Mathematics

In its Honors Program the Mathematics Department awards one level of Honors to student research projects. The projects listed below have been defended successfully, and a copy of the thesis deposited in Swem Library.

Key:

• Student, "Thesis" (Honors level)
  Committee Chair + Other Committee Members

2012-13

• Kiah Hardcastle, "A Population Density Model of Domain Calcium-Mediated Inactivation of L-Type Ca Channels" (Honors) 
  Gregory Smith +Sarah Day, Larry Leemis, Seth Weinberg
• Daniel J. Luckett, "Statistical Inference Based on Upper Record Values" (Honors)
  Tanujit Dey + Ross Iaci, Drew LaMar, Lawrence Leemis 
•  Tyler Moran, "On Almost Normal Matrices" (Honors)
  Ilya Spitkovsky + Charles Johnson, Ryan Viinroot, Donald Campbell  
•   Allison Oldham, "Finding Open Locating Dominating Sets on Finite and Infinite Graphs" (Honors) 
  Gexin Yu + Rex Kincaid, Lisa Anderson 

2011-12

• Timothy Becker, "A Model for Blue Crab Population in the Chesapeake Bay" (Honors)
  Leah Shaw + Romuals Lipcius, Junping Shi, Ryan Vinroot 
• Matthew Becker, "Synchronous Oscillatory Solutions in a Two Patch Predator-Prey Model" (Honors)
  Junping Shi + Leah Shaw, Daniel Vasiliu, Gexin Yu 
• Allison Corish, "Global Dynamics of Pulse-Coupled Oscillators" (Honors) 
  Sarah Day + Drew LaMar, Rex Kincaid, Gregory Smith 
• Zachary Gates, "Strongly Real Conjugacy Classes of the Finite Unitary Group" (Honors) 
  Ryan Vinroot + Wouter Deconinck, Gexin Yu 
• Patrick King, "The Laplacian on Isotropic Quantum Graphs: Solutions and Applications" (Honors)
  Junping Shi + Joshua Erlich, Daniel Vasiliu, Gexin Yu 
• Sarah Kunkler, "Finding the Minimum Randic Index" (Honors) 
  Rex Kincaid + Drew LaMar, Michael Lewis, David Phillips  
• Timothy McDade, "Analysis and Simulation of an Optimal Control Model of an Oyster Population Displaying an Allee Effect" (Honors)
  Junping Shi + Robert Lewis, Romuald Lipcius, Leah Shaw 
• Jeffrey Soosiah, "Perfect Partitioning of Some (O, 1)-Matrices" (Honors) 
  Gexin Yu + Weizhen Mao, Ryan Vinroot 
• Luis Valentin, "Permutations with Extremal Routingson Cycles" (Honors)
  Gexin Yu + Virginia Torczon, Ryan Vinroot
• Brian Waldman, "Circadian Oscillations of the Intestinal Stem Cell Lineage" (Honors)
  Jianjun Tian + Paul Heideman, Robert Lewis, Junping Shi 
• Nicholas Woods, "Fixed Points of Pick and Stieltjes Functions: A Linear Algebraic Approach" (Honors) 
  Vladimir Bolotnikov + Joshua Gert, Ilya Spitkovsky, Jianjun Tian 

2010-11

• Charles Albert, "Factoring Banded Permutations and Bounds on the Density of Vertex Identifying Codes on the Infinite Snub Hexagonal Grid" (Honors)
  Gexin Yu + Ryan Vinroot, Virginia Torczon
• Ariel Cukierman, "A New Lower Bound on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid" (Honors)
  Gexin Yu + Ilya Spitkovsky, Chris Carone
• Yael Gilboa, "Poles and Zeros of Generalized Carathéodory Class Functions" (Honors)
  Vladimir Bolotnikov + Ilya Spitkovsky, Leiba Rodman, Julie Agnew
• Benjamin Holman, "Topological Characterization of Extinction in a Coupled Ricker Patch Model" (Honors)
  Sarah Day + Junping Shi, Michael Lewis, Leah Shaw
• Matthew Peppe, "Persistent Activity in Assortative Networks of Integrate and Fire Neurons" (Honors)
  Gregory Smith + Junping Shi, Leah Shaw
• Georgia Pfeiffer, "Basins of Attraction in Stage Structured Populations" (Honors)
  Sarah Day + Junping Shi, Larry Leemis, Matthias Leu
• Olivia Walch, "Critical Exponents: Old and New" (Honors)
  Charles Johnson + Ilya Spitkovsky, Josh Erlich
• Dian Yang, "Solution Theory for Systems of Bilinear Equations" (Honors)
  Charles Johnson + Ryan Vinroot, John Delos

2009-10

• Michael Christopher Essman, "Mathematical and Numerical Analysis of Coupled Nonlinear Schrodinger Equations" (Honors)
  Junping Shi + Chi-Kwon Li, Robert Lewis, Justin May
• Aaron Paul Herman, "Preservers of Eigenvalue Inclusion Sets" (Honors)
  Chi Kwong Li + Robert Lewis, David Armstrong
• William Crowell Jordan-Cooley, "Bistability in Differential Equation Model of Oyster Population and Sediment Volume" (Honors)
  Junping Shi + Rex Kincaid, Romulad Lipcius, Leah Shaw, Jian Shen
• Yuanyuan Liu, "The Dynamical Behavior of a Two Patch Predator-Prey Model" (Honors)
  Junpink Shi + Olivier Coibion, Lawrence Leemis, Jianjun Paul Tian
• Austin Powell, "The Maximum Cut Problem: Investigating Computational Approaches" (Honors)
  David Phillips + Robert Lewis, Rex Kincaid, Virginia Torczon
• Patrick Robert Steele, "Understanding and Minimizing Flight Delay" (Honors)
  Tanujit Dey + David Phillips, Rex Kincaid, Larry Leemis, Carlisle Moody
• Andrew Gordon Wilcox, "Finding a Sparse Solution of a Linear System with Applications to Coding Theory and Statistics" (Honors)
  Tanujit Dey + Chi-Kwong Li, Larry Leemis, Donald Campbell
• Harold Lee Williams II, "Equitable and Defective Coloring of Sparse Graphs" (Honors)
  Gexin Yu + Chi-Kwong Li, Christopher Abelt

2008-09

• Kassie Archer, "Box-Counting Dimension and Beyond" (Highest Honors)
  Sarah Day + David Lutzer, Michael Lewis, John Delos
  
• Sean Clark, "A Study of Multiplicative Preservers" (Highest Honors)
  Chi-Kwong Li + Leiba Rodman, Ryan Vinroot, Shiwei Zhang
  
• David Gould, "Modeling the effects of harvesting on Virginia's Black Bear population" (Highest Honors)
  Sarah Day + Tanjuit Dey, Junping Shi, Dan Cristol
  
• Daniel Hariprasad, "Three Pool Model of Calcium Signaling" (Highest Honors)
  Junping Shi + Jianjun Paul Tian, Michael Lewis, Greg Smith
  
• Jacob Hill, "The Set of All Countable Ordinals: An Inquiry into its Construction, Properties, and a Proof Concerning Hereditary Subcompactness" (High Honors)
  David Lutzer + Vladimir Bolotnikov, George Rublein, Laura Ekstrom
• Jennifer Mahle, "Quantum Error Correction and the Joint Higher Rank Numerical Range" (High Honors)
  Chi-Kwong Li + Leiba Rodman, David Phillips, Drew Lamar
  
• Brian Paljug, "Investigating Computational Aspects of the Coincidence Condition for Substitutions of Pisot Type" (High Honors)
  Sarah Day + C.K. Li, David Phillips, Weizhen Mao
• Carolyn Troha, "Braid Groups and Evolution Algebra" (High Honors)
  Jianjun Tian + David Lutzer, Ryan Vinroot, Vassiliki Panoussi
• Elizabeth Truelove, "Mutualism between Clownfish and Sea Anemones: A Computational Model" (Highest Honors)
  Robert Lewis + Rex Kincaid, Dan Cristol
• Niha Zubair, "Reproduction Rate Strategies in White-Footed Mice" (Highest Honors)
  Sarah Day + Tanjuit Dey, Junping Shi, Paul Heideman
  

2007-08

• Tanner Jennings Crowder, "A Study of Genetic Code by Combinatorics and Linear Algebra Approaches" (Highest Honors)
  Chi-Kwong Li + Sarah Day, Jianjun Paul Jian, Margaret Saha
• Paul Robert McMichael. "Multiplicity Lists for Classes of Hermitian Matrices whose Graph is a Certain Tree" (Highest Honors)
  Charles Johnson + Ilya Spitkovsky, Marc Sher
• Lauren Nicole Merrill, "A Survey of Social Choice Failures: Majority and Borda Rules" (Highest Honors)
  Charles Johnson + Laurence Leemis, Don Campbell
• Jonathan Edward Nuckols, "Trees and the Implicit Construction of Eigenvalue Multiplicity Lists" (Highest Honors)
  Charles Johnson + Leiba Rodman, George Rublein, John Morreall
• Evan Alexander Saltzman, "Multivariate Nonhomogeneous Poisson Processes" (Highest Honors)
  Lawrence Leemis + John Drew, Don Campbell

2006-07

• Katherine Paige Benedetto, "Polyomino Tiling Graphs" (Highest Honors)
  Nicholas Loehr + Vladimir Bolotnikov, Weizen Mao
• Katherine Victoria Field, "Counting Hessenberg Matrices" (High Honors)
  David Lutzer + Nicholas Loehr, Virginia Torczon
• Abraham Daniel Bergsagel Isgur, "Almoist Periodic Factorization and Applications to the Spectral Theory of Toeplitz Operators" (Highest Honors)
  Ilya Spitkovsky + Vladimir Bolotnikov, Mark Sher
• Hakan Ali-John Seyalioglu, "Exponential Attacks on Blockcipher Families" (Highest Honors)
  Moses Liskov + George Rublein, Nicholas Loehr

2005-06

• Kevin Duke, "Domain Theory: Modeling Generalized Ordered Modifications of the Real Line" (Highest Honors)
  David Lutzer + Vladimir Bolotnikov, Nahum Zobin, Steve Knudson
• Michael Holroyd, "Synchronizability and Connectivity of Discrete Complex Systems" (High Honors)
  Rex Kincaid + Sebastian Schreiber, Christopher del Negro
• Joshua Link, "The Presence of Triangles in Patterns with Given Minimum Risk" (Highest Honors)
  Charles Johnson + David Lutzer, Nick Loehr, Marc Sher
• David Rose, "Minimal Length Uncertainty and the Quantum Mechanics of Non-Commutative Space-Time" (Highest Honors)
  Ilya Spitkovsky + David Lutzer, Vladimir Bolotnikov, Chris Carone
• Matthew Ruprecht
  Robert Lewis
• Paul Smith, "Boundary Nevanlinna-Pack Interpolation for Generalized Nevanlinna Functions" (Highest Honors)
  Vladimir Bolotnikov + David Lutzer, Ilya Spitkovsky, Bill Cooke

2004-05

• Kristina Hofman
  Michael Trosset + Michael Lewis, Evgenia Smimi