Undergraduate Research Projects

The following is a partial list of undergraduate research projects that have been performed in mathematics at Virginia Tech since 1996. This list is provided in order to give the reader a sense of the scope and types of topics that could be expected in a project.

Sandy Blevins, in the Mathematics Department, 460 McBryde, has a file of all UR papers (in binders in the bookcase at her desk).

Projects, students and advisors

Spring 2012

Joshua Deutschmann, Improving AKS-class primality test (Brown)
Kristen Deger, Mathematical modeling of iron metabolism (Laubenbacher)
Eric Evert, An introduction to stability via state space approach (Ball)
Marisa Gidwani, Solving LMIs with model reduction methods (Borggaard)
Seth Hutcherson, Numerical simulation of large scale oceanic flows (Iliescu)
Mary Katherine Huffman, Diffuse optical tomography, inverse problems, and optimization (de Sturler)
Kevin King, Mathematical Modeling of Cellular Ionic Processes, (Turner)
Mark Lewers, Metric distances between Cayley tables of finite groups (Linnell)
Hao Li, The space of locally invariant orders on a group (Linnell)
James Mayberry, Critical orbitsof elliptic functions (Clemons)
Ariella Grim McNally, Improving the near diagonal dominance of slater matrices for insulators (de Sturler)
Andrew Nicholas, Assesing web resources for teaching Mathematics (Norton)
Sophia Novitzky, Distance to uncontrollability via sum-of-squares approximation (Zietsman)
Ahmed Roman, Zero divisors of Hopf algebras: A generalization of the classical zero-divisor conjecture (Linnell)
Jackson Walters, Ideals in Free Group Rings (Linnell) Layman Prize Winner

Fall 2011

Chelsea L. Cook, Mathematical visualization (Anderson)
Joshua Deutschmann, A study of the AKS primality test (Brown)
Eric Evert, Studies in Analysis (Ball)
Lorraine Feury, The construction of Kadyeisha’s fractional concepts (Norton)
Mary Katherine Huffman, Diffuse optical tomography, inverse problems, and optimization (de Sturler)
Hao Li, The space of locally invariant orders on a group (Linnell)
Ariella Grim McNally, Improving the near diagonal dominance of slater matrices for insulators (de Sturler)
James Jesse Robison, The mathematics of bilogy (Turner)
Marissa Renardy, Further Analysis of the convergence of BiCG (de Sturler)
Chen Weikon, Analyzing matrix reordering methods for quantum Monte Carlo computations (de Sturler)

Summer 2011

Christopher Mehfoud and Chane Jackson, Mathematical Modeling of the Forward Problem in Cardiac Electrophysiology(Turner)
Lorraine Feury, The Construction of Kadyeisha's Fraction Schemes (Norton)
Sean Lewis, A Video Analysis of Fractional Reasoning in Interaction (Norton)

Spring 2011

Danielle Bernabe and Vikram Tiwari, Towards the Numerical Simulation of the Electrocardiogram (Turner)
Chelsea Black, Genomes and Parking Function (Niese)
Kathryn Brewer, The Mathematics of Patterns: An on-line resource for children, parents, and teachers (Laubenbacher)
Jacob Carey, Network Modeling (Laubenbacher)
Elise Ferrari, Analysis of Slater Matrices for Iterative Methods (de Sturler)
Caleb Magruder, Model Reduction of Inhomogeneous Initial Conditions (Gugercin), Layman Prize Winner
Christopher Mehfoud and Chane Jackson, Mathematical Modeling of the Forward Problem in Cardiac Electrophysiology (Turner)
Drayton Munster, Modeling Thermal Fluids in Buildings (Borggaard)
Benjamin Reid, Ultraproducts of Group Rings, (Linnell)
Ahmed Roman, On the Zero Divisors of Hopf Algebras, (Linnell)
Joseph Sullivan, The Zero Divisor Conjecture and Self-Injectivity for Monoid Rings (Linnell)

Spring 2010

James Duvall, The Characterization of Fixed Points in a Sequential Dynamical System (Mortveit)
Will Frey and Curtis Ogle, Higher-Order Ambisonic Audio Reproduction (Rogers)
Pauline Kim, A literature review and case study of the use of TI-NSpire technology in a High School Geometry Class (Hagen)
Ben Reid, Ultraproducts of finite groups (Linnell), Layman Prize Winner

Fall 2009

Clinton Durney, Numerical simulations of bubble motion in viscoelastic flows (Yue)

Spring 2009

Andrew Dove, On the enumeration of cycle-equivalent classes of sequential dynamical systems (Mortveit)
Robert Hagan, Numerical methods for iso-surface rendering (Zietsman)
Caleb Magruder, Option Valuation with Sinusoidal Heteroskedasticity (de Sturler)
Harold Metz and Patrick Sheridan, A pole-residue framework for optimal H_2 model reduction (Gugercin)
Drayton Munster, Parameter Identification: A Comparison of Numerical Methods (Zietsman)
Ryan Ritch, Interpolation of Second Order Dynamical Systems (Beattie)
Jan Michael San Pedro, Identifying Challenging mathematical Problems: A Challenge in Itself (Norton)

Fall 2008

Harold Metz and Patrick Sheridan, A pole-residue framework for optimal H_2 model reduction (Gugercin)
Toby Shearman, A mathematical model of the immune system's role in obesity-related chronic inflammation (Zietsman), Layman Prize Winner

Spring 2008

Nicholas O. Andrews, Unsupervised Relationship Discovery from Large Corpora (Parry)
Kevin Finelli, Spectra of Lax Operator (Klaus)

Fall 2007

Megan Clay, Modeling the Insulin Signaling Network in Cells (de Sturler)
Shane Hutton, Hysteretic convergence in a shockless economy (Rogers)

Spring 2007

Jeremy Henry, Spatial filtering in proper orthogonal decomposition (Iliescu)
Jessica Kline, Sudokus or pseudo-clues (Brown)
Jennifer Meister, Singular value decomposition and some applications (Gugercin)
Brad Shapiro, Bond percolation: critical probability of the inhomogeneous case on the square lattice (Floyd)
Rob Tompkins, Latin square Thue-Morse sequences are overlap-free (Elder), Layman Prize Winner

Fall 2006

Jessica Kline, Sudoku research (Brown)
Rob Ackermann, Complex dynamics (Floyd and Kay)
Rob Tompkins, Morse-Thue sequences over groups (Elder)

Spring 2006

Jeremiah Rogers, The dynamics of directed NOR networks (Jarrah)
Matthew Yancey, In response to peg jumping for fun and profit (Letzter), Layman Prize Winner

Fall 2005

Wade Mattox, Fermat Equations over Quadratic Fields (Elder)
Matthew Yancey, In response to peg jumping for fun and profit (Letzter)

Spring 2005

Brian Baitis, Large eddy simulation of gravity currents: a finite element analysis (Iliescu)
William Carter, Trivial units in group rings using Promislow's example of a torsion-free nonunique product group (Linnell)
Destiny Coslett, Observations on a high-school mathematics class: issues and implications (Lloyd)
Benjamin Horton, Minimizing parallel (v,k,s)-covering designs (Brown)

Fall 2004

Brian Baitis, Large eddy simulation of gravity currents: a finite element analysis (Iliescu)
William Carter, Trivial units in group rings using Promislow's example of a torsion-free nonunique product group (Linnell)
Destiny Coslett, A closer look at fraction division: how does comprehension and confidence of the subject change preservice teachers' perception of instructional practice? (Lloyd)
Bernard Farley, Two approaches to proving Goldbach's conjecture (Parry), Layman Prize Winner Spring 2005

Spring 2004

Morgan Baldwin, Computer simulation of water waves (Russell)
Grant Boquet, GRiTS: Global re-indexing for triangular (tetrahedral) simplices (Borggaard and Iliescu)
Cory Brunson, Projective geometry and rational identities in division rings (Farkas)
John Hurwitz, An introduction to self-similarity by way of the Cantor sets (Haskell)
Claire Ihlendorf and Erin Kelly, Cayley graphs and metric spaces: An investigation of groups and their generators (Haskell)
Lisa McFerrin, Population models with mixed boundary conditions and constant yield harvesting (Klaus)
Anthony Narkawicz, Generalizations of Fermat's little theorem in rings with a multiplicative identity (Linnell)

Fall 2003

Marlene Roush, Combinatorics and cryptography (Green)

Summer 2003

Anthony Narkawicz, Hausdorffness and vanishing of the first cohomology group H¹(G,M) (Linnell), Layman Prize Winner Spring 2004
Firmin Ndeges, Non-oscillatory spectral analysis: Elimination of Gibbs phenomena from reconstructed piecewise continuous signals (Borggaard, Baumann and Herdman)
Shomir Wilson, Construction of a crystal graph simulation engine (Shimozono)

Spring 2003

John Hurwitz, Optical solitons (Klaus)
Praphat Fernandes, Topology of Graph Configuration Spaces (Haskell), Layman Prize Winner
Micah Leamer, Polynomial models of time series over (Z/p)ⁿ (Green)

Fall 2002

Praphat Fernandes, Graph configuration spaces, (Haskell)
Micah Leamer, Boolean networks (Green)

Summer 2002

Michael Felice, A study of Gibbs' phenomenon for linear approximations (Wheeler)

Spring 2002

Shanon Fraker, Optimal inventory scheduling (Johnson)
Steven Hair, Discrete hyperbolic transformations as unique product groups (Linnell), Layman Prize Winner

Fall 2001

Daniel Russell, Cyclic error correcting codes (Green)

Spring 2001

Dave Parnell, Femlab Toolbox (Shaw)
Claude Cundiff, Nonlinear ODEs and RPM (Borggard)
John Janik, Parametric Sensitivity (Herdman)
Elizabeth Joslin, Knot Theory (Linnell)
Aaron Krowne, Examples of Hopf Algebras and Topics in Linear Algebra (Green)
Jean Phillippe Meline, Permutation Groups (Farkas)
Daniel Russell, Algebraic Coding Theory (Green)
Stephen Gossin, VT Graph Visualization (Brown)
James Losh, Numerical Algorithms (M. Renardy)
Erika Roberts, Discrete Morse Theory and Invariants (Haskell), Layman Prize Winner
Brian Weber, Numerical Error in Matrix Multiplication in PSL(2,C) and O(3,1) (Floyd)

Fall 2000

Aaron Krowne, The Hopf Project (Green)
Dave Parnell, Shooting Method to Analyze Eigenvalues in Fiber Optic Systems (Shaw)
Erika Roberts, Discrete Morse Theory for the Circle, Sphere and Torus (Haskell)
Keith Astoria and Stephen Gossin, VT Graph Visualization Project (Brown and Green)

Spring 2000

Brian Sutton, Rewriting systems and Grobner bases (Green), Layman Prize Winner
David Ferguson, Another application of Pascal's triangle Mod 2 (Brown)
Anthony Faulds, PDE control and sensor placement (King)

Spring 1999

Jeffry Hall and Jarrod Raines, Study of Gibbs phenomena (Borggaard)

Fall 1998

Chris Stoltz, Time-dependent pattern formation for two-layer convection (Y. Renardy)

Summer 1998

Dorothy Strater (D. Gao)

Spring 1998

Neural Networks, Melissa Walborn, Anthony Young, Vinh Nguyen, John Shebey, Julie Rollek (Shaw), Layman Prize Winner
Ben Linstid, Molecular Dynamics (Rogers)
An Introduction to Noncommutative Groebner Bases, Eric Lanquist (Green)

Fall 1997

Integer Sequences: An Exploration, George Yuhasz (Layman), paper accepted for poster session presentation, CUR, DC, April, 1998.

Spring 1997

Regular strictly bi-transitive graphs, Karen Potanka (Brown), Layman Prize Winner
Eigenvalues of infinite mass-spring systems, Thomas Ngo (Klaus)
Cell cycle controls in budding yeast, Arun Nava (Tyson-biology)
Numerical optimization for a missile intercept model, Kristine Gross, Tamara Tucker (Herdman), collaboration, Kristine Gross' honors project
Decomposing algebras-acomputational approach, John Harding (Green)

Spring 1996

Coin flipping by computing square roots mod p, Jason Martin (Brown)
Math anxiety: writing to overcome it, Margaret O'Neil (Mick, Shaw)
Finite field computer algebra, Emery Conrad, Karen Potanka, Steve Sinnot, Michael Uy (Green)
Analysis in extended Timoshenko beam theory, Thomas Ngo (Gao)
Modeling of elastic bodies, Evan Greenberg (Russell)
Numerical approximation and parameter identification, Sarah Burrowbridge, Greta Soechting (Herdman)

Layman Prize Winners

2012 Jackson Walters, $250
2011 Caleb Magruder, $250
2010 Ben Reid, $250
2009 Toby Shearman, $250
2007 Rob Tompkins, $250
2006 Matthew Yancey, $250
2005 Bernard Farley, $250
2004 Anthony Narkawicz, $250
2003 Praphat Fernandes, $250
2002 Steven Hair, $250
2001 Erika Roberts, $250
2000 Brian Sutton, $250
1998 Neural Networks Group, $250 (Walborn, Rollek, Nguyen, Shebey, Young)
1997 Karen Potanka, $250
1996 Jason Martin, $250

full text of some undergraduate research projects