The University of Arizona

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
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