URA Program Participants
During the years when VIGRE grant funding was available, students applied for formal URA positions and funding, and submitted finished work at the end of the semester.
Spring 2010
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Garrett Vanhoy | title | Bergevin |
Fall 2009
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Caree Wheeler | A Study of Solving Hamiltonian Systems | Sims |
| Sean Howe | Conductors of Elliptic Curves Over Q | Joshi |
| Isaac Upsal | Modeling the Invariant Density Curve of a Noisy Chaotic Map | Lin, Venkataramani |
Spring 2009
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Kyle Marshal | A modification of Neal's algorithm for a continuous state space and application to the Fokker-Planck equation | Lin |
| Dustin Keys | An Introduction to Channel Capacity with Applications to Coupled Map Lattices | Lin |
| Raymundo Navarrete | Determining the Behavior of the Rotating Disk Electrode System | Venkataramani |
| Garrett Vanhoy | Nonlinear Diffusion | Lega |
Fall 2008
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Dustin Keys | Chaotic Coupled Map Lattices | Lin, Indik |
| Johnson Truong | Convergence Rules for Non-smooth data and non-smooth functions | Greenlee |
| Andrew Binder | Exploring Nonlinear Oscillator Models for the Auditory Periphery | Bergevin |
| Joseph Thomas | Refining the Lattice package | Lux |
| Heather McLeod | Research on Student Learning of College Algebra, Pre-Calculus and Calculus Concepts | McGraw |
Summer II 2008
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Alex Henniges | Combinatorial Ricci flow | Glickenstein |
| Thomas Williams | Combinatorial Ricci flow | Glickenstein |
| Mitch Wilson | Combinatorial Ricci flow | Glickenstein |
| Jason Dittman | Convective adjustment in box models | Moloney, Brio |
| Alex Blount | Exploring the relationship between coupled chaotic systems and their higher order Lyapunov exponents | Indik |
| Dustin Keys | Exploring the relationship between coupled chaotic systems and their higher order Lyapunov exponents | Indik |
Spring 2008
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Joseph Thomas | A Computational Approach to Finding Irreducible Representations | Lux |
| Marco Lopez | A measure on Self-avoiding Loops in the Complex Plane | Kennedy |
| Andrew Pyzdek | Bridge Courses in the United States | Dorin Dumitrascu |
| Andrew Mackey | Cayley Graphs and the Discrete Fourier Transform | Lux |
| Amanda Schaeffer | Coxeter Groups and Complex Representations | Lux |
| Andrew Binder | Modeling Otoacoustic Emissions | Bergevin |
| Michelle Solis | Quantum Information and Teleportation | Wehr |
Fall 2007
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Amanda Schaeffer | Iterative methods for eigenvalues of symmetric matrices as fixed point theorems | Greenlee |
Summer II 2007
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| David Love | Optimization of VECSEL Mirrors to Compensate for Nonlinear Distortions | Moloney |
Spring 2007
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Sean Howe | Efficiently Calculating Phase Data based on Magnitude of Near and Far Fields | Indik |
| Haokun Xu | Elliptic Curves | Rogers |
| Julio Brau | Involutions and representations of the finite orthogonal groups | Vinroot, Lux |
| Brendan Fry | Symmetric groups, partitions and representations | Cossey |
| Charles Campbell | The Period of the Fibonacci Sequence Modulo j | Rogers |
| Cheyne Pierce | Theoretical Models of Oxygen Transport in Capillaries | Secomb |
| Andrew Winslow | Use of a Conformal Mapping Algorithm for Pattern Recognition | Kennedy |
| Harshil Seth | Using Copulas to Calculate Portfolio Value | Meyers, Lamoureux |
Fall 2006
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Haokun (Sam) Xu | Elliptic Curves | Nick Rodgers |
| Cheyne Pierce | Mathematical models of oxygen flows in the microcirculation | Secomb |
| Brendan Fry | Symmetric groups, partitions and representations | James Cossey |
| Maria Miranda | Zipper Algorithm | Kennedy |
Summer II 2006
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Karl Dutson | Synchroization of Chaos | Indik |
| Christopher McMurdie | Unit Groups | Nick Rodgers |
Spring 2006
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| John Pate | Geometric Aspects of the Heisenberg Group | Dumitrascu |
| Jacob White | On Linearity of Braid Groups | Cossey |
| Matthew Moore | P-adic Continued Fractions | Levitt, Thakur |
| Peter Gross | Parameter Estimation for the Black-Scholes Equation | Dai |
| Petr Moravsky | The Zipper Algorithm | Kennedy |
Fall 2005
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Nikhil Prahlad Patil | An Excursion into Set Theory Using a Constructivist Approach | Simic |
| Gabriel Marcus | Fluid Mechanics of Flagellated Microorganisms and Possible Pathways for Evolutionary Transition to Multicellularity | Goldstein |
| Jeffrey Gilbert | Generalizations of Continued Fractions | Pawloski, Lux |
| Daryl "Jeffrey" Springer | Iterative Methods for Eigenvalues of Symmetric Matrices as Fixed Point Theorems | Greenlee |
| Matthew Moore | P-adic Contineud Fractions | Levitt, Thakur |
Summer II 2005
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Taylor Dupuy | Asymptotic Analysis | McLaughlin |
| Samuel Alexander | Polynomials with small Mahler measure | Madden, McCallum |
| Matthew Moore | Solving Quintic Polynomials | Levitt, Thakur |
Spring 2005
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Arjang Talattof | Developing a Model System to Understand and Predict Photoactive Yellow Protein Behavior | Cusanovich, Indik |
| Samuel Alexander | Formulas for Computable Functions (published in Rose-Hullman Undergraduate Math Journal Vol 7, No 2 (2006)) | Simic |
| Daniel Norwood | Modeling of a Simple Swimmer at a Low Reynold's Number | Lega |
| Carlos Chiquette | Optical Phase Reconstruction Using Near and Far Field | Indik, Shkaraev |
| Christofer Summitt | Optical Phase Reconstruction Using Near and Far Field Magnitudes | Indik, Shkaraev |
| Matthew Green | SLE and Self Avoiding Walks | Kennedy |
Fall 2004
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Aaron Ellis | Efficient Dynamically Adaptive Mesh | Brio, Ditchen |
| Taylor Dupuy | Investigating Cellular Automata | Wootton |
| Daniel Norwood | Modeling of a Simple Swimmer at a Low Reynold's Number | Lega |
| Jeffrey Gilbert | Study of "Primes is in P" | Wootton |
Summer II 2004
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| William Toussaint | Construction of an Efficient Computer Primality Testing Algorithm | Urtis |
| Kenny Headington | Dynamical Systems and Chaos | Indik |
| Aaron Ellis | Efficient Dynamically Adaptive Mesh | Brio, Ditchen |
| Genevieve Patterson | Linear Codes by Java example | Leitner |
| Christopher McMurdie | The Non-Commutative Geometry of Penrose Tilings | Caine, Pickrell |
Spring 2004
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Matthew Green | Binary Strings and Graphs | Hartman |
| Mel Koppens | Combinatorial Proofs | Jayawant, Leonard |
| Peter Manning | Development of a Matrix Preconditioner from a Polynomial Approximation of 1/x | Restrepo, Hasson |
| Ivan Barrientos, Kenny Headington, Dorian Smith |
Dynamical Systems and Chaos | Indik, Soneson |
| Christopher McMurdie | Gelfand's Theorem | Caine, Pickrell |
| Genevieve Patterson | Linear Codes by Java Example | McCallum, Leitner |
| Michelle Roehler | Middle School Students? Intuitive Techniques for Solving Algebraic Word Problems | Horak |
| Greta Flaaten | Students' Reasoning for Fleeing Mathematics and Related Fields | Horak |
| Lauren Luecke | The Mathematics of Speech | Rychlik |
| Allison Bourke | Torque with Respect to Lift and Drag | Restrepo, Beauregard |
| Brendan Moloney | Vector Maxwell Simulations | Brio |
| Jessica Ryder | Vehicle Roll Over Proposal | Lomen |
Fall 2003
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Federico Chialvo | A Connected Sum Operation, Maximally Connected Planar Graphs and Colorability | Jayawant, Watts |
| William Toussaint | Applications of Linear Algebra towards the world of sports | Carlson |
| Jefferson Taft | High-Speed Photography in Mathematics | Goriely |
| Michelle Roehler | Middle School Students? Intuitive Approaches to Algebraic Word Problems | Horak |
| Christopher McMurdie | Penrose Tilings and Periodicity | Caine, Pickrell |
| Alexia Puig | Periodic Functions On Non-Linear Temporal Models | DeVito |
| Shixin Xiao | Sand Movement | Pelletier, Restrepo |
| Greta Flaaten | Students? Reasoning for Fleeing Mathematics-Related Fields | Horak |
| Zheng Cai | Use of GIS in analyzing environmental cancer risks as a function of geographic scale | Myers |
| Bapy Dibakor | Valid Models for space-time variograms | Myers |
| Dave Schumann | Variable Speed of Light | Narayanan |
| Brendan Moloney | Vector Maxwell Simulations | Brio |
Summer I 2003
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Gordon Davis | Criteria for Assessing a Ranking Method | Carlson |
| Maria Francis-Moullier | Cryptography | Ulmer |
| Jefferson Taft | High Speed Photography | Goriely |
| Jad Halimeh | Mahler?s Measure and Lehmer?s Conjecture | Madden |
| Grayson Williams | Proving the Lehmer Conjecture for Polynomials of Degree 10 | Madden |
| Mark Miles | Simulation of waves and shocks | Brio, Dineen |
| Zheng Cai | Use of GIS in analyzing environmental cancer risks as a function of geographic scale | Myers, Rogan |
| Brendan Moloney | Vector Maxwell Simulations | Brio |
Spring 2003
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Jamil Mortada | Composition of twists along simple closed curves | Gay (David T.) |
| Alexia Puig | Periodic Functions On Non-Linear Temporal Models | DeVito |
| Maria Francis-Moullier | Primes is in P | Ulmer |
| Alex Toussaint | Ranking Basketball Teams | Carlson |
| Jefferson Taft | The Propagation of Waves through a Cracking Whip | Goriely |
| Jad Halimeh | Theoretical Proof of Lehmer's Conjecture for Polynomials of Small Degree | Madden |
| Zheng Cai | Use of GIS in analyzing environmental cancer risks as a function of geographic scale | Myers |
Fall 2002
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| J.W. Gaberdiel | An Exploration of Nontraditional Conceptualizations of Knots | Robinson |
| Shixin Xiao | Modeling the movement of Sand | Restrepo |
| Benjamin Armbruster | Static solutions of an elastic rod in a helical shape without twist | Goriely |
| Jamil Mortada | Study of Topological Surfaces | Gay (David T.) |
Summer II 2002
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Teja Muppirala | Convection in a differentially heated narrow slot | Chan |
| Mario Sweeney | Dependence of Stock Market Prices | Wright |
| Jason Dyer | Exponent Attacks: Lattice Reduction | McCallum |
| Ellen Preiss | Factorization Attacks | McCallum |
| Franco Cafiero | Factorization: Possible Factor Neighborhoods | McCallum |
| Andrew Crites | Particle Image Velocimetry | Goldstein |
| Matt Green | Primality Testing: Pseudoprimes and Carmichael Numbers | McCallum |
Spring 2002
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Teja Muppirala | Convection in differentially heated systems | Chan |
| David Wood | Modeling Flour Beetle Populations | Cushing, Perlis |
| Matthew Jallo | Sediment Dynamics Simulation via Cellular Automata Artificial Intelligence | Restrepo |
| Adam Kiel | Solvable Quintics : A New Approach | DeVito |
| Andy Klein, Travis Singleton |
The Meta RSA Page | Goff |
| Benjamin Armbruster | Verifying Return Addresses: Bounds on the Efficiency of Distributed Packet Filtering | Smith (Cole), Lomen |
Fall 2001
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| David Wood | Fractal Dimension in models of Flour Beetle Population | Cushing, Edmunds |
| Rex Cook, Samantha Zaplinski |
Plume-Driven Mixing in Stratified Fluids | Restrepo, Goldstein, Pesci |
Summer II 2001
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Steven Bethard, Ethan Dolle |
An Exploration of Surfaces | Gay (David A.) |
| Michelle Cobeaga | Analysis of migrating bands of chemotactic bacteria | Lega |
| Catherine Ott | Bacillus subtilis: Colony Dynamics | Lega |
| Brian Weleck | Calculus Experiments | Velez |
| David Brown | Galois Group of Cyclotomic Fields of Fermat Primes | Madden |
| Chi-kwan Chan | Generalized Functions in Minkowski Space | DeVito |
| Justin Miller | Isomorphic Groups of Rational Points of Elliptic Curves over Finite Fields | Ulmer |
Spring 2001
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Catherine Ott | Bacillus subtilis: Colony Dynamics | Lega |
| Karen Carter | Cryptography and Finite Fields | Ulmer |
Fall 2000
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Pojen Huang | Modeling of the Semiconductor Laser with Optical Feedback | Indik |
| Chris Bergevin | Synchronization of Chaotic Electronic Circuits: Can we control Chaos? | Goldstein, Indik |
Summer II 2000
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Santiago Canez | Continued Fraction Factorization | Madden |
| Tom Wilkening | Creating Materials for a New Course on the Mathematics of Investing | Wright |
| Nathaniel Blair-Stahn | Investigation of the Behavior of the Eigenvalues of Random Permutation Matrices | Wieand |
| Peter Lewis | Parametric Representation of Keplerian Orbits | Alexander |
| Ali Amjad | Stochastic Differential Equations | Bayly |
Spring 2000
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| J.W. Gaberdiel | A Study of Perfect Numbers and Related Topics, With Special Emphasis on the Search for an Odd Perfect Number | McCallum |
| Chi Chen | Beowolf-Class Supercomputing Task-Farming Utilities | Restrepo |
| Diane Kohl | Bounding Sound Wave Errors | Hillyard |
| Julianne Lazarr | Computer Modeling of the Growth of Microvascular Networks | Secomb |
| Justin Miller | Computing homology groups of simplicial complexes | Rychlik |
| Pojen Huang | Control in Chaos | Indik, Lega, Ercolani |
| Siwei Shen | Convexity at a Point | Laetsch |
| Joseph Robles | Design and Building of an Apparatus for Investigation of the Granular Dynamics and Fluid Dynamics of Sand Ripples | Restrepo |
| Anna Szidarovszky | Sightings of the Rare Primitive Pythagorean Triangles | Stevenson |
| Trevor Arnold | Small degree extensions of the rational numbers | McCallum |
| Travis Sherman | Summation of Glaisher- and Apery-like Series | Brillhart |
Fall 1999
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Po-Jen Huang, James Roche, Steve Steinke, Robert Thompson |
Control of the Quadratic Map Using Delay | Indik, Lega, Ercolani |
Summer II 1999
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Justin Miller | Families of Continued Fractions | Madden |
Spring 1998
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Adam Arluke, Chris Bergevin, Tod Cadwallader, Hyun-jeong Han, Robert Thompson |
Dynamical systems, chaos and control | Ercolani, Indik, Lega, Hsu |
Spring 1997
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Chris Bergevin, Po-Jen Huang, Steve Steinke |
Synchronization of chaos, delay, and application to the Ikeda map | Indik, Ercolani, Lega |
Fall 1996
| Student(s) | Project Title | Advisor(s) |
|---|---|---|
| Chris Sinclair | Java Applets | Ercolani |