# Honors in Mathematics

The Mathematics Department offers accomplished students the opportunity to pursue sustained research culminating in an Honors Thesis. Honors Standing is acknowledged at graduation.

#### To qualify:

- Students must be exceptional, with a minimal 3.7 average GPA in mathematics, a cumulative average GPA of 3.4, and no grades of D or E in mathematics classes.
- Students must have completed a program of 300-level courses that serves as adequate preparation for research. Consult your academic advisor for suggestions.

#### Expectations for an Honors Thesis:

An honors thesis involves an intensive and deep study which transcends the undergraduate curriculum and approaches masters level mathematics in difficulty and content. New results are not required, though the project should be grounded in a research frame of mind; this has historically involved analysis of research papers, providing data towards a conjecture, creating new mathematical models, finding elementary proofs of known results, or discovering and proving new results.

The work involved in a thesis is usually publishable in an undergraduate research journal. However, the process of publication may be delayed beyond graduation and included within a greater work co-published with the project supervisor.

#### The procedure:

- The student, in consultation with mentoring faculty, applies to the Chair of the Math Department. The Department Honors Committee reviews the student’s transcripts to assess whether a student qualifies.
- The student enrolls in a total of 4 to 6 credits of independent study in mathematics over two semesters, 1 to 3 credits per semester. In the first semester, this credit may be taken as Math 398 (Directed Research), Math 399 (Directed Study), or as MATH 393 (Honors Thesis in Mathematics). The first semester is usually dedicated to research, bibliography, and planning. In the second semester, the student must be enrolled in Math 393 (Honors Thesis in Mathematics). The second semester usually includes the completion of research and the writing of the Honors Thesis.
- Student completing an honors thesis or capstone project for the Edgar Fellows Program may receive departmental honors for that project if the student and the project meet the criteria set out above. As with any honors thesis, prior approval of the department chair and honors committee must be obtained. In this case, students will be enrolled in HONR 393 for two semesters.
- An Honors Thesis is usually done in the final two semesters as an undergraduate, though exceptions may be made in special cases.
- One week before the last day of classes (of the terminating semester), the student submits a draft of the thesis in tentatively complete form to the Honors Committee. One faculty reader, other than the student’s mentor, assesses the work and submits comments to the student. The student must respond to the outside reader’s suggestions, either by implementing the suggested changes or defending against them. The faculty supervisor will determine a grade for the final semester of Math 393. The Honors Committee, reader, and supervisor will come to an agreement on whether to award Honors in Mathematics.
- The student must present a talk on his or her research in a formal setting to an audience of peers and faculty. Venues include colloquia sponsored by the math clubs, MAA sectional meetings, and G.R.E.A.T. Day.
- The thesis, in its final form, must be submitted to the committee by the last day of classes for approval and final grading by the reading faculty and mentor. An extension into Final Exam week may be allowed, with permission of the Honors Committee.
- A copy of the student's thesis, in final form, will be kept on file in by the Math Department or Milne Library.

#### Format of the thesis:

A template for the thesis can be found here: Thesis Template

Please use the given template to prepare your thesis. The writing phase of the Honors Thesis should be done by the student, without significant contribution by the supervisor. It should reflect a deep understanding of the chosen topic, with sufficient background exposition to be understood by a junior mathematics major. It may also contain reflection about the process with which the student came to his or her conclusions.

#### Some recent Honors in Mathematics recipients:

**James Canning**, 2020,*"Space-Efficient Knot Mosaics for Prime Knots with Crossing Numbr 10 or Less"*

(supervised by Heap and Baldwin)**Eric Piato**, 2020,*"Moore Graphs"*

(supervised by Aguilar)**Greg Vinal**, 2019,*"Space-Efficient Knot Mosaics of Size 7"*

(supervised by Heap and Baldwin)**Stephanie Allen**, 2017,*"A Two-Stage Vehicle Routing Algorithm Applied to Disaster Relief Logistics after the 2015 Nepal"*

(supervised by Haddad)**Jenna Zomback**, 2017,*"Colored Unlinking"*

(supervised by Johannes)**Jane Coons**, 2015,*"On the Numerical Ranges of Integer Matrices"*

(supervised by Rault)**Jack Jenkins**, 2015,*"On the Boundary of Numerical Ranges"*

(supervised by Rault)**Doug Knowles**, 2015,*"Numerical Ranges Over Finite Fields"*

(supervised by Rault)**Rayanne Luke**, 2015,*"Pushing the Bounds of Numerical Ranges"*

(supervised by Rault)**Suraj Uttamchandani**, 2014,*"Hilbert's 10*^{th}Problem"

(supervised by Leary)**Alex Chichester**, 2014,*"A Philosophical Survey of the Foundations of Mathematics"*

(supervised by Leary)**Kaitlyn Gayvert**, 2012,*"Mathematical Model Creation for Tumor Growth in Advanced Neuroendocrine Pancreatic Cancer"*

(supervised by Leary)**Dan Rossi**, 2012,*"On the numerical range of 4x4 doubly stochastic matrices"*

(supervised by Rault)**Kevin Palmowski**, 2011,*"Topics in Numerical Linear Algebra: Numerical Methods for Eigenvalue Approximation"*

(supervised by Haddad)**Tyler Massaro**, 2011,*"Stability Analysis of Fitzhugh-Nagumo with Smooth Periodic Forcing"*

(supervised by Esham)**Nicholas Devin**, 2009,*"Exploring the Jones Polynomial"*

(supervised by Heap and Johannes)**Arunima Ray**, 2009,*"Exploring the connections between Fourier analysis and wavelets"*

(supervised by Nicodemi)

##### Other Topics:

- Galois Theory a la Galois
- Problems in Knot Theory
- The Validity of Projective Theorems in Hyperbolic and Elliptic Planes
- Circulant-like graphs
- Group testing
- Combinatorial search problems
- Simplified searching for two defects