Past Senior Honors Theses
The following is a list of recent senior honors theses and the faculty advisors. These theses are kept in a volume in the mathematics undergraduate office in 115 Vincent Hall. You are invited to view them if you are contemplating doing an honors thesis.
2018-2019
| Student | Thesis | Advisor |
|---|---|---|
| Manaswinee (Mansi) Bezbaruah | “Numerical Simulations of Plasmons on Graphene" | F.Santosa |
| Andrew Brettin | “Ecological Management Practices Informed by Flow-kick Dynamics” | R.McGehee |
| Jacob Elafandi | “Use of Marching Algorithms to Detect Edges of Breakage on Scans of Bone Fragments” | J.Calder |
| Logan Knorr | “Ranking Systems in NCAA Men's Basketball” | J.Rogness |
| Linda Peng | “Fuzzy Logic and Its Applications to Insurance” | R.Ashkenazi |
| Julie Sherman | “Constraints on the Oceanic Carbon Sink Using Atmospheric Oxygen Data” | R.McGehee |
| Warut Thawinrak | "Bruhat Order and the Rook Monoid" | V.Reiner |
2017-2018
| Student | Thesis | Advisor |
|---|---|---|
| Paul Aarsvold | “Manifolds and the Shape of the Universe" | J.Rogness |
| Bat-Orgil Batsaikhan | “Generative Capsule Network” | G.Lerman |
| Kelly Catlin | “Finding an Optimal Velocity for a Race” | Y.Mori |
| Maria Gilbert | “Hurwitz Actions in Complex Reflection Groups” | V.Reiner |
| Elena Hafner | “Face Structure and Volume of the Birkhoff Polytope” | G.Musiker |
| Owen Levin | “Approximation Algorithms for Network Connectivity” | V.Reiner |
| Ian McMeeking | "Computing with Noncongruence Subgroups" | B.Brubaker |
| Mark Richard | “On Random Schrodinger Operators” | W-K. Chen |
| Ryan Vogt | “Detection of Non-Symmetric Balanced Configurations” | R.Moeckel |
| Lucy Yang | “Quadratic Operad Algebras Induce BV Algebras” | A.Voronov |
2016-2017
| Student | Thesis | Advisor |
|---|---|---|
| Rejendra Beekie | “Stability of Pinned Fronts in Nonlocal Equations" | A.Scheel |
| Grant Goodman | “The Poincare'-Hopf Theorem” | A.Akhmedov |
| Tikhon Gritskevich | “Factorization Homology and TQFT” | A.Voronov |
| Morganne Igoe | “A Comparison of Individual-Based and Mean Field Model Approaches as Applied to Vector-Borne Pathogen Spread” | D.Nykamp |
| Grace Meyer | “Modeling the Effects of Discount Rate Assumptions and Funding Levels on the Minnesota State Retirement System Defined Benefit Plans” | R.Ashkenazi |
| Bradford Olson | “Nim Take A All But B” | B.Fristedt |
| Kobie Spaeth | "Polling Errors and Their Effect on the Modeling of the 2016 Presidential Election" | R.Ashkenazi |
| Samuel Stromwall | “Effectiveness of Recursive Algorithms on Word Shortening” | P.Webb |
| Han Yong Wunrow | “Dynamics of Billiard Systems in Regular Polygons” | R.Moeckel |
2015-2016
| Student | Thesis | Advisor |
|---|---|---|
| Benjamin Feigenbaum | “One-Dimensional energy Balance Model" | B.Maultsby |
| Christian Gaetz | “Critical Groups and the McKay Correspondence” | V.Reiner |
| Thomas Gebhart | “Demand Drivers of Bitcoin” | R.Ashkenazi |
| Joseph Lawson | “Classification of Unlabeled Data” | G.Lerman |
| Carolyn Reinhart | “Moebius Functions and Euler Characteristics for Categories” | P.Webb |
| Andrew Senger | “The Spectral Artin Representability Theorem” | T.Lawson |
| Marshall Smith | "Cohomology of Braided Vector Spaces" | C.Westerland |
| Kazmer Schmanski | “A Probability Theory Framework for Baseball Strategy and Simulations” | M.Weimerskirch |
| Di Wu | “Is There a Set that Is Not Almost Open But Still Measurable in R?” | S.Adams |
| Yao Rui Yeo | “Dessin d'Enfants” | V.Reiner |
2014-2015
| Student | Thesis | Advisor |
|---|---|---|
| Ethan Heinzen | “Second-Order Neural Networks and Synchrony" | D.Nykamp |
| Joel Knighton | “The Immerman-Szelepcsenyi Theorem and the Second LBS Problem” | W.Richter |
| Christopher Lovdal | “The Critical Value of the Speed of an Interface Propagating Energy Relaxation” | A.Scheel |
| Michael Neaton | “Minimal Covers of Manifolds” | T-J.Li |
| Anton Okhrimchuk | “Monte Carlo and Quasi-Monte Carlo Methods of Integral Approximation” | D.Bilyk |
| Yunpeng Shi | “Experiments on Robust Camera Motion Estimation” | G.Lerman |
| Maxwell Shinn | "Synergy, Redundancy, and Integrated Information in the Brain" | D.Nykamp |
| Benjamin Wilson | “Infinite Hats: Cycle Structures of Large Permutations” | G.Anderson |
| Fadumo Yusuf | “Teaching Methods in Mathematics” | M.Weimerskirch |
| Chelsea (Xi) Zhao | “A Study on Capital Asset Pricing Model and Its Illustrations” | R.Ashkenazi |
2013-2014
| Student | Thesis | Advisor |
|---|---|---|
| Benjamin Bachmeier | "Modeling the Effects of Sea Ice on Phytoplankton Growth Dynamics" | R.McGehee |
| Ana Liard-Blanco | "Bernstein-Sato Polynomials" | E.Witt |
| Haojun Caoxu | "Reimann's 1859 Paper and the History of Complex Analysis" | P.Garrett |
| Jason Checky | "Branching Processes adn Cell Populations" | J.Baxter |
| Andrew Dean | "An Information Theoretic Study of Rhythmic Variations of Poetic Accents in Hip-Hop" | D.Clark |
| Thomas Edwards | "Discontinuous Galerkin Methods for Ordinary Differential Equations" | B.Cockburn |
| Yifan Feng | "Effect of Dynamic Pricing on Inventory Costs: A Mathematical Model" | J.Baxter |
| Robin Heinonen | "Contractions of Superintegrable Darboux Systems" | W.Miller Jr. |
| Amber Hill | "Linear Programming and Its Economic Applications" | G.Anderson |
| John Karlen | "Fermat's Principle and Its Applications" | V.Sverak |
| Ryan Lee | "Applications of Entropy Rates to Relative Poverty as a Measure of Longitudinal Economic Mobility" | A.Scheel |
| Jiacheng Liao | "A Study on Hidden Markov Model and Its Application" | J.Baxter |
| Alexandra Nelson | "Use of Color Exchange to Classify Regular Graphs of Order 12 by Power Sequence" | J.Butterfield |
| Eric Seifert | "An Expository of Elliptic Curve Cryptography" | J.Butterfield |
| Haiyun Zhao | "Matrix Nearness Problems with Indefinite Lorentz Metric" | W.Miller Jr. |
2012-2013
| Student | Thesis | Advisor |
|---|---|---|
| Gong Chen | "Vibrations of Suspended Chains" | V.Sverak |
| Jean Costello | "Proof of the AKS Primality Test" | D.Stanton |
| Xavier Garcia | "Pathological Billiards" | R.Moeckel |
| Kelsey Gladen | "Markov Chain Monte Carlo and Its Applications" | J.Baxter |
| Matthew Howard | "Chance Operations in Musical Compositions" | L.Gray |
| John Kilgore | "Exotic 4-Manifolds" | A.Akhmedov |
| Matthew Larionov | "Finite Model Theory and Logics for PTIME" | W.Richter |
| Tyler Maunu | "A Robust PCA Framework with Randomized Singular Value Decompositions" | G.Lerman |
| Aaron Schneberger | "Critical Groups of Certain Graphs and their Cryptographic Implementation" | G.Musiker |
| Benjamin Tolzmann | "Advanced Statistics and Prediction in American Professional Sports" | A.Odlyzko |
| Thomas Vandenboom | "Light-wave Localization Phenomena in Layered Dielectric Media" | F.Santosa |
2011-2012
| Student | Thesis | Advisor |
|---|---|---|
| Wei Chen | “On Certain Non-linear Second-order Ordinary Differential Equations and Applications" | M-C Calderer |
| Patrick Floryance | “Random Walks, Electrical Networks and Perfect Squared Squares” | V.Reiner |
| Nathan Fox | “Some Applications of the Mobius Function” | P.Webb |
| Daniel Hess | “Finiteness of the Stable Homotopy Groups of Spheres” | T.Lawson |
| Xin Jin | “Bandit Problems and Gitton-index Theorem” | B.Fristedt |
| Madeleine Kotzagiannidis | “The Triangular Distance Histogram in Object Recognition” | P.Olver |
| Enming Mao | "A Model of Order Book Dynamics" | J.Baxter |
| David Nichols | “Nonstandard Analysis As a Tool for Instruction and Discovery” | W.Richter |
| Grant Remmen | “Dynamics of a Rigid Spinning Ring in the Schwartzchild Metric: A Solution to a Gravitational Problem in Mathematical Physics” | W.Miller |
| Jennie Schneider | “The Fibonacci Number in Nature” | A.Scheel |
2010-2011
| Student | Thesis | Advisor |
|---|---|---|
| Aaron Barkley | "Projecting a Matrix onto the Special Linear Group" | W.Miller |
| Bjorn Berntson | "Analysis of Kepler-Type Problems in Non-Eudclidian Geometries of Constant Curvature using Superintegrability Methods" | W.Miller |
| Matthew Coudron | "A Note on Eigenvalues of Non-Hermitian Anderson Operators" | G.Anderson |
| Christopher Fredregill | "A Comparative Study of Markov Chain Monte Carlo Algorithms" | C.Geyer, J.Baxter |
| Daniel Hoff | "Differential Invariant Signatures for Object Recognition and Automatic Solutions of Jigsaw Puzzles" | P.Olver |
| Eunjeong Jo | "NTRU Encrypt Public Key Cryptosystem" | A.Odlyzko |
| Li Lin | "Compressive Sampling" | W.Miller |
| Cordelia McGehee | "Parasites and Peristalsis: Towards a Computational Understanding of A.suum Motility in the Small Intestine" | H.Weinberger |
| Chatanya Rachabattuni | "Flow of Particles in Dynamical Model Systems" | W.Miller |
| Sean Vig | "Periodic Orbits of the Isosceles Three Body Problem and Their Stability" | R.Moeckel |
2009-2010
| Student | Thesis | Advisor |
|---|---|---|
| Danielle Sandler | "The Implications of 2nd Orter Motifs on Neural Network Structure" | D.Nykamp |
| Max Siegel | "Large Deviations and Statistics" | O.Zeitouni |
2008-2009
| Student | Thesis | Advisor |
|---|---|---|
| Dan Brinkman | "Invariant Histograms" | P.Olver |
| Joseph Loubert | "Bott Periodicity" | T.Lawson |
| Tom Vacek | "Ehrhart Reciprocity" | S.Sperber |
2007-2008
| Student | Thesis | Advisor |
|---|---|---|
| David Barta | “An Introduction to Gaussian white noise analysis in sensory system Neurophysiology” | D.Nykamp |
| John Bergdall | “Aspects of the Theory of p-Adic Galois Representations” | W.Messing |
| Derek Dalle | “Invariant Numerical Approximations to EquiAffine Curvature using Moving Frames” | P.Olver |
| Andrew Hampton | “A Finite Expression of FO-Inexpressibility” | W.Richter |
| Robert Hank | “Using Spectral Sequences to Compute Homology” | T.Lawson |
| David Morrissey | “Mathematical Modeling of Point Vortices” | M-C Calderer, D.Spirn |
| Nicholas Switala | “p-Divisibility of the number of F_p rational points on certain hypersurfaces” | S.Sperber |
| Rebecca Weiler | “An Introduction to Minimizing Energy Functions” | M-C Calderer |
2006-2007
| Student | Thesis | Advisor |
|---|---|---|
| Dan Colestock | “Growth Distributions and Enumerations of Subtrees” | B.Fristedt |
| Bradley Froehle | “An Introduction to Combinatorial Garside Structures” | P.Webb |
| Alexander Miller | “Smith Invariants and Dual Graded Graphs” | V.Reiner |