# 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 H
^{1}(*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