Middlebury

 

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

 

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