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Proceedings from the OSU REU Program

Proceedings from the OSU REU Program

Oregon State University has held a National Science Foundation sponsored REU program nearly every summer since 1987. Each year, the students produce a written account of their research projects to be added to the REU proceedings, which can be accessed through the accordion below.

Previous proceedings

Ling Chen of Occidental College, Isabelle Hernandez of Oregon State University, and Zain Shields of University of California, Berkeley (Advisor: Holly Swisher)

Analogues of Alder-Type Partition Inequalities for Fixed Perimeter Partitions

Liam Armstrong of Oregon State University, Bryan Ducasse of University of Central Florida, and Thomas Meyer of Amherst College (Advisor: Holly Swisher)

A Generalized Alder-Type Partition Inequality

Miles Smith, Clare Spinner, and Hannah Stein, of Occidental College, University of Portland, and Lewis and Brown University (Advisor: Hoe Woon Kim)
An Explicit and Analytical Solution to the Stokes Equations on the Half-Space $\mathbb{R}^{3}_{+}$ with Initial Conditions and Boundary Conditions For Velocity using Integral Transforms

Alex Negrón, Clarice Pertel, and Christopher Wang of Illinois Institute of Technology, Cornell University, and Columbia University (Advisor: Yevgeniy Kovchegov)
Extensions of True Positive Skewness for Unimodal Distributions

Lexi Arlen and Tanner Fromcke of Washington University in St. Louis and Oregon State University (Advisor: Patrik Nabelek)
One-Gap Solutions to the Kaup-Broer System

Tyler Beauregard and Janabel Xia of Truman State University and Massachusetts Institute of Technology (Advisor: Mike Rosulek)
Private Set Intersection: Problems on Sampling from the Intersection

Abigail Ezell, Darwin Nesheim, and Kevin Sweet, of Colorado College, Oregon State University, and Lewis and Clark College (Advisor: Blessing Emerenini)
Mathematical Modeling and Characterization of the Effect of Quorum Sensing Regulated T6SS Killing on Biofilm Structure

Devin Goodwin, Nga Yu Lo, Kristen Maggard, and Miranda Reed of Oregon State University, Macaulay Honors College at Hunter College, University of Virginia, and Western Washington University (Advisor: Juan Restrepo)
Economic Drivers in Modeling Pandemics

Adriana Duncan, Simran Khunger, and Ryan Tamura of Tulane University, Carnegie Mellon University, and University of California, Berkeley (Advisor: Holly Swisher)
Generalizations of Alder's Conjecture via a Conjecture of Kang and Park

Cassandra Williams and Krista Wurscher, of New Paltz State University of New York and University of Oregon (Advisor: Blessing Emerenini)
Mathematical Modeling and analysis of within-host Influenza infection dynamics

Nico Diaz-Wahl, Marcel Hudiani, and Connor Thompson, of Carnegie Mellon University, University of Arizona, and Macalester College (Advisor: Clay Petsche)
Preperiodic Points and Linearization in $p$-adic Dynamics

Justin Bloom and Lalita Devadas, of Oregon State University and Columbia University (Advisor: Mike Rosulek)
Secure Montgomery Multiplication and Repeated Squares for Modular Exponentiation

Savana Ammons, Young Jin Kim, and Laura Seaberg of Harvey Mudd College, Reed College, and Haverford College (Advisor: Holly Swisher)
An Analogue of K-marked Durfee Symbols for Strongly Unimodal Sequences

Nicholas Anderson, Asimina Hamakiotes, and Benjamin Oltsik of San Francisco State University, Macaulay Honors College at Baruch College, and Hamilton College (Advisor: Holly Swisher)
Eta-quotients of Prime or Semiprime Level and Elliptic Curves

Jacqueline Alvarez and Andrew Fisher, of Cal Poly Pomona and Walla Walla University (Advisor: Nathan Gibson)
Approximating Dispersive Materials With Parameter Distributions in the Lorentz Model

Claire Campregher and Jesse Johnson, of Cal State Long Beach and Oregon State University( Advisor: Yevgeniy Kovchegov)
Properties of Level Set Trees of Geometric Random Walks

Karina Cho and Jacob Naranjo, of Harvey Mudd College and Kalamazoo College (Advisor: Ren Guo)
Extensions of Euclidean Relations and Inequalities to Spherical and Hyperbolic Geometry

Brian Frost-LaPlante and Collin Victor, of Cooper Union and the University of Nebraska-Lincoln (Advisor: Juan Restrepo)
Enhancing Models for Gradient Sensing by Chemotaxis and Cell Communication

Joshua Gerstein and Annie Raichev, of Carleton College and the University of California, San Diego (Advisor: Mike Rosulek)
Sustained Memory Complexity for Memory Hard Functions

Kenneth Allen and David DeMark, of the University of Massachusetts, Lowell and Carleton College (Advisor: Clayton Petsche)
Horseshoes, Attractors, and Good Reduction: Dynamics of the P-Adic Henon Map

Catherine Babecki and Geoffrey Sangston, of Penn State University and the University of Miami (Advisor: Chris Jennings-Shaffer)
Rank- and Crank-Like Functions Generated by Bailey Pairs

Estonia Black and Caleb Smith, of the University of Tennessee and Oregon State University (Advisor: Ren Guo)
Strengthened Euler's Inequality in Spherical and Hyperbolic Geometries

Brian Diaz and Erin Ellefsen, of St. Mary's University and Luther College (Advisor: Holly Swisher)
Extending a Catalog of Quantum Modular Forms to an Infinite Class

Anna-Sophia Hirst and Rachel Linder, of California State University, Dominguez Hills and the University of Maryland, Baltimore County (Advisor: Yevgeniy Kovchegov)
Self-Similarity in Level Set Trees of Geometric Random Walks

Ethan Alwaise and Elena Iannuzzi, of Emory University and Vassar College (Advisor: Holly Swisher)
A proof of Mao's Conjectures on Partition Rank Inequalities and an Investigation of Rank Difference Functions

Autumn Asay and Jenia Rousseva, of Oregon State University and Eastern Washington University (Advisor: Yevgeniy Kovchegov)
Alternating Inhomogeneous Quantum Walks on $\Z$

Robert Costa and Patrick Dynes, of Tufts University and Clemson University (Advisor: Clay Petsche)
A $p$-adic Perron-Frobenius Theorem

Jessica Covington and Megan Golbek, of College of Charleston and California State University Monterey Bay (Advisor: Mike Rosulek)
Secure Multiparty Computation

Kai Lei and Melissa Sherman-Bennett, of Simmons College and Bard College at Simon’s Rock (Advisor: Glencora Borradaile)
Large Induced Outerplanar and Acyclic Subgraphs of Planar Graphs

Robert Weber (Advisor: Glencora Borradaile)
Embedded Width, A Variation of Treewidth for Planar Graphs

Nicole Wein (Advisor: Glencora Borradaile)
On Cyclewidth

Alexander Beckwith and Joseph Dickens of Kenyon College and St. Olaf College (Advisor: Clay Petsche)
Finite Dynamical Systems: A Probabilistic Approach

Acadia Larsen and Alexa Rust of Whittier College and University of Washington (Advisor: Holly Swisher)
Inequalities For Positive Rank and Crank Moments of Overpartitions

Gillian Grindstaff and Kevin Wilson of Pomona College and University of Oregon (Advisor: Yevgeniy Kovchegov)
A Model of Coinless Quantum Walks and Quantum Markov Chain Monte Carlo

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Allison Arnold-Roksandich, Zoe Jansen, and Anthony Lazzaro of Harvey Mudd College, Wellesley College, and Oregon State University (Advisor: Holly Swisher)
Expressing the k-Rank Generating Function and Rank Difference Functions for Multipartitions as Modular Forms

Celeste Burkhardt and Thomas Pitts of University of North Carolina Asheville and Oregon State University (Advisor: Paul Cull)
Hamiltonian Paths and Perfect One-Error-Correcting Codes on Iterated Complete Graphs

Angelica Deibel, Kevin Schwenkler, and Laura Veith of Arizona State University, Hampshire College, and University of Washington (Advisor: Yevgeniy Kovchegov)
Inhomogeneous Quantum Walks

Eddie Maldonado and Roy Oursler of Reed College and University of Wyoming (Advisor: Glencora Borradaile)
Degree Distributions and Random Graphs

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Mary Ambrosino and Patrik Nabelek, The College of New Jersey and Oregon State University (Advisor: Nick Michalowski)
A Weak Type Estimate for Bases of Rectangles in R3

Emily Carlson and Tselil Schramm, Bard College and Harvey Mudd College (Advisor: Paul Cull)
Sequences for Solving Puzzles and Touring Graphs

Ben Cornelis and Sangpo Sherpa, University of British Columbia and MIT (Advisor: Yevgeniy Kovchegov)
A Quantum Computing Algorithm for Card Shuffling

Michael Donatz and Nicole Marsaglia, Oregon State University and University of Oregon (Advisor: Holly Swisher)
Generalizing Euler's Pentagonal Number Theorem to Multipartitions

Jennifer Iglesias and Antonio Ochoa, Harvey Mudd College and Cal Poly Pomona (Advisor: Glencora Borradaile)
Orienting Graphs is Sometimes Hard

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Michael Abram, University of the Pacific (Advisor: Paul Cull)
On the Behavior of Ratios of Solutions to Nonnegative Difference Equations

Erin Bela & Erik Hortsch, Chapman University & Oregon State University (Advisor: Nathan Gibson)
Generalized Polynomial Chaos and Dispersive Dielectric Media

Oleg Lazarev, Matt Mizuhara & Ben Reid, Princeton University, Bucknell University & Virginia Polytechnic Institute and State University (Advisor: Holly Swisher)
Some Results in Partitions, Plane Partitions, and Multipartitions

Leanne Merrill & Tony Van, SUNY Potsdam &University of Pennsylvania (Advisor: Paul Cull)
A Tale of Two Puzzles

Denise Shigeta, University of Portland (Advisor: Yevgeniy Kovchegov)
Gaps: The Strategy Behind a Speedy Coupling of Card Shuffling

Jennifer Thompson, Jesus College Cambridge (Advisor: Yevgeniy Kovchegov)
Optimal Couplings for Card Shuffling

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Elyse Azorr, Samuel J. Ghitelman, Ralph Morrison and Greg Rice (Advisor: Yevgeniy Kovchegov)
Coupling Times for Random Walks with Internal States

Lindsay Baun and Sonia Chauhan (Advisor: Paul Cull)
Puzzles on Graphs: The Towers of Hanoi, The Spin-Out Puzzle, and The Combination Puzzle

Marie Milne and Danielle Wedde (Advisor: Nathan Gibson)
Simulating Polydisperse Materials with Distributions of the Debye Model

Alex Montoye and Natalie Rich (Advisor: Holly Swisher)
Non-Conjugate, Rook Equivalent T-Cores

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Karen Barrese and Neel Chugh (Advisor: Nathan Gibson)
Approximating Dispersive Mechanisms Using the Debye Model with Distributed Dielectric Parameters

Benjamin Coate (Advisor: Yevgeniy Kovchegov)
The Lorentz Lattice Gas Model

Elizabeth DeYoung and Jonathan Hanselman (Advisor: Yevgeniy Kovchegov)
Multiple Particle Edge Reinforced Random Walks on Z

John Drinane (Advisor: Yevgeniy Kovchegov)
Rate of Convergence of Polya's Urn to the Beta Distribution

Julie Linman and Jason Murphy (Advisor: Donald Solmon)
Reconstructing Planar Convex Bodies Using Point X-rays from Two Sources

Elizabeth Skubak and Nicholas Stevenson (Advisor: Paul Cull)
A New Puzzle for Iterated Complete Graphs of Any Dimension

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Kirsten Aagesen and David Steinberg; Oregon State University & Trinity University (Advisor: Donald Solmon)
On the Uniqueness of a Convex Body Given X-ray Data from Two Exterior Sources

Joanna Furno and Patrick Waters; Wisconsin Lutheran College & Oregon State University (Advisor: Holly Swisher)
Investigations Regarding Partitions and Multipartitions

Natasha Komarov, Reagin McNeill and Justin Webster; Carnegie Mellon, Smith College, and San Diego University (Advisor: Dennis Garity)
Normal Subgroups of the Free Group

Christopher Pryby; University of Georgia (Advisor: Donald Solmon)
Point X-rays of a Convex Body from an Interior and an Exterior Source

Katherine Walsh and Jonathan Wherry; George Washington University and Oregon State University (Advisor: Paul Cull)
Population Dynamics in One Dimension

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Michael Chmutov, Thomas Hulse, Andrew Lum, and Peter Rowell (Advisor: Juha Pohjanpelto)
Plane And Spherical Curves: An Investigation of Their Invariants

Scott Ewert (Advisor: Donald Solmon)
Investigation of The Boundary Points of a Shadow Body of a Triangle

Samantha Nieveen and Allison Smith (Advisor: Dennis Garity)
Covering Spaces and Subgroups of the Free Group

Dusty Ross and Kathleen Tuite (Advisor: Donald Solmon)
Investigation of Two Bodies With Equal Point X-Rays at Two Sources

Margaret A. Sanders (Advisor: Paul Cull)
Counting Bits with Fibonacci And Zeckendorf

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Matt Cardwell, Rosanna Haut, and Kenny Barrese (Advisor: Juha Pohjanpelto)
Knot Invariants and their Implications for Closed Plane Curves

Nick Meredith (Advisor: Paul Cull)
Stability and Instability in One Dimensional Population Models

David Miller (Advisor: Don Solmon)
Investigating Equal X-Ray Bodies to the Triangle

John Oberlin (Advisor: Juha Pohjanpelto)
Some Classifications of Free Curves in Euclidean Space

Jason Siefken and Lena Spargo (Advisor: Don Solmon)
An Algorithm for Reconstruction of a Convex Body from Two Point Sources

Elizabeth Weaver (Advisor: Paul Cull)
Gray Codes and Puzzles on Iterated Complete Graphs

Stephanie Young (Advisor: Paul Cull)
Faster Fibonacci

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Robin Baur; Harvey Mudd (Advisor: Juha Pohjanpelto)
Regular Homotopy Classes of Curves on the Torus

Jennifer Biermann and Jonathan Dent; Lawrence University and Calvin College (Advisor: Juha Pohjanpelto)
Nonnegative Defect

Frank Chemotti and Andrea Rau; Davidson College and St. Olaf College (Advisor: Dennis Garity)
Intersection Numbers of Closed Curves on the Punctured Torus

Sam Ganzfried; Harvard University (Advisor: Paul Cull)
A Simple Algorithm for Knight's Tours

Jessica Kincaid; Oregon State University (Advisor: Paul Cull)
A Graphical Exploration of Stable Characteristics of Simple Population Models

Kathleen King; Olon College of Engineering (Advisor: Paul Cull)
A New Puzzle Based on the SF Labelling of Iterated Complete Graphs

Pamela Russell; University of Pennsylvania (Advisor: Paul Cull)
Perfect One-Error-Correcting Codes on Iterated Complete Graph

Scott Weaver; Oregon State University
Advisor: Dennis Garity
Special Classes of Whitehead Automorphisms on the Free Group

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Mary Avery, Brian Klos and Jonas Meyer (Advisor: Donald Solmon)
Reconstructing Convex Polyhedrons in R^3

Andrew Barker and Ian Biringer (Advisor: Juha Pohjanpelto)
On Defect of Plane Curves

Jason Dagit and Huyen Pham (Advisor: Juha Pohjanpelto)
Almost Tree-Like Plane Curves

Meredith Kadlac (Advisor: Paul Cull)
Explorations of the Minesweeper Consistency Problem

Stephanie Kleven (Advisor: Paul Cull)
Perfect Codes on Odd Dimension Serpinski Graphs

Adam Murakami (Advisor: Paul Cull)
Computing Fibonacci Numbers Fast using the Chinese Remainder Theorem

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Andrew Blood (Advisor: Dennis Garity)
The Maximal Number of Transverse Self-Intersections of Geodesics on the Punctured Torus

Drew Butcher and Ashley Medin (Advisor: Donald Solmon)
Infinite Dimensionality and Unboundedness for Sets of Planar Convex Bodies with a Common Directed X-ray

Bobbe Cooper and Eric Rowland (Advisor: Dennis Garity)
On Equivalent Words in the Free Group on Two Generators

David Fithian (Advisor: Donald Solmon)
Verifying a Triangle From Two Directed X-rays

Christopher Frayer and Shalini Reddy (Advisor: Paul Cull)
Perfect One Error Correcting Codes and Complete Iterated Graphs

Ananda Leininger and Kevin McGown (Advisor: Paul Cull)
Knight's Tour

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Shawn Alspaugh, Nathan Knight, and Kathleen Meloney (Advisor: Paul Cull)
Perfect One Error Correcting Codes on Iterated Complete Graphs

Danica Dralus (Advisor: Donald Solmon)
Effects of a Scaling Factor on the Error Vector in Dykstra's Algorithm

William Johnson (Advisor: Donald Solmon)
Determining a Triangle from Two X-ray Sources

Jennifer Kimble (Advisor: Donald Solmon)
Functions that are Directed X-rays of Planar Convex Bodies

Emily Putnam (Advisor: Dennis Garity)
Distinctness of Self-Intersecting Curves on the Punctured n-Holed Torus

Daniel Rubinstein and Braden Soper (Advisor: Dennis Garity)
Self-Similar Constructions of the Rigid Antoine Necklace in Euclidean Three-Space

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William Black and David Koop (Advisor: Donald Solmon)
Properties of Planar Convex Bodies from One directed X-ray

Michael Cenzer, Sarah Lobser and Ellen Veomett (Advisor: Paul Cull)
Perfect Domination in Knesser Graphs

Christine Devena (Advisor: Juha Pohjanpelto)
Families of Partially Reducible Plane Curves

Christian J. Grostic (Advisor: Juha Pohjanpelto)
Connected sums and Decompositions of Plane Curves

Rachel Lash (Advisor: Juha Pohjanpelto)
Continuous, Non-singular transformations from the Klein Bottle to the Torus

Tim Ritter (Advisor: Juha Pohjanpelto)
Classification of Extremal Curves with 6 Double Points and of Tree-like Curves with 6 Double Points and I=5

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Danielle Arett (Advisor: Paul Cull)
Coding Theory on the Generalized Towers of Hanoi

Elizabeth Birchall and Jason Tedor (Advisor: Paul Cull)
Perfect One Error Correcting Codes on Iterated Complete Graphs

Jason E. Durham (Advisor: Juha Pohjanpelto)
Irreducible Plane Curves

Sarah Gulde (Advisor: Juha Pohjanpelto)
Classification of Plane Curves

Mike Lauzon and Ben Schmidt (Advisor: Donald Solmon)
Tomography of Non-convex Polygons from a Single Point X-Ray

Kimberly Moerman and Jenny Weisenberg (Advisor: Juha Pohjanpelto)
Symmetry Reduction of Maxwell's Equations: A Case Study

Patrick W. Yaner (Advisor: Paul Cull)
Expected Cycle Length in Random Boolean Networks of Connectivity 2

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David Bode (Advisor: Paul Cull)
Alternate Labelings for Graphs Representing Perfect-One-Error-Correcting Codes

Jason Burns (Advisor: Dennis Garity)
Some Observations on Packability of Spheres

Matthew Boylan and Peter Caldwell (Advisor: Don Solmon)
Bounds on the Rate of Convergence of the Kacmarz Method in Computed Tomography

Jennifer Chaffee (Advisor: Paul Cull)
Global Stability in Discrete One-Dimensional Population Models

Dorothy Lam (Advisor: Donald Solmon)
Point-Source Geometric Tomography

Rebecca Virnig (Advisor: Dennis Garity)
Whitehead Automorphisms and Equivalent Words

Cover Page

Erin Scott, Dennis Simmons, and Ian Winokur (Advisor: Robert Burton and Thomas Schmidt)
Low Discrepancy Sequences and Quasi-Monte Carlo Integration

Jessica E. Cavanaugh and Kevin Stoller (Advisor: Paul Cull)
Perfect-One-Error-Correcting Codes on a Family of N Dimensional Graphs

Jill Lombaer (Advisor: Dennis Garity)
Classification of Loops with Self-Intersections on the Twice Punctured Torus

Michael Lau (Advisor: Dennis Garity)
A Computer Implementation of Whitehead's Algorithm

Margaret Taub (Advisor: Dennis Garity)
Classification of Groups with Two Self-intersections on the Once Punctured Torus with Genus N

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Damon Bell (Advisor: Paul Cull)
Lower Bound on Open Knight's Tours

Ryan Gould, Jean Steiner and Beverly Steinhoff (Advisor: Dennis Garity)
Classification of Loops with Self-intersections on the Once Punctured Torus with Genus N

Laura A. Pace and Carlos Salazar-Lazaro (Advisor: Robert Burton)
Uniformly Distributed Sequences and their Discrepancies

Douglas Squirrel (Advisor: Paul Cull)
A Warnsdorff-Rule Algorithm for Knight's Tours on Square Chessboards

Holly R. Wiitala (Advisor: Paul Cull)
The Knight's Tour Problem on Boards with Holes

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Mande Butler, Jeanne Carton and Emil Kraft (Advisor: Dennis Garity)
Geodesics with Three Intersections on the Punctured Torus

Susan Garner Garille (Advisor: Nathan Gibson)
A Mathematica Program for Classifying Geodesics with k Self Intersections on the Once Punctured Torus

Matthew Hall (Advisor: Dennis Garity)
Fan Beam Tomography

Kristy Hyman and Tom Coffey (Advisor: Robert Burton)
Explorations in Fractal Percolation

Ingrid Nelson (Advisor: Paul Cull)
Coding Theory on the Towers of Hanoi

Brian Stein (Advisor: Paul Cull)
Two Independent Hamiltonian Circuits and Embedding Mesh of Trees on the Mobius Cube

Shasta Willson (Advisor: Paul Cull)
Explorations into Global Stability of Population Models

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Stephen Caulk and Poul E. J. Petersen (Advisor: Dennis Garity)
Knots of the Form [a,b,c,d,e]

Susan Dziadosz, Thomas Insel and Peter Wiles (Advisors: Dennis Garity and Thomas Schmidt)
Geodesics with Two Self-Intersections on the Punctured Torus

Nancy Heinschel (Advisor: Paul Cull)
Sufficient Conditions for Global Stability in Population Models

Chris Kaltwasser (Advisor: Paul Cull)
Computing Fibonacci Numbers with Gates

Amy Pool and Suzanne Zawistowksi (Advisor: Thomas Schmidt)
On Isolated Values in the Markoff Spectrum

Kelley Seibel (Advisor: Paul Cull)
The Knight's Tour on the Cylinder and Torus

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Helga Fuller (Advisor: Dennis J. Garity)
A Construction of the Universal Menger Curve

Charles Humphreys (Advisor: Paul Cull)
Hypercube Variant Linkages

John Karro (Advisor: Paul Cull)
The Complexity of Computing Fibonacci Numbers

Kenneth H. Keppen (Advisor: Robert Robson)
On K-Stage Euclidean Domains

Mark MacLean (Advisor: Andre Weideman)
Eigenvalue Computations: The Power and Lanczos Methods

Nicole M. Mayer (Advisor: Paul Cull)
Random Neural Nets with Small Connectivities

Eva F. Wailes and Cassandra S. McGee (Advisor: Dennis J. Garity)
The Unknotting Number for 2k + 3, 2j + 1, 2k + 2 and Other Knots of the Form a, b, c

Amy Pilkington (Advisor: Andre Weideman)
Numerical Analysis of Love's Equation

Romyar Sharifi (Advisor: Robert Robson)
On Cyclotomic Polynomials, Power Residues, and Reciprocity Laws

Eric Thomas (Advisor: Andre Weideman)
A Comparison of Approximation Methods for the Convection-Diffusion Equation

Nora Barbara and Jennifer Playdon (Advisor: Paul Cull)
The Game of Zigzag

James A. Bernhard (Advisor: Dennis Garity)
Unknotting Numbers and Minimal Knot Diagrams

Nathanial Brown, Nathan Dunfield, and Greg Perry
Colorings of the Plane

Vesta Coufal
Primes and Twin Primes

Allison Mitchell
Upper Bounds for the Stick Number of Torus Knots

Isamu Shigeyama
Puzzles: What Patterns are Possible?

Augustine P. Waters (Advisor: Dennis Garity)
The Towers of Hanoi: The Case of Four Towers