## Senior Thesis

**The Mathematics Department** is one of several departments at Middlebury that requires a senior project. MATH 0704 is intended to be the capstone experience in the major, where, working with the friendly assistance of a faculty advisor, students independently explore in significant depth a topic of their own choosing.

In addition to meetings with your advisor, you will meet regularly throughout the semester with your fellow thesis companions to discuss progress, commiserate, and practice the presentation that you will give at the end of the term. There are lists of suggested topics, but some of the most interesting projects are initiated by student suggestions. Perhaps you have taken a course that you sincerely enjoyed and want to learn more about the subject. Perhaps you have read something in a recent journal or heard something at a seminar talk about a new theory or algorithm that you would like to investigate. Often it helps to have conversations with professors you have worked with in previous classes about subjects that they think would be interesting. Areas not covered in the department's elective offerings are fruitful ground for thesis topics.

Bound copies of all theses are retained in a collection of the Middlebury College Library. All of the theses from the previous four or five years are bound and available for browsing in the department's suite in Warner. As you look at the work of your peers you will notice the wide variety of topics students have undertaken. In some cases, the research is a survey of known results of interest to the author, in some cases it is an application of a learned technique to a new problem, and in some exceptional cases there is an attempt to do original research into a previously unsolved problem. No matter what you decide to do, you will get the experience of:

- researching mathematical literature,
- working independently,
- organizing, revising, and writing a 60-100 page paper.

These skills will be of invaluable help to you in graduate or professional school or as you enter the job market.

Presentation day is always a festive occasion. You get to be the expert and share the results of your semester's work with friends, professors, and classmates. Though your grade does not depend on your presentation skills, this too is good practice. Mostly though, it is a day to celebrate and be proud.

Click to see a list of potential topics suggested by faculty members. Below are actual thesis titles from previous years.

2011

Alice Bennett, A Mathematical Model for the Transmission of Fanactic Ideologies, Olinick

Sieuwerd Gaastra, Unique Prime Factorization in the Integers of Imaginary Quadratics Fields, Bremser

Byron Langford, A Mathematical Model in the Oil & Gas Industry, Olinick

Nicholas Osorio, An Introduction to the classification of Crystallagraphic Groups, Dorman

Benjamin Silton, Stochastic Models Use in Measuring Air Pollution Damages, Emerson

Steven Xu, Communication By Numbers: The Manipulation of Finite Fields in Coding Theory, Bremser

Jing Zhuang, Quadratic Programming, W. Peterson

2010

Neil Baron, Combinatorial Game Theory, Hex, and the Brouwer Fixed-Point Theorem, Schumer

Christopher Chung, Dynamics of the Discrete Logistic Equation, Dorman

Daniel Crow, Lie Groups, Reprsentation Theory, and the Peter-Weyl Theorem, Dorman

Mahash Dahal, Logistic Regressio, Emerson

Andrew DeLoach, Primality Testing and Factorization Methods, Schumer

Linh Dinh, Google PageRank and Extension, W. Peterson

Shi Fang, Bayesian Statistical Analysis, Emerson

Nathaniel Fasman, The Van der Waerden Function and Random Walks, Abbott

Annabelle Fowler, Simple Continued Fractions and Farey Sequences, Schumer

Angelo Fu, Embedded Graph Expansions, Swenton

Hallie Gammon, Kites and Cartwheels: Penrose's Aperiodic Tilings, Bremser

Benjamin Horne, The Four-Color Problem, W. Peterson

Benjamin Kunofsky, How long are these supposed to be? Would this work?, Abbott

Dallas Moody, Matroids and the Greedy Algorithm, W. Peterson

Thu Thi Thanh Phung, Global Dynamic Properties of Lotka-Volterra Systems, Olinick

Richard Saunders, The Condorcet Principle, Olinick

Jinzhi Shao, Using Linear Programming to Price American Perpetual Warrants, Olinick

Lauren Vollmer, Words, Words, Words: An Investigation of the Etymological Distribution of Shakespeare's I Henry IV, W. Peterson

Patrick Walsh, Evaluating Credit Risk to Calculate Capital Requirements, Emerson

Shengen Zhai, Information and Optimal Betting System, W. Peterson

2009

Cepan Chen, The Binomial Asset Pricing Model for Options, W. Peterson

Alexander Glaser, Finite Fields and Their Cryptographic Applications, Bremser

Sarah Ladner, Gauss, Eisenstein, and Pythagoras: An Introduction to Algebraic Number Theory and Some Implications for the Construction of Triangles, Bremser

Victor Larsen, Hyperbolic Structures on Knot Complements, Swenton

Phuong Chi Le, The Foundations of Riemannian Geometry, Proctor

Benjamin Liang, The Probabilistic Method in Combinatorial Applications, Schmitt

Olivia Minkhorst, Arts and Crafts with Riemann Surfaces, Proctor

Benjamin Molberger, Combinatorial Game Theory, Schmitt

Kathryn Patton, Fourier Series in Hilbert Space, Abbott

Mengzhe Zhou, Constrained Optimization, W. Peterson

Yijie Zhu, Inequalities and Their Applications in Analysis and Applied Mathematics, Abbott

2008

Sarri Labib Al-Nashashibi, Adaptive Error Correcting Codes, Schmitt

Hasat Cakkalkurt, Evolutionary Game Theory, Olinick

Ellen Dickson, Deterministic Mathematical Models of Colorectal Tumor Growth, Olinick

Owais Gilani, Logistic Regression, Emerson

Karen Levin, Google PageRank, W. Peterson

Stephanie Levine, Waring's Problem, Schumer

Saitulaa Naranong, The Simplicial Homology Groups - and Their Topological Invariance, Swenton

Emily Ovitt, Aperiodic Tilings, Bremser

Samuel Shoutis, Manifolds: Topology, Differentiability, and Beyond..., Proctor

Jeffrey Wehrwein, Random Number Generation, Emerson

2007

Anna R. Blasiak, Graph Pebbling, Schmitt

Tamara Bogojevic, Matrix Groups, Proctor

Lawrence Budasoff, Don't Take the Pencil Away from the Child...The Imp.of Student-Cent. Lrng., Bremser

Andrew Harger, Principal Component Analysis, W. Peterson

Cameron Palmer, The Riemann Zeta Function , Abbott

Kanchan Pathak, Dynamics in Planar System, Swenton

Kristin Thorpe, Modeling Social Mobility with Markow Chains, Olinick

Magdalena Widjaja, The world isn't flat after all - An exploration of non-Euclidean geometry, Proctor