Senior Thesis Archives

Each year below contains a list of students who took Math 197 in that year and their corresponding thesis information. Full theses and abstracts are available from Scholarship@Claremont.

Clicking a student’s name will take you to their Scholarship@Claremont profile. Clicking on a thesis title will take you directly to the thesis PDF.

2021–2022

Student	Advisor	Second Reader	Project Title
Mason Acevedo	Michael Orrison	Darryl Yong	An Exploration of Voting with Partial Orders
Madelyn Andersen	Haydee Lindo	Michael Orrison	What is a Trace Module? A Short Peek into Ring Theory
Eric Chavez	Sam Nelson	Francis Su	Trivial Quotients of Fundamental Tribrackets and Link Homotopy
Aitzín Cornejo-Reynoso	Dagan Karp	Robin Wilson	Tracking in the 2022 Revision of the California Math Framework
William Gilroy	Jamie Haddock	Heather Zinn-Brooks	Check Yourself Before You WREK Yourself: Unpacking and Generalizing Random Extended Kaczmarz
Amit Harlev	Francis Su	Mohamed Omar	On the Polytopal Generalization of Sperner's Lemma
Max Holloway	Susan Martonosi	Yaron Raviv	Mechanisms for the Efficient Hedging of Public Information Events
Benjamin Langton	Mohamed Omar	Michael Orrison	Results on the Generalized Covering Radius of Error Correcting Codes
Athena Li	Darryl Yong	Ilana Horn	Acoustic Localization in the Classroom: A Mathematician's Journey into the World of Engineering
Ryan Martinez	Sam Nelson	Alfonso Castro	Algebraic Invariants of Knot Diagrams on Surfaces
Lian Morales	Lisette de Pillis	Jishnu Das	Discovering Underlying Molecular Networks between two Different Rheumatoid Arthritis Endotypes
Fletcher Nickerson	Francis Su	Satyan Devadoss	Folding Hypercubes (and failing)
Phousawanh Peaungvongpakdy	Heather Zinn-Brooks	Andrew Bernoff	An Adaptive Hegselmann-Krause Model of Opinion Dynamics
Kye Shi	Nicholas Pippenger	Arthur Benjamin	Games for One, Games for Two: Computationally Complex Fun for Polynomial-Hierarchical Families
Solomon Valore-Caplan	Heather Zinn-Brooks	Vin de Silva	Smoothed Bounded-Confidence Opinion Dynamics on the Complete Graph

2020–2021

Student	Advisor	Second Reader	Project Title
Aria Beaupre	Mohamed Omar	David Milan	On the Inverse Hull of a One-sided Shift of Finite Type
Zoe Bell	Nicholas Pippenger	Ran Libeskind-Hadas	Going Meta on the Minimum Circuit Size Problem: How Hard Is It to Show How Hard Showing Hardness Is?
Ellie Byrnes	Jon Jacobsen	Jasper Weinburd	Fractals, Fractional Derivatives, and Newton-Like Methods
Max Chao-Haft	Francis Su	Dagan Karp	Discrete Vector Fields on Polytopal Complexes
Natasha Crepeau	Dagan Karp		On the Tropicalization of Lines onto Tropical Quadrics
Elisha Dayag	Nicholas Pippenger	Jasper Weinburd	An Exploration of Gaussian Resampling
Daniela Elizondo	Arthur Benjamin	Haydee Lindo	Counting on the Hosoya Triangle
Matthew LeMay	Mohamed Omar	Nicholas Pippenger	The Complexity of Symmetry
John Lentfer	Arthur Benjamin	Francis Su	Tiling Representations of Zeckendorf Decompositions
Feiyang Lin	Gregg Musiker	Dagan Karp	On Rank-Two and Affine Cluster Algebras
Kailee Lin	Francis Su	Arthur Benjamin	Exploring Winning Strategies for the Game of Cycles
Jawahar Madan	Dagan Karp	Renzo Cavalieri	Towards Tropical Psi Classes
Thomas Martinez	Mohamed Omar	Arthur Benjamin	The Slice Rank Polynomial Method
Lake Trujillo	Vin de Silva	Dagan Karp	A Coherent Proof of Mac Lane's Coherence Theorem
Miguel Velez	Andrew Bernoff	Jasper Weinburd	Modelling the Transition from Homogeneous to Columnar States in Locust Hopper Bands
Young Zhang	Dagan Karp	Jordan Kostiuk	Generalize the Chip-Firing Process of Graphs for Adinkras

2019–2020

Student	Advisor	Second Reader	Project Title
Savana Ammons	Francis Su	Dagan Karp	A Discrete Analogue for the Poincaré-Hopf Theorem
Havi Ellers	Michael Orrison	Hadi Salmasian	On the Mysteries of Interpolation Jack Polynomials
Lily Friedberg	Dagan Karp	Darryl Yong	Reflections on Critical Math Education in the College Classroom: Critical Pedagogy and Modular Approaches
Hanna Hoffman	Dagan Karp	Hannah Markwig	Pascal's Mystic Hexagon in Tropical Geometry
Forest Kobayashi	Francis Su	Sam Nelson	Where the Wild Knots Are
Hannah Larson	Andrew Bernoff	Jasper Weinburd	Agent-Based Modeling of Locust Foraging and Social Behavior
Cassidy Le	Lisette de Pillis	Blerta Shtylla	Use of Kalman Filtering in State and Parameter Estimation of Diabetes Models
Nick Richardson	Nicholas Pippenger	Michael Orrison	Composing Probabilistic Graphical Models with Adaptive Basis Methods
Marcelo Almora Rios	Alfonso Castro	Jon Jacobsen	Radial Singular Solutions to Semilinear Partial Differential Equations
Mengyi Shan	Weiqing Gu	Nicholas Pippenger	Geometric Unified Method in 3D Object Classification
Ricky Shapley	Arthur Benjamin	Curtis Bennett	An Exploration of Combinatorial Interpretations for Fibonomial Coefficients

2018–2019

Student	Advisor	Second Reader	Project Title
Quentin Barth	Andrew Bernoff	Theresa Lynn	Stability Theory of Lattice Configurations of Swarms
Karina Cho	Sam Nelson	Francis Su	Enhancing the Quandle Coloring Invariant for Knots and Links
Adam Dhillon	Nicholas Pippenger	Michael Orrison	An Analog Computing Analogue for Computational Complexity
Conner DiPaolo	Weiqing Gu	Nicholas Pippenger	Randomized Numerical Linear Algebra and its Applications to Machine Learning
Madelyn Gaumer	Michael Orrison	Neil Rhodes	Using Neural Networks to Classify Probability Distributions on Circular Data
Jenny Lee	Dagan Karp	Luis A. Levya	On Self Regulation in College-Level Mathematics Classes
Ethan Sargent	Alfonso Castro	ShuZhi Song	Radial Solutions to Semipositone Dirichlet Problems
Gianna Wu	Lisette de Pillis	Blerta Shtylla	A Simplified Single Compartment Model for Type 1 Diabetes

2017–2018

Student	Advisor	Second Reader	Project Title
Lucius E.J. Bynum	Susan E. Martonosi	Michael E. Orrison	From Partially Ranked Data to Fully Ranked Decisions: Prescriptive Analytics for Professional Basketball Data
Marissa A. Gee	Lisette de Pillis	Rachel Levy	Modeling the Onset and Treatment of Type-1 Diabetes in the Human Pancreas
Alex Goldstein	Michael E. Orrison	Chris Clark (Engineering)	Game Theory and the Symmetric Group
Christopher R. Hoyt	Dagan Karp	Mohamed Omar	On The Landscape Of Random Tropical Curves
Hamzah I Khan	Susan E. Martonosi	Jim Boerkoel (CS)	A Metric for Measuring the Quantity of Synchronization Tasks in Simple Temporal Networks
Bryce McLaughlin	Mohamed Omar	Dagan Karp	Applying the Polynomial Method to Problem in Discrete Geometry
Joshua A. Miller	Nicholas J. Pippenger	Susan E. Martonosi	Sequential Probing with a Random Start
Matthew Simon	Weiqing Gu	Mohamed Omar	TBA
Xinrui Yan	Weiqing Gu	Vatche Sahakian (Physics)	Mathematics of Emergent Gravity Based on Quantum Entanglement

2016–2017

Student	Advisor	Second Reader	Thesis
Aaron R. Bagheri	Dagan Karp	Mendez-Diez, Stefan (Bard College)	Classifying the Jacobian Groups of Adinkras
Dylan Baker	Talithia Williams	Tanya Srebotnjak	The Document Similarity Network: A Novel Technique for Visualizing Relationships in Text Corpora
Kathryn Dover	Weiqing Gu	Dagan Karp	Pattern Recognition in Stock Data
Magda Hlavacek	Dagan Karp	Meldoy Chan (Brown University)	Random Tropical Curves
Nathaniel Leslie	Theresa W. Lynn (physics)	Francis E. Su	Maximal LELM Distinguishability of Qubit and Qutrit Bell States Using Projective and Non-Projective Measurements
Calvin Leung	Jason Gallicchio (physics)	Andrew J. Bernoff	Quantum Foundations with Astronomical Photons
Shiyue Li	Dagan Karp	Dhruv Ranganathan (Yale University)	Tropical Derivation of Cohomology Ring in Heavy/Light Hassett Spaces
Caitlin Lienkaemper	Mohamed Omar	Dagan Karp	Toric Ideals, Polytopes, and Convex Neural Codes
Sam Kim Miller	Mohamed Omar	Nicholas J. Pippenger	Combinatorial Polynomial Hirsch Conjecture
Connie Okasaki	Jon Jacobsen	Julie Blackwood (Williams College)	Slowing the Evolution and Outbreak of Antibiotic Resistance
Micah G. Pedrick	Michael E. Orrison	Nicholas J. Pippenger	Complexity of Linear Summary Statistics
Dan Schmidt	Andrew J. Bernoff	Alan E. Lindsay (University of Notre Dame)	Kinetic Monte Carlo Methods for Computing First Capture Time Distributions in Models of Diffusive Absorption
Ian R.W. Schweickart	Weiqing Gu	Amanda R. Ganguly (Claremont McKenna College)	Investigating Post-Earnings-Announcement Drift Using Principal Component Analysis and Association Rule Mining
Dina Sinclair	Susan E. Martonosi	Banafsheh Behzad (CSU—Long Beach)	Incorporating the Centers for Disease Control and Prevention into Vaccine Pricing Models
Natchanon Suaysom	Arthur T. Benjamin	Puck Rombach (UCLA)	Iterative Matrix Factorization Method for Social Media Data Location Prediction
Zöe Tucker	Michael E. Orrison	Bill Alves (HSA)	Emergence and Complexity in Music
Kira A. Wyld	Francis Edward Su	Kenji Kozai	Sudoku Variations on the Torus
Bo Zhang	Weiqing Gu	Nicholas J. Pippenger	Machine Learning on Statistical Manifold
Jialun Zhang	Andrew J. Bernoff	Chad Topaz (Macalester College)	Dynamics and Clustering in Locust Hopper Bands

2015–2016

Student	Advisor	Second Reader	Thesis
Kennedy Agwamba	Jon Jacobsen	Rachel Levy	An Interactive Tool for the Computational Exploration of Integrodifference Population Models
Robert Bennett	Arthur T. Benjamin	Nicholas J. Pippenger	Fibonomial Tilings and Other Up-Down Tilings
Casey Chu	Weiqing Gu	Dagan Karp	The Geometry of Data: Distance on Data Manifolds
Matthew Dannenberg	Weiqing Gu	Satyan L. Devadoss (Williams College)	Pattern Recognition in High-Dimensional Data
Alec Dunton	Andrew J. Bernoff	Chad M. Topaz (Macalester College)	Topological Data Analysis for Systems of Coupled Oscillators
Mitchell Horning (Fall, 2016)	Nicholas J. Pippenger	Ran Libeskind-Hadas (CS)	The MINCUT Linear Arrangement Problem
Margaux Hujoel	Lisette G. de Pillis	Matina Donaldson-Matasci (Biology)	Assessment of Treatment and Screening Procedures for Chlamydia trachomatis Infections in a College Setting (held until 2017)
R. Amzi Jeffs	Mohamed Omar	Nora Youngs	Convexity of Neural Codes
Ryan Jones	Andrew J. Bernoff	Chad M. Topaz (Macalester College)	Hopper Bands: Locust Aggregation
Cheng Wai Koo	Mohamed Omar	Nicholas J. Pippenger	A Bound on the Number of Spanning Trees in Bipartite Graphs
Bo Li	Alfonso Castro	Ivan Ventura	Steady State Solutions for a System of Partial Differential Equations Arising from Crime Modeling
Matthew Lin	Dagan Karp	Satyan L. Devadoss (Williams College)	Graph Cohomology
Joana Perdomo	Lisette G. de Pillis	Darryl H. Yong	Mathematical Modeling of Blood Coagulation (held until 2017)
John Phillpot	Ran Libeskind-Hadas (CS)	Nicholas J. Pippenger	Line-of-Sight Pursuit and Evasion Games on Polytopes in $\mathbb{R}^n$
Weerapat Pittayakanchit	Andrew J. Bernoff	Chad M. Topaz (Macalester College)	The Global Stability of the Solution to the Morse Potential in a Catastrophic Regime
Victor Shang	Theresa W. Lynn (Physics)	Andrew J. Bernoff	Computational Progress towards Maximum Distinguishability of Bell States by Linear Evolution and Local Measurement
Patrick Tierney	Satyan L. Devadoss (Williams College)	Dagan Karp	Realizing the 2-Associahedron
Madeleine Weinstein	Dagan Karp	Charles Doran (University of Alberta)	Adinkras and Arithmetical Graphs
Matthew Wilber	Eliot C. Bush (Biology)	Darryl H. Yong	Building a History of Horizontal Gene Transfer in E. Coli
Joyce Yang	Nicholas J. Pippenger	Arthur T. Benjamin	Interval Graphs

2014–2015

Student	Advisor	Second Reader	Thesis
Andrew Brockmann	Talithia Williams	Arthur T. Benjamin	A Plausibly Deniable Encryption Scheme for Personal Data Storage
Elizabeth Kelley	Su	TBA	(not available)
Matthew Lam	Nicholas J. Pippenger	Michael Orrison	A Combinatorial Exploration of Elliptic Curves
Jazmin Ortiz	Mohamed Omar	Michael Orrison	Chromatic Polynomials, Orbital Chromatic Polynomials, and Their Roots
Eric Stucky	Arthur T. Benjamin	Maria Klawe	An Exposition of Kastalyan's Solution of the Dimer Model
Ksenia V Zakirova	Andrew J. Bernoff	Robert Thompson	Perturbation Dynamics on Moving Chains

2013–2014

Student	Advisor	Second Reader	Thesis
Allison F. Arnold-Roksandich	Christopher Towse	Michael E. Orrison	There and Back Again: Elliptic Curves, Modular Forms, and L-Functions
Sorathan Chaturapruek	Weiqing Gu	Zachary Dodds	A Mathematical Framework for Unmanned Aerial Vehicle Obstacle Avoidance
Emily M. Fischer	Alfonso Castro	Weiqing Gu	Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear Laplace-Beltrami Equations on the Unit Sphere
Samuel C. Gutekunst	Susan E. Martonosi	Mohamed Omar	Characterizing Forced Communication in Networks
Shreyas Kumar	Rachel Levy	Darryl Yong	Simulations of Surfactant Driven Thin Film Flow
David Alan Lingenbrink, Jr.	Michael E. Orrison	Mohamed Omar	A New Subgroup Chain for the Finite Affine Group
Matthew McDermott	Michael E. Orrison	Mohamed Omar	Fast Algorithms for Analyzing Partially Ranked Data
Peter Megson	Rachel Levy	Jon Jacobsen	Experiments on Surfactants and Thin Fluid Films
Alexa Serrato	Nicholas J. Pippenger	Mohamed Omar	Reed's Conjecture and Cycle-Power Graphs
Tongjia Shi	Nicholas Pippenger	Michael E. Orrison	Cycle Lengths of $\theta$-Biased Random Permutations
Carling Sugarman	Jon Jacobsen	Michael E. Orrison	Using Topology to Explore Mathematics Education Reform
Jeremy Usatine	Dagan Karp	Melody Chan	Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem

2012–2013

Student	Advisor	Second Reader	Thesis
Connor Ahlbach	Francis Edward Su	Michael E. Orrison	A Discrete Approach to the Poincar�-Miranda Theorem
Olivia Beckwith	Dagan Karp	Dusty Ross	On Toric Symmetry of $\mathbb{P}^1 \times \mathbb{P}^2$
Rosalie J. Carlson	Francis Edward Su	Michael E. Orrison	Voter Compatibility In Interval Societies
Michael Ernest	Nicholas Pippenger	Francis Edward Su	Extortion and Evolution in the Iterated Prisoner's Dilemma
Peter Fedak	Weiqing Gu	TBA
J. Zachary Gaslowitz	Dagan Karp	Dustin Cartwright	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
Taylor McAdam	Jon Jacobsen	Alfonso Castro	Analysis of Time-Dependent Integrodifference Population Models
Kevin O'Neill	Dagan Karp	Angelica Cueto	Lines in Tropical Quadrics
John Peebles	Nicholas Pippenger	Michael E. Orrison	Hypergraph Capacity with Applications to Matrix Multiplication
Nathan Pinsky	Weiqing Gu	Darryl H. Yong	Mathematical Knowledge for Teaching and Visualizing Differential Geometry
Elizabeth Sarapata	Lisette G. de Pillis	Ami Radunskaya	A Comparison and Catalog of Intrinsic Tumor Growth Models
Ryan Takahashi	Michael E. Orrison	Nicholas Pippenger	Structured Matrices and the Algebra of Displacement Operators

2011–2012

Student	Advisor	Second Reader	Thesis
Craig Burkhart	Francis Edward Su	Ann N. Trenk (Wellesley)	Approval Voting Theory with Multiple Levels of Approval
Trevor Caldwell	Alfonso Castro	Jon T. Jacobsen	Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics
John Choi	Nicholas Pippenger	Arthur T. Benjamin	Counting Vertices in Isohedral Tilings
Harris Enniss	Alfonso Castro	Jon T. Jacobsen	A Refined Saddle Point Theorem and Applications
Patrick Eschenfeldt	Francis Edward Su	Nicholas Pippenger	Approval Voting in Box Societies
August Guang	Francis Edward Su	Stephen E. Adolph	Switching Between Cooperation and Competition in Social Selection
Katie Hawley	Nicholas Pippenger	Arthur T. Benjamin	A Survey on Random Topological Surfaces (not available)
Curtis Heberle	Arthur T. Benjamin	Kimberly Kindred	A Combinatorial Approach to $r$-Fibonacci Numbers
Jennifer Iglesias	Ran Libeskind-Hadas (CS)	Nicholas Pippenger	Searching Stars for a Moving Hider
Kym Louie	Arthur T. Benjamin, Art Horowitz (Pomona)	Tom Leabhart (Pomona)	Flatterland: The Play
Palmer Mebane	Michael Orrison	Nicholas Pippenger	Uniquely Solvable Puzzles and Fast Matrix Multiplication
Jack Newhouse	Matthew Davis	Michael Orrison	Explorations of the Aldous Order on Representations of the Symmetric Group
Alice Paul	Susan E. Martonosi	Nicholas Pippenger	Detecting Covert Members of Terrorist Networks
Aaron Pribadi	Michael Orrison	Weiqing Gu	Algebraic Methods for Log-Linear Models
Dhruv Ranganathan	Dagan Karp	Davesh Maulik (MIT)	Gromov-Witten Theory of Blowups of Toric Threefolds
Louis Ryan	Andrew J. Bernoff	Chad M. Topaz	Analysis of Swarm Behavior in Two Dimensions
Maia Valcarce	Rachel Levy	Darryl Yong	Russian Mathematical Pedagogy in Reasoning Mind

2010–2011

Student	Advisor	Second Reader	Thesis
Kate M. Burgers	Jon Jacobsen	Rachel Levy	Finding the Beat in Music: Using Adaptive Oscillators
Georgi Dinolov	Rachel Levy	Dagan Karp	Swarm Control Through Symmetry and Distribution Characterization
Ann Johnston	Michael Orrison	Matt Davis	Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data
Max B. Kutler	Dagan Karp	Eric Katz (UT-Austin)	Group Actions and Divisors on Tropical Curves
Sarah Loeb	Kimberly Kindred	Susan Martonosi	Extending List Colorings of Planar Graphs
Kyle Luh	Nicholas Pippenger	Francis Su	Martingale Couplings and Bounds on Tails of Probability Distributions
Chandler May	Susan Martonosi	Kimberly Kindred	Verification of Solutions to the Sensor Location Problem
Allison M. Park	Darryl Yong	Stacy Brown (Pitzer)	Comparing the Cognitive Demand of Traditional and Reform Algebra 1 Textbooks
Austin Quan	John Milton (Scripps)	Darryl Yong	Noise, Delays, and Resonance in a Neural Network
Elizabeth (Lizard) Reiland	Arthur Benjamin	Kimberly Kindred	Combinatorial Interpretations of Fibonomial Identities
Andrew S. Ronan	Andrew Bernoff	Chad M. Topaz (Macalester College)	Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms
Jacob N. Scott	Francis Su	Nicholas Pippenger	Approval Ratios of Two-Intersecting Double-Interval Societies (held until 2012)
Dmitri Skjorshammer	Ursula Whitcher	Dagan Karp	Tops in Higher Dimensions (held until 2012)
Donald Lee Wiyninger III	Nicholas Pippenger	Michael Orrison	Continued Fractions: A New Form
Jeffrey Wong	Rachel Levy	Andrew Bernoff	Simulations of Surfactant Spreading

2009–2010

Student	Advisor	Second Reader	Thesis
Richard Strong Bowen	Nicholas Pippenger	Ran Liebeskind-Hadas (CS)	Minimal Circuits for Very Incompletely Specified Boolean Functions
Bo Chen	Arthur Benjamin	Kimberly Tucker	Combinatorial Proofs Using Complex Weights
Rachel Cranfill (Fall, 2009)	Michael Orrison	Keri Kornelson (U. Oklahoma)	Group Frames and Rank Data
Alyssa W. Dray	Talithia Williams	Johanna Hardin (Pomona), Susan Lewallen (Kilimanjaro Centre for Community Ophthalmology)	A Multistage Incidence Estimation Model for Diseases with Differential Mortality
Jacob Feldman	Susan Martonosi	John M. Bossert	Optimizing Restaurant Reservation Scheduling
Ivan Hernandez	Rachel Levy	Stacy Brown (Pitzer)	Algebraic Reasoning in Elementary School Students
Kwang B. Ketcham	Dagan Karp	Michael Orrison	Group Frames and Partially Ranked Data
Stephen C. Lee	Michael Orrison	Anna Bargagliotti (U. Memphis)	Understanding Voting for Committees Using Wreath Products
Ross C. Merriam	Nicholas Pippenger	Christopher Towse (Scripps)	Arithmetic on Specializable Continued Fractions
Yaniv J. Ovadia	Susan Martonosi	Nicholas Pippenger	Computational Feasibility of Increasing the Visibility of Vertices in Covert Networks
Hannah P. Savage	Lisette de Pillis	Ami Radunskaya (Pomona)	A Nonlinear ODE Model of Tumor Growth and Effect of Immunotherapy and Chemotherapy Treatment in Colorectal Cancer

2008–2009

Student	Advisor	Second Reader	Thesis
Nadia Abuelezam	Lisette de Pillis	Karl Haushalter	Mathematical AIDS Epidemic Model: Preferential Anti-Retroviral Therapy Distribution in Resource Constrained Countries
Natalie Durgin	Francis Su	David Perkinson (Reed College)	Abelian Sandpile Model on Symmetric Graphs
Sarah Fletcher	Francis Su	Kimberly Tucker	Exploring Agreeability in Tree Societies
Ben Fogelson	Lisette de Pillis	Rachel Levy	Mathematical Model of the Chronic Lymphocytic Leukemia Microenvironment
Andrew Hunter	Nicholas Pippenger	Ran Liebeskind-Hadas	Locality and Complexity in Path Search
Hendrik Orem	Michael Orrison	Nicholas Pippenger	Fast Matrix Multiplication via Group Actions
Ben Preskill	Alfonso Castro	Adolfo Rumbos (Pomona College)	Existence of Continuous Solutions to a Semilinear Wave Equation
Ted Spaide	Michael Orrison	Nicholas Pippenger	Branching Diagrams for Group Inclusions Induced by Field Inclusions

2007–2008

Student	Advisor	Second Reader	Thesis
Kevin Fleming	Nicholas Pippenger	Francis Edward Su	Boundary Cycles in Random Triangulated Surfaces
Sara Gussin	Jon T. Jacobsen	Darryl Yong	Wavelets and Wavelet Sets
Kenji Kozai	David Bachman	Francis Edward Su	Intrinsic Linking and Knotting of Graphs
Andrew Leverentz	Andrew J. Bernoff	Chad M. Topaz	An Integrodifferential Equation Modeling 1-D Swarming Behavior
Greg Minton	Kimberly Tucker	Michael Orrison	Dot Product Representations of Graphs
David R. Morrison	Susan E. Martonosi	Kimberly Tucker	Characteristics of Optimal Solutions to the Sensor Location Problem
Sean Plott	Arthur T. Benjamin	Kimberly Tucker	Functions of the Binomial Coefficient
Brian Rice	Nicholas Pippenger	Christopher Towse	Rigid Divisibility Sequences Generated by Polynomial Iteration
Douglas Rizzolo	Jon T. Jacobsen	Francis Edward Su	Approximating Solutions to Differential Equations via Fixed Point Theory
Parousia Rockstroh	Francis Edward Su	Sanjai Gupta	Properties of the Golomb Topology and Fibonacci Cycles under Integer Moduli
Mutiara Sondjaja	Francis Edward Su	Jon T. Jacobsen	Sperner's Lemma Implies Kakutani's Fixed Point Theorem
George Tucker	Andrew J. Bernoff	Elizabeth Mann	Formation of Labyrinth Patterns in Langmuir Films
Jason Winerip	Nicholas Pippenger	Michael Orrison	Graph Linear Complexity

2006–2007

Student	Advisor	Second Reader	Thesis
Jonathan Azose	Arthur T. Benjamin	Kristina Garrett (St. Olaf)	Applications of the q-Binomial Coefficients to Counting Problems
Kazh D. Brito	Andrew J. Bernoff	Shenda Baker	Hole Closure in Langmuir Fluid Monolayers
Victor H. Camacho	Darryl Yong	Jon T. Jacobsen	Analyzing Traveling Waves in a Viscoelastic Generalization of Burgers' Equation
Michael W. Hansen	Francis Edward Su	Michael Orrison	Algebra and Phylogenetic Trees
Andrea Heald	Ghassan Sarkis (Pomona)	Michael Orrison	Understanding Counterexamples to Lubin's Conjecture
Nicholas Herman (Fall, 2006)	Darryl Yong	Maria Klawe	Investigating the Use of Brainfingers in Children with Cerebral Palsy for Spatial-Motor Education
Alexander Izsak	Nicholas Pippenger	Ran Libeskind-Hadas (CS)	Special Cases of Carry Propagation
Marie Jameson	Michael Orrison	Nathan Ryan (UCLA)	Voting Paradoxes Caused by Dropping Candidates in an Election
Masanori Koyama	Michael Orrison	Nathan Ryan (UCLA)	A Decimation-in-Frequency Fast-Fourier Transform for the Symmetric Group
James R. Moore	Jon T. Jacobsen	Lisette de Pillis	An ODE Model of Biochemotherapy Treatment for Cancer
Eugene Lee Quan	Susan E. Martonosi	Francis Edward Su	Effective Cost Allocation for Deterrence of Terrorists
Chee Meng Tan	Alfonso Castro	Jon T. Jacobsen	Infinitely Many Radial Solutions to a Superlinear Dirichlet Problem
Ivan Ventura	Alfonso Castro	Jon T. Jacobsen	Radial Solutions to an Elliptic Boundary Valued Problem
Daniel Walton	Arthur T. Benjamin	Sanjai Gupta	A Tiling Approach to Chebyshev Polynomials

2005–2006

Student	Advisor	Second Reader	Thesis
Robin Baur (Fall, 2005)	Andrew J. Bernoff	Jon T. Jacobsen	An Investigation of Rupture in Thin Fluid Films
Deborah Berg (Fall, 2005)	Francis Edward Su	Michael Orrison	Connections Between Voting Theory and Graph Theory
Tristan Brand	Michael Orrison	Ghassan Sarkis (Pomona)	A Fast Fourier Transform for the Symmetric Group
Alexander Eustis	Arthur T. Benjamin	Sanjai Gupta (Scripps)	The Negs and Regs of Continued Fractions
Julijana Gjorgjieva	Jon T. Jacobsen	Pablo Padilla (Universidad Nacional Autónoma de México)	Turing Pattern Dynamics for Spatiotemporal Models with Growth and Curvature
John Hearn	Ran Libeskind-Hadas	Michael Orrison	Kolmogorov Complexity of Graphs
Joesph Majkut	Andrew J. Bernoff	Chad M. Topaz (UCLA)	Foraging Fruit Flies: Lagrangian and Eulerian Descriptions of Insect Swarming
Kenneth Maples	Weiqing Gu	Anthony Bright (Eng.)	Optimal Control of a Building During an Earthquake
Jessica May	Jim Hoste	Francis Edward Su	Matrix Representation of Knot and Link Groups
Stephanie Moyerman (Math/Physics)	Jim Eckert (Physics)	Andrew J. Bernoff	Magnetoresistance and Neutron Scattering of Ultrathin Films
Tracy Powell	Lesley Ward	Estelle Basor (CalPoly-SLO)	The Singular Values of the Exponientiated Adjacency Matrixes of Broom-Tree Graphs
Nikolas Rauh	Francis Edward Su	Michael Orrison	An Exploration in Subtropical Algebra
Tyler Seacrest	Weiqing Gu	Darryl Yong	Mathematical Models of Image Processing
Elan Segarra	Michael Raugh	Darryl Yong	An Exploration of Riemann's Zeta Function and Its Application to the Theory of Prime Distribution
Simon Stump	Jon T. Jacobsen	Alfonso Castro	Succession, Invasion, & Coexistence: PDEs in Ecology

2004–2005

Student	Advisor	Second Reader	Thesis
Ruben Arenas	Weiqing Gu	Vatche Sahakian	Constructing a Matrix Representation of the Lie Group G2
Steven Avery (Math/Physics)	Vatche Sahakian (Physics)	Weiqing Gu	Noncommutative Geometry
Tim Carnes	Ran Libeskind-Hadas (CS)	Francis Edward Su	Permutation Routing in the Hypercube and Grid Topologies
Zajj Daugherty	Michael Orrison	J.Alongi (Pomona College)	An Algebraic Approach to Voting Theory
Jeff Jauregui	Weiqing Gu	Jon T. Jacobsen	Solving for Volume-Minimizing Cycles in G2-Manifolds
Akemi Kashiwada	Francis Edward Su	Steve Adolph	Constructing Phylogenetic Trees from Subsplits
Owen Lewis	Jon T. Jacobsen	Lesley Ward	Generalized Julia Sets: An Extension of Cayley's Problem
Eric Malm	Michael Orrison	Weiqing Gu	Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group
Jason Murcko	Henry Krieger	Lesley Ward	Cesaro Limits of Analytically Perturbed Stochastic Matrices
Gwen Spencer	Francis Edward Su	Alfonso Castro	Combinatorial Consequences of Relatives of the Lusternik-Schnirelmann-Borsuk Theorem
Kathe Todd-Brown (Fall, 2004)	Lisette de Pillis	Weiqing Gu	-
Carl Yerger	Francis Edward Su	Anant Godbole (Eastern Tennesee State University)	Extensions of Graph Pebbling

2003–2004

Student	Advisor	Second Reader	Title
Melissa Banister	Michael Orrison	Weiqing Gu	Separating Sets for Finite Groups
Ariel Barton (Fall 2003)	Lesley Ward	Henry Krieger	Convergence of Planar Domains and of Harmonic Measure Distribution Functions
William Chang	Michael Orrison	Weiqing Gu	Representation Theoretical Methods in Image Processing
Grant Clifford	Jon Jacobsen	Michael Orrison	Representation Theoretical Approach to n-Candidate Voting
Robert Gaebler	James Hoste (Pitzer)	Weiqing Gu	Alexander Polynomials of Tunnel Number One Knots
David Gaebler	Henry Krieger	Michael Raugh	Toeplitz Operators on Locally Compact Abelian Groups
Eric Harley	Lisette de Pillis	Jon Jacobsen	Modeling Cancer Cell Response to Immunotherapy
Matthew Holden (Pomona)	Weiqing Gu	Sandy Grabiner (Pomona)	Volume Minimizing Cycles in G2-manifolds
Jessica Nelson	Lisette de Pillis	Arthur Benjamin	Eigenvalue Etch-A-Sketch

2002–2003

Student	Advisor	Second Reader	Title
Dan Beutel	Andrew Bernoff	Thomas Donnelly (Physics)	Modelling Advection and Diffusion in Microchannels
Adam Bliss	Francis Su	Henry Krieger	Covering Numbers of the Cubes
Benjamin Bryant	Andrew Bernoff	Annette Hosoi	Modeling Moving Droplets: A Precursor Film Approach
Melissa Chase	Ran Libeskind-Hadas (CS)	Arthur Benjamin	Shortest Path Problems: Multiple Paths in a Stochastic Graph
David Clarke (Physics)	John Townsend (Physics)	Weiqing Gu	The Kapitza–Dirac Effect: An Approach from QED
John Cloutier	Francis Su	Lesley Ward	A Combinatorial Analog of the Poincaré–Birkhoff Fixed Point Theorem
Nate Eldredge	Michael Orrison	Shahriar Shahriari (Pomona)	An Eigenspace Approach to Isotropic Projections for Data on Binary Trees
Daniel Gianotti	Ali Nadim (CGU)	Andrew Bernoff	Fluid Drop Coalescence in a Hele-Shaw Cell
Stephen Haas	Lesley Ward	Henry Krieger	The Hausdorff Dimension of the Julia Set of Polynomials of the Form zd + c
Andrew Iannaccone	Byron Walden (Santa Clara)	Lesley Ward	The Conformal Center of a Triangle or Quadrilateral
Peter Lamb	Ali Nadim (CGU)	Andrew Bernoff	Ridge Coarsening in Evaporatively Driven Climbing Films
Matthew Macauley	Michael Orrison	James Hoste (Pitzer)	Braids and Juggling Patterns
Christopher Pries	Weiqing Gu	Jon Jacobsen	Searching for Supersymmetric Cycles: A Quest for Cayley Manifolds in the Calabi–Yau 4-Torus
Ross Richardson	Weiqing Gu	Zach Dodds	Designing Smooth Motions of Rigid Objects: Computing Curves in Lie Groups
Jeremy Rouse	Arthur Benjamin	Naiomi Cameron	Combinatorial Proofs of Congruences
Micah Smukler	Weiqing Gu	Francis Su	Geometry and Topology of the Minkowski Product
Kira Sushkoff	Weiqing Gu	Michael Orrison	Minkowski Actions of Quaternion Sets and their Applications
David Uminsky	Michael Orrison	Francis Su	Generalized Spectral Analysis for Large Sets of Approval Voting Data

2001–2002

Student	Advisor	Second Reader	Thesis
Daniel Boylan	Lesley Ward, Melissa O'Neill (CS)	Henry Krieger	Dyadic and Triadic Doubling Measures
Mark Dean	Francis Su	Arthur Benjamin	Randomizing the 15 Puzzle
Bradley Forrest (Math/Physics)	Andrew Bernoff	Thomas Donnelly (Physics)	Modeling Small Droplet Ejection from a Fluid Due to Capillary Waves
Michael Gratton	Andrew Bernoff	Anette Hosoi	Dispersion of a Passive Scalar in Helical Pipe Flow
Josh Greene	Arthur Benjamin	Gregory Levin	Various Results in Discrete Mathematics
Colin Little	Christopher Towse (Scripps)	Weiqing Gu	Complex Multiplication on Elliptic Curves
Cam McLeman	Christopher Towse (Scripps)	Michael Orrison	p-adic Dynamics and Formal Groups
Lara D. Mercurio	Weiqing Gu	Thomas Helliwell (Physics)	Quantum `Particles' In a Classically Defined Spacetime
Elizabeth Norton	Michael Orrison	Shahriar Shahriari (Pomona)	Representations and the Symmetric Group
Timothy Prescott	Francis Su	Gregory Levin	Tucker's Labeling in Branched Spheres and Connections to Topology
Michael P. Schubmehl	Thomas Donnelly (Physics)	Andrew Bernoff	Generation and Sizing of Sub-Micron Mists Math Thesis
Anne Short	Ghinta (Brown), Christopher Towse (Scripps)	Michael Orrison	Spectral Questions and Expander Graphs
Wesley Turner	Joshua Hodas (CS)	Weiqing Gu	A Logically Fully Abstract Concrete Interpretation of PCF+
Curtis Vinson	Thomas Helliwell (Physics)	Anette Hosoi	Quantum Particles and Singularities
Zach Walters	Thomas Helliwell (Physics)	Weiqing Gu	Quantum Singularities in Classical Spacetimes

2000–2001

Student	Advisor	Second Reader	Title
Kylie Bryant (Fall 2000)	Arthur Benjamin	Lisette de Pillis	Genetic Algorithms and the Travelling Salesman Problem
Christopher Hanusa (also French thesis)	Francis Su	Arthur Benjamin	Continued Fractions and their Interpretations
Teri Krebs (Math/Biology)	Michael Moody	James Groome (Biology)	Excitable Media
Angela Kurle (Math/Psychology)	Ronald Riggio (CMC Psychology)	Henry Krieger	Developing Scoring Methods for a Non-Additive Psychometric Measure of Social Skills/Interpersonal Competence
Marco Latini	Andrew Bernoff	Mario Martelli (CMC)	Mixing in Curved Pipes
Karl Mahlburg	Rhett Bull (Pomona)	Francis Su	Structure Attacks in Cryptographic Protocols
Ari Nieh	Gregory Levin	Arthur Benjamin	Fractional Analogues in Graph Theory
Anand Patil (Physics)	Andrew Bernoff	Thomas Donnelly (Physics)	Computational Simulation of Fluid Dynamics in Thin Films
Jane Pratt	Lisette de Pillis	Leaf Turner, Los Alamos National Labs	Turbulence, Magnetics, and Closure Equations
Greg Preston	Arthur Benjamin	Michael Raugh	Combinatorial Explanations of Known Harmonic Identities
Mike Rust (Math/Physics)	Ronald Cave (Chemistry)	Michael Moody	The Approximate Inclusion of Triple Excitations in EOM-type Quantum Chemical Methods
Paul SanGiorgio (Math/Physics)	Thomas Donnelly (Physics)	Lisette de Pillis	Measuring Electron Gas Relaxation in Gold through Second Harmonic Generation
Tracy van Cort (Math/Linguistics)	Elizabeth Sweedyk (Computer Science)	Karen Kossuth (Pomona Linguistics), Gregory Levin	Computational Evolutionary Linguistics
Ian Weiner	Weiqing Gu	Thomas Helliwell	Super-Symmetric Three-Cycles in String Theory

1999–2000

Student	Advisor	Second Reader	Title
Otto Cortez	Lesley Ward	Jorge Aarao (CMC)	Brownian Motion and Planar Regions: Constructing Boundaries from h-Functions
Ryan Haskett	Weiqing Gu	Thomas Helliwell (Physics)	Examples of Volume-Preserving Great Circle Flows of S3
Michael Lauzon	Francis Su	Lesley Ward	Reconstruction of Convex Bodies in the Plane from Three Non-Collinear Point Source Directed X-Rays
Philip Martin	Henry Krieger	Arthur Benjamin	Optimal Expected Values for Cribbage Hands
Joel Miller	Andrew Bernoff	Jorge Aarao (CMC)	Rates of Convergence to Self-Similar Solutions of Burgers' Equation
Helen Monroe (Fall, 1999)	Arthur Benjamin	Lesley Ward	N-Person Coalitional Games: The Power of More Than One
Elisha Peterson	Francis Su	Arthur Benjamin	Combinatorial Proofs of Generalizations of Sperner's Lemma
Yinan Song	Weiqing Gu	Adolfo Rumbos (Pomona)	Finite Invariance of Cayley Calibration Form

1997–1999

Prior to 2000, theses were not archived in a consistent way. Listed below are the titles of some of the older senior theses submitted by students, along with the graduate schools each student went on to attend.

Author	Year	Title	Graduate School
Matthew Fluet	1999	Searching for Optimal Strategies in Knock 'm Down	Cornell University
Dominic Mazzoni	1999	Three-Player Nim and More	Carnegie Mellon University
David Rudel	1999	Solving x2 + y2 = zk	Dartmouth University
Itai Seggev	1999	Quantum Singularity in Static Space-Times	University of Chicago
Marie Snipes	1999	Brownian Motion and the Shape of a Region's Boundary: Generating Step Functions from Circle Domains	United States Air Force
Aaron Archer	1998	On the Upper Chromatic Numbers of the Reals	Cornell University
Dylan Helliwell	1998	Quaternion Determinants	University of Washington
Brian Johnson	1998	Improving Algorithms for the Quillen–Suslin Theorem	University of Chicago
Solly Sieberts	1998	Accuracy of Approximate Confidence Bounds for Reliability of Series Systems	University of Washington
Michael Wood-Vasey	1998	Outflow Boundary Conditions for Numerical Simulations	UC Berkeley
Kan Yasuda	1998	The Square Sum Property of Magic Squares	University of Tokyo
Jeffrey Beck	1997	Internally Coated Cylindrical Wave Guides	Northwestern University
Jessica Sidman (Scripps)	1997	Splitting Numbers: Probabilistic Bounds and Computational Complexity	University of Michigan