraged to discuss with potential advisors the rubric to be employed for grade assignment prior to enrolling in MTH492H.

At the end of the semester, the student must submit to the Director of Undergraduate Studies,

• An electronic copy of the undergraduate thesis.
• A copy of the "Oral Presentation Feedback Form" (signed and completed by the faculty panel).
• (Optional) A FERPA/Copyright release form.
  This form is only required if the student wishes to allow the Math Department to showcase their research by making their undergraduate thesis publicly available on the department webpage.