undergraduate thesis in mathematics

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Mathematics Undergraduate Theses

Theses from 2019 2019.

The Name Tag Problem , Christian Carley

The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis? , Chloe Munroe

Theses from 2018 2018

A Convolutional Neural Network Model for Species Classification of Camera Trap Images , Annie Casey

Pythagorean Theorem Area Proofs , Rachel Morley

Euclidian Geometry: Proposed Lesson Plans to Teach Throughout a One Semester Course , Joseph Willert

Theses from 2017 2017

An Exploration of the Chromatic Polynomial , Amanda Aydelotte

Complementary Coffee Cups , Brandon Sams

Theses from 2016 2016

Nonlinear Integral Equations and Their Solutions , Caleb Richards

Principles and Analysis of Approximation Techniques , Evan Smith

Theses from 2014 2014

An Introductory Look at Deterministic Chaos , Kenneth Coiteux

A Brief Encounter with Linear Codes , Brent El-Bakri

Axioms of Set Theory and Equivalents of Axiom of Choice , Farighon Abdul Rahim

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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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Undergraduate Honors & Senior Thesis

Students excelling in their major coursework and interested in pure math should consider Departmental Honors. Departmental Honors means you will graduate “With Distinction” as opposed to College Honors which is “With Honors”.  The most important component of graduating with Departmental Honors is researching and writing a Senior Thesis.

Requirements for Departmental Honors:

• Must complete a B.S. Mathematics Degree.
• Must satisfactorily complete at least one three-quarter sequence 402-3-4, 424-5-6, or 441-2-3; or two two-quarter sequences from this list. Exceptions must be approved by the chair of the Departmental Honors Committee.
• Must earn a GPA of 3.5 or better in Math coursework completed at the UW.
• Must write a senior thesis (earn a numerical grade for MATH 496).
• Must have a 3.3 minimum cumulative GPA at UW.

Please note: If you are not interested in the College Honors or Departmental Honors in Mathematics, you may still write a Senior Thesis. The process is the same as above, but it does not need to be approved by the Honors Committee.

Research credit (Math 498) may be available with faculty permission.

Beginning of your final year at the UW : think about a thesis topic and seek out a faculty supervisor.  Read below for more details about selecting a topic.

First week of classes the quarter before you expect to graduate: submit a thesis proposal form to the Dept. Honors Committee.  The form is online here: Math Dept. Honors Thesis Proposal Form

Last day of your final quarter: Once your advisor approves the thesis, email it to [email protected] and cc your faculty advisor.  You may also wish to upload it to the University Libraries archive .

Nature of the thesis

The senior thesis shall be an expository account of a topic in pure or applied mathematics related to the student’s area of interest. (Original results or proofs are welcome but are definitely not expected.) The thesis must contain some nontrivial mathematical arguments. (E.g., a non-technical essay on “fractals in nature” would not be acceptable.) The thesis should normally be about 20 to 30 pages in length (double spaced, Times New Roman 12pt font, 1” margins). These figures are guidelines, not rigid requirements. The topic should be something that cannot simply be read out of a standard textbook. Writing the thesis should involve:

• obtaining material from the periodical literature, or
• consulting several books and synthesizing material from them, or
• reading an account of a topic in a book that is substantially more advanced than the student’s regular coursework, digesting it, and putting it into readable form.

Choosing a topic

Finding a topic is the students’ responsibility, although consultation with faculty members is encouraged. The topic must be approved by a faculty member of the Mathematics Department who will supervise the work (the “supervisor”) and by the chair of the Departmental Honors Committee. A Senior Thesis Topic Proposal form can be found at the link above, and should be filled out by the student with the supervisor's support (the Dept. will check in with your supervisor). The topic proposal must be submitted to the chair of the Departmental Honors Committee no later than the end of the first week of classes the quarter preceding the quarter in which the student expects to graduate. Exceptions to this deadline may be granted only by the chair of the Departmental Honors Committee. Students contemplating writing a thesis are strongly encouraged to start thinking about a topic in the autumn quarter of their senior year.

Writing the thesis

The student must register for Math 496 (Honors Senior Thesis) during the last quarter of thesis work. The student may receive three credit hours of W-course credit for writing the thesis. Normally, the students will register for a reading course (Math 498) with the supervisor during the preceding quarter (s). The student will receive three hours of credit for each of these courses, but in exceptional cases, with the approval of the supervisor, the number or credit hours may be increased. The supervisor may allow the student to replace Math 498 with a suitable topics course; however, it is still expected that the student will meet periodically with the supervisor.

There is no specific required thesis template for an undergraduate thesis.  Some students may choose to use a modified version of the graduate thesis templates, but this is not required.

Approval of thesis

The student shall submit a draft of the thesis to the supervisor for comments and criticisms, and then shall submit a final version with appropriate revisions. The supervisor shall read the thesis and certify its acceptability with respect to both content and exposition. In order to ensure sufficient time for these things, the student must submit the first draft no later than three weeks before the last day classes of the quarter in which the student expects to graduate, and the final draft no later than the last day of classes. Exceptions to these deadlines may be granted only by the chair of the Departmental Honors Committee.

Once the thesis has been approved by your faculty supervisor, you will need to email the document to [email protected] (required) as well as submit it to the ResearchWorks archive , part of the University Libraries (optional but strongly recommended).  Submission to the archive will allow your thesis to be included in the dissemination and preservation of scholarly work.  Your thesis will be made publicly available.

Interdisciplinary theses

Theses which are concerned with the application of some part of mathematics to some others field are acceptable, as long as they contain some substantial mathematics. In exceptional cases the student may wish to work most closely with a faculty member in another department in preparing the thesis. However, in such cases the thesis topic and the thesis itself must still be approved by a member of the Mathematics Department.

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2024 Senior Theses - Graduated with Distinction

Angikar ghosal.

Representation Theoretic Formulation of Quantum Error Correcting Codes Advisor: Robert Calderbank

Benjamin Goldstein

Soap-Film-Like Surfaces of Revolution Advisor: Demetre Kazaras

Noah Harris

Black Hole Thermodynamics, Large N Gauge Theories, and Deriving the AdS/CFT Correspondence Advisor: Paul Aspinwall

Long-Time Behavior of Some ODEs with Partial Damping Advisor: Kyle Liss

Aram Lindroth

Towards a Functional Equation for the $\mathbb{A}^1$-Logarithmic Zeta Function Advisor: Kirsten Wickelgren

Emmanuel Mokel

Monitoring Nonstationary Variance to Assess Convergence of Markov Chain Monte Carlo Advisor: Jonathan Mattingly

Nathan Nguyen

Towards Solving Variational Graphon Problem for Random Hypergraphs Advisor: Nicholas Cook

Nathanael Ong

On the Betti Numbers of Rank 2 Compact Locally Symmetric Spaces Advisor: Mark Stern

Jean-Luc Rabideau

Random Restrictions in the p-Biased Measure Advisor: Henry Pfister

Riki Shimizu

Unveil Sleep Spindles with Concentration of Frequency and Time (ConceFT) Advisor: Hau-Tieng Wu

December 2023

Quantum State Tomography via Tensor Ring Representation Advisor: Jianfeng Lu

Jesse Zhang

Answer Filtration with Filtration: Toward a Theory of Lifetime Filtration for Multiparameter Persistence Modules Advisor: Ezra Miller

Alex Burgin

The Schrodinger Maximal Function and Generalizations Advisor: Lillian Pierce

Nick Chakraborty

Improve Accuracy and Speed of Manifold Reconstruction and De-Noising from Scattered Data in R 2 Advisor: Hongkai Zhao

Jeffrey Cheng

Mixing in Measure Preserving Dynamical Systems Advisor: Tarek Elgindi

Carson Dudley

A Mathematical Model of a Peritoneal Staphylococcus Aureus infection Advisor: Anna Nelson

Riley Fisher

Pattern Formation in Evolving Domains Advisor: Tom Witelski

Multitaper Wave-Shape F-Test For Detecting Non-Sinusoidal Oscillations Advisor: Hau-Tieng Wu

Diffusing on multiple fibers Advisor: Ingrid Daubechies and Shira Faigenbaum

December 2022

Symmetric Formulas for Products of Permutations Advisor: Benjamin Rossman

A homotopic variant of policy gradients for the linear quadratic regulator problem Advisor: Andrea Agazzi

Nathan Geist

Homological algebra of modules over real polyhedral groups Advisor: Ezra Miller

Braden Hoagland

Percolation Processes on Dynamically Grown Graphs Advisor: Rick Durrett

Daniel Hwang

Analyzing the bistability of the minimally bistable ERK network using the discriminant locus Advisor: Maggie Regan

Wallace Peaslee

Dolbeault Cohomology of Non-Compact Metric Graphs Advisor: Joseph Rabinoff

Mathematical Modeling of TIE1 and Endothelial Metabolism Advisor: Michael Reed

December 2021

Some Mathematical Problems in Quantum Computing and Quantum Information Advisor: Robert Calderbank

Anuk Dayaprema

Solitons for the closed G2 Laplacian flow in the cohomogeneity-one setting Advisor: Mark Haskins

Ziyang Ding

At the Intersection of Deep Sequential and State-space Model Framework Advisor: Sayan Mukherjee

Lucas Fagan

Schur Polynomials and Crystal Graphs Advisor: Spencer Leslie

Resolving Simpson’s Paradox in NC Public School Grading System Advisor: Greg Herschlag

Phoebe Klett

Implementing non-canonical Sylvan Resolutions Advisor: Ezra Miller

Jianyou Wang

Deep Reinforcement Adaptive Computational Processor Advisor: Vahid Tarokh

Alex Damian

Theoretical Guarantees for Signal Recovery Advisor: Hau-tieng Wu

Blythe Davis

The Spherical Manifold Realization Problem Advisor: Faramarz Vafaee

Onkar Gujral

Khovanov Homology and Knot Concordance dvisor: Adam Levine

Xiayimei Han

Hodge Representations of Calabi-Yau 3 Folds Advisor:  Colleen Robles

Remy Kassem

Symmetry Detection of Unknown Volumes from Projected Variations Advisor: Xiuyuan Cheng

Joey Li

Algebraic Data Structures for Decomposing Multipersistence  Modules Advisor: Ezra Miller 

Evaluating Bayesian Convolutional Neural Networks in the Clinic Advisor: Paul Bendich

Jonathan Michala

Uniqueness of Ranked Pairs Advisor: Hubert Bray 

Benjamin Nativi

An Analogue of Gauss Composition for Binary Cubic Forms Advisor: Aaron Pollack

Computing Values of Symmetric Square L-Functions using Ichino's Pullback Formula Advisor: Aaron Pollack

Junmo Ryang

Embedding Lagrangian Surfaces Advisor: Robert Bryant

Irina Cristali

Poisson Percolation on the Square Lattice Advisors: Rick Durrett, Matthew Junge

Creating Musical Rubato Using Deep Learning Advisor: Ezra Miller

Zhenhua Liu

Stationary One-Sided Area Minimizing Hypersurfaces with Isolated Singularities Advisors: William Allard, Hubert Bray, Robert Bryant

Xueying Wang

Unfolding High-Dimensional Convex Polyhedra Advisor: Ezra Miller

Claire Wiebe

Analyzing the Effects of Partisan Correlation on Election Outcomes using Order Statistics Advisor: Jonathan Mattingly

Gaitling Zhou

Elliptic Curves over Dedekind Domains Advisor: William Pardon

(you can search for archived versions of these theses here )

• Surabhi Beriwal  Statistical analysis of fruit fly wing vein topology  (2018) [with E. Miller]
• Trung Can  The Heisenberg-Weyl Group, Finite Symplectic Geometry, and their applications   (2018) [with R. Calderbank]
• Feng Gui  On Calibrations for Area Minimizing Cones  (2018) with [H. Bray]
• Neel Kurupassery   Cryptographic Primitives in Artin Groups of Type I k (m)    (2018)  [with M. Abel]
• Eric Peshkin  T he quantification of markers of economic development from time-series satellite imagery using deep learning   (2018) with [with P. Bendich and D. Thomas]
• Weiyao Wang   Understanding Operator Reed-Muller Codes Through the Weyl Transform   (2018) [with R. Calderbank]
• Alexander Pieloch  The Topology of Moduli Spaces of Real Algebraic Curves  (2017) [with R. Hain]
• Samadwara Reddy  The Vietoris–Rips Complexes of Finite Subsets of an Ellipse of Small Eccentricity  (2017) [with H. Adams]
• Lindsey Brown  An Application of Abstract Algebra to the Neural Code for Sound Localization in Barn Owls  (2016) [with M. Reed]
• David Builes  The Large Cardinal Hierarchy  (2016) [with R. Hodel]
• Kyle Casey  Siegel Modular Forms  (2016) [with L. Saper]
• Bryan Runjing Liu  Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control  (2016) [with A. Layton]
• Francois Thelot A Maximum Entropy Based Approach for the Description of the Conformational Ensemble of Calmodulin from Paramagnetic NMR (2016) [with M. Maggioni and B. Donald]
• Will Victor  Efficient algorithms for Traffic Data Analysis  (2016)[computer science with P. Agarwal]
• Paul Ziquan Yang  Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields  (2016) [with C. Schoen]
• Rex Zhitao Ying  Approximation Algorithms of Dynamic Time Warping and Edit Distance  (2016) [computer science with P. Agarwal]
• Roger Zou  Deformable Graph Model for Trackng Epithelial Cell Sheets in Florescence Microscopy  (2016)[computer science with C. Tomasi]
• Anne Talkington  Modeling the Dynamics of Cancerous Cells in vivo  (2015) [with R. Durrett]
• Rowena Gan  Geometry of Impressionist Music  (2015) [with E. Miller]
• David Hemminger  Augmentation Rank of Satellites with Braid Pattern  (2015) [with L. Ng and C. Cornwell]
• Mandy Jiang  Dynamic random network model for human papilloma virus transmission  (2015) [with M. Ryser]
• Hunter Nisonoff  Efficient Partition Function Estimatation in Computational Protein Design  (2015) [with M. Maggioni]
• Eugene Rabinovich  The Conformal Manifold in N=(2,2) SCFTs    (2015)  [physics  with R. Plesser]
• Marshall Ratliff  Introducing the Cover tree to Music Information Retrieval  (2015) [with P. Bendich]
• Brett Schnobrich  Heisenberg-Weyl Group, Subspace Packings, and Image Processing  (2015) [with R. Calderbank]
• Christy Vaughn  Stochastic Study of Gerrymandering  (2015) [with J. Mattingly]
• Aashiq Dheeraj  A Stochastic Spatial Model for Tumor Growth  (2014) [with R. Durrett]
• Joshua Izzard  Rank p 2  Representations of Semisimple Lie Algebras  (2014) [with J. Getz]
• Kathleen Lan  Coalescing random walks on n-block Markov chains  (2014) [with K. McGoff]
• Leslie Lei Lei  Infinite Swapping Simulated Tempering  (2014) [with J. Lu]
• Julia Ni  A convex approach to tree-based wavelet compression  (2014) [with A. Thompson]
• Jiarou Ivy Shen  Merge times and hitting times of time-inhomogeneous Markov chains  (2014) [with D. Sivakoff]
• Daniel Stern  Low-Order Lagrangians Depending on a Metric and a Matter Field of Arbitrary Rank  (2014) [with H. Bray]
• Daniel Vitek  Knot Contact Homology and the Augmentation Polynomial  (2014) [with C. Cornwell]
• Alexander Wertheim  Complex Multiplication on Elliptic Curves  (2014) [with L. Saper]
• Luxi Wei  Modeling Credit Risk using Rating and Environmental Factors  (2014) [with R. Durrett]
• Timothy Chang  On the existence of a simple winning strategy in the T(4.3) knot game  (2013) [with D. Herzog]
• Conrad de Peuter  Modeling basketball games as alternating renewal-reward processes and predicting match outcomes  (2013) [with R. Durrett]
• Bryan Jacobson  A practical approximation of persistent local homology  (2013) [with P. Bendich]
• Kara Karpman  Simulating mucociliary transport using the method of regularized Stokelets  (2013) [with A. Layton]
• Carmen Lopez  Modeling the folate pathway in Escherichia coli  (2013) [with A. Layton]
• James Mallernee  Strategy and honesty based comparison of preferential ballot voting methods  (2013) [with H. Bray]
• William Zhang  Evolutionary dynamics in host pathogen model  (2013) [with R. Durrett]
• Ben Bellis  Investigation of a Local Computation of the Signature from the Triangulation of a Manifold  (2012) [with M. Stern]
• Adrian Chan  Pricing financial derivatives with multi-task machine learning and mixed effects method  (2012) [with J. Bouvrie]
• Kyu Won Choi  Relative contributions of common jumps in realized correlations  (2012) [with A. Petters]
• Veronica Ciocanel  Analysis of the nonlinear dynamics of the forced planar string pendulum  (2012) [with T. Witelski]
• Kaveh Danesh  A branching process model of ovarian cancer  (2012) [with R. Durrett]
• Theo Frehlinghuysen  Carbon sequestration via forest management techniques  (2012) [with D. Kraines]
• Yingyi Shen  A study of edge toric ideals using associated graphs  (2012) [with S. Mapes]
• Daniel Thielman  Complex-balanced steady state of chemical reaction networks that contain an Eulerian cycle  (2012) [with C. Berkesch]
• Kaitlin Daniels  Noise driven Transitions between stable equilibria in stochastic dynamical systems  (2011) [with A. Athreya]
• Alan Guo  Lattice point methods for combinatorial games  (2011) [with E. Miller]
• Nils Hultgren  Centrality and network analysis: A perturbative approach to dynamical importance  (2011) [with I. Matic]
• Hans Kist  Estimating carbon sequestration potential in the boreal forests  (2011) [with D. Kraines]
• Misha Lavrov  Invariants in Legendrian links in the solid torus  (2011) [with D. Rutherford]
• Philip Pham  Tubuloglomerular feedback signal transduction in the loops of Henle  (2011) [with A. Layton]
• Thames Sae Sue  A simple cardiac model exhibiting stationary discordant alternans  (2011) [with D. Schaeffer]
• Max Tabachnik  An analysis of preferential ballot voting methods  (2011) [with H. Bray]
• Bo Waggoner  A model of the foot and ankle in running  (2011) [with E. Bouzarth]
• Wutichai Chongchitmate  Classification of Legendrian knots and links  (2010) [with L. Ng]
• Jason D. Lee  Multiscale analysis of dynamic graphs  (2010) [with M. Maggioni]
• Jeremy Semko  Statistical analysis simulations of coarsening droplets coating a hydrophobic surface  (2010) [with T. Witelski]
• Amy Wen  Model of feedback-mediated dynamics of coupled nephrons with compliant thick ascending limbs  (2010) [with A. Layton]
• Jason Ferguson  Factorization of Primes in Biquadratic Extensions of Q  (2009) [with C. Schoen]
• Jared Haftel  A Closer Look at ADC multivariate GARCH  (2009) [with M. Huber]
• Mark Hallen  Improving accuracy and scope of quantitative FRAP analysis  (2009) [with A. Layton]
• Andy Ng  Retinoid Transport in the Vision cycle  (2009) [with J. Mercer]
• Aaron Pollack  Relations between special derivations arising from modular forms  (2009) [with R. Hain]
• Jesse Thorner  Simplicial homology and DeRham’s theorem  (2009) [with W. Allard]
• Barry Wright III  Objective measures of preferential ballot voting systems  (2009) [with H. Bray]
• Michael Bauer  Existence and stability of patterns arising from square wave forcing of the damped Mathieu equation  (2008) [with A. Catlla]
• Tirasan Khandhawit  On Legandrean and transverse knots  (2008) [with L. Ng]
• Aalok Shah  An overview of fast marching and optimal control methods for trajectory optimization  (2008) [with W. Allard]
• Charles Staats III  Application of discrete geometry to the construction of Laurent-rational zeros  (2008) [with S. Sharif]
• Elliott Wolf  Computational pathways to Godel’s first incompletness theorem  (2008) [with R. Hodel]
• Lingen Zhang  The motion of sets of vortices  (2008) [with T. Witelski]
• Morgan Brown  An algorithm for tracking persistence pairing of a discrete homotopy of Morse functions on S 2   (2007) [with J.Harer]
• Brandon Levin  Class field theory and the problem of representing primes by binary quadratic forms  (2007) [with L. Saper]
• Stepan Paul  Lines and conics relative to degenerating divisors in CP 2   (2007) [with J. Davis]
• James Zou  3-D reconstruction and topological analysis of root architecture  (2007) [with J. Harer]
• Pradeep Baliga  Dynamic cellular automata model of toll plaza traffic flows  (2006) [with W. G. Mitchener]
• Adam Chandler  Dynamic cellular automata model of toll plaza traffic flows  (2006) [with W. G. Mitchener]
• Matthew Fischer  Mapping model of cardiac-membrane dynamics  (2006) [with D. Schaeffer]
• Qinzheng Tian  Simulation of Newtonian fluid flow between rotating cylinders  (2006) [with T. Witelski]
• Yee Lok Wong  Models of instant runoff voting  (2006) [with J. Mattingly]
• Oaz Nir  Mechanical arms and algebraic topology  (2005) [with J.Harer]
• Mayank Varia  Explicit calculation of the L invariant for Kummer surfaces  (2005) [with J. Hanke]
• David Arthur  On the higher Hasse-Witt matrices and related in variants  (2004) [with W. Pardon]
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• Senior Thesis

A thesis is a more ambitious undertaking than a project. Most thesis writers within Applied Mathematics spend two semesters on their thesis work, beginning in the fall of senior year.  Students typically enroll in Applied Mathematics 91r or 99r (or Economics 985, if appropriate) during each semester of their senior year.  AM 99r is graded on a satisfactory/unsatisfactory basis.  Some concentrators will have completed their programs of study before beginning a thesis; in situations where this is necessary, students may take AM 91r for letter-graded credit, for inclusion in Breadth section (v) of the plan of study.  In the spring semester, the thesis itself may serve as the substantial paper on which the letter grade is based.  Econ 985 is also letter-graded, and may be included in the Breadth section of the plan of study in place of AM 91r.

Another, somewhat uncommon option, is that a project that meets the honors modeling requirement (either through Applied Mathematics 115 or 91r) can be extended to a thesis with about one semester of work.  Obviously the more time that is spent on the thesis, the more substantial the outcome, but students are encouraged to write a thesis in whatever time they have. It is an invaluable academic experience.

The thesis should make substantive use of mathematical, statistical or computational modeling,  though the level of sophistication will vary as appropriate to the particular problem context.  It is expected that conscientious attention will be paid to the explanatory power of mathematical modeling of the phenomena under study, going beyond data analysis to work to elucidate questions of mechanism and causation rather than mere correlation. Models should be designed to yield both understanding and testable predictions. A thesis with a suitable modeling component will automatically satisfy the English honors modeling requirement; however a thesis won't satisfy modeling Breadth section (v) unless the student also takes AM 91r or Econ 985.

Economics 985 thesis seminars are reserved for students who are writing on an economics topic. These seminars are full courses for letter-graded credit which involve additional activities beyond preparation of a thesis. They are open to Applied Mathematics concentrators with suitable background and interests.

Students wishing to enroll in AM 99r or 91r should follow the application instructions on my.harvard.

Thesis Timeline

The timeline below is for students graduating in May. The thesis deadline for May 2024 graduates is Monday, April 1 at 2:00PM. For off-cycle students, a similar timeline applies, offset by one semester. The thesis due date for March 2025 graduates is Friday, November 22, 2024. Late theses are not accepted.

Mid to late August:

Students often find a thesis supervisor by this time, and work with their supervisor to identify a thesis problem. Students may enroll in Econ 985 (strongly recommended when relevant), AM 91r, or AM 99r to block out space in their schedule for the thesis.

Early December:

All fourth year concentrators are contacted by the Office of Academic Programs. Those planning to submit a senior thesis are requested to supply certain information. This is the first formal interaction with the concentration about the thesis.

Mid-January:

A tentative thesis title approved by the thesis supervisor is required by the concentration.

Early February:

The student should provide the name and contact information for a recommended second reader, together with assurance that this individual has agreed to serve. Thesis readers are expected to be teaching faculty members of the Faculty of Arts and Sciences or SEAS. Exceptions to this requirement must be first approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies. For AM/Economics students writing a thesis on a mathematical economics topic for the March thesis deadline, the second reader will be chosen by the Economics Department. For AM/Economics students writing for the November deadline, the student should recommend the second reader.

On the thesis due date:

Thesis due at 2pm. Late theses are not accepted. Electronic copies in PDF format should be delivered by the student to the two readers and to [email protected] (which will forward to the Directors of Undergraduate Studies, Associate and Assistant Director of Undergraduate Studies) on or before that date and time. An electronic copy should also be submitted via the SEAS  online submission tool  on or before that date. SEAS will keep this electronic copy as a non-circulating backup and will use it to print a physical copy of the thesis to be deposited in the Harvard University Archives. During this online submission process, the student will also have the option to make the electronic copy publicly available via DASH, Harvard’s open-access repository for scholarly work.

Contemporaneously, the two readers will receive a rating sheet to be returned to the Office of Academic Programs before the beginning of the Reading Period, together with their copy of the thesis and any remarks to be transmitted to the student.

The Office of Academic Programs will send readers' comments to the student in late May, after the degree meeting to decide honors recommendations.

Thesis Readers

The thesis is evaluated by two readers, whose roles are further delineated below.  The first reader is the thesis adviser.  The second and reader is recommended by the student and adviser, who should secure the agreement of the individual concerned to serve in this capacity.  The reader must be approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies.  The second reader is normally are teaching members of the Faculty of Arts and Sciences, but other faculty members or comparable professionals will usually be approved, after being apprised of the responsibilities they are assuming.   For theses in mathematical economics, the choice of the second reader is made in cooperation with the Economics department.  The student and thesis adviser will be notified of the designated second reader by mid-March.

The roles of the thesis adviser and of the outside reader are somewhat different.  Ideally, the adviser is a collaborator and the outside reader is an informed critics.  It is customary for the adviser's report to comment not only on the document itself but also on the background and context of the entire effort, elucidating the overall accomplishments of the student.  The supervisor may choose to comment on a draft of the thesis before the final document is submitted, time permitting.  The outside reader is being asked to evaluate the thesis actually produced, as a prospective scientific contribution — both as to content and presentation.  The reader may choose to discuss their evaluation with the student, after the fact, should that prove to be mutually convenient.

The thesis should contain an informative abstract separate from the body of the thesis.  At the degree meeting, the Committee on Undergraduate Studies in Applied Mathematics will review the thesis, the reports from the two readers and the student’s academic record. The readers (and student) are told to assume that the Committee consists of technical professionals who are not necessarily conversant with the subject matter of the thesis so their reports should reflect this audience.

The length of the thesis should be as long as it needs to be to make the arguments made, but no longer!

Thesis Examples

The most recent thesis examples across all of SEAS can be found on the Harvard DASH (Digital Access to Scholarship at Harvard) repository . Search the FAS Theses and Dissertations collection for "applied mathematics" to find dozens of examples.

Note: Additional samples of old theses can be found in McKay Library. Theses awarded Hoopes' Prizes can be found in Lamont Library.

Recent thesis titles

Theses submitted in 2021, theses submitted in 2020, theses submitted in 2019, theses submitted in 2018 , senior thesis submission information for a.b. programs.

Senior A.B. theses are submitted to SEAS and made accessible via the Harvard University Archives and optionally via  DASH  (Digital Access to Scholarship at Harvard), Harvard's open-access repository for scholarly work.

In addition to submitting to the department and thesis advisors & readers, each SEAS senior thesis writer will use an online submission system to submit an electronic copy of their senior thesis to SEAS; this electronic copy will be kept at SEAS as a non-circulating backup. Please note that the thesis won't be published until close to or after the degree date. During this submission process, the student will also have the option to make the electronic copy publicly available via DASH.  Basic document information (e.g., author name, thesis title, degree date, abstract) will also be collected via the submission system; this document information will be available in  HOLLIS , the Harvard Library catalog, and DASH (though the thesis itself will be available in DASH only if the student opts to allow this). Students can also make code or data for senior thesis work available. They can do this by posting the data to the Harvard  Dataverse  or including the code as a supplementary file in the DASH repository when submitting their thesis in the SEAS online submission system.

Whether or not a student opts to make the thesis available through DASH, SEAS will provide an electronic record copy of the thesis to the Harvard University Archives. The Archives may make this record copy of the thesis accessible to researchers in the Archives reading room via a secure workstation or by providing a paper copy for use only in the reading room.  Per University policy , for a period of five years after the acceptance of a thesis, the Archives will require an author’s written permission before permitting researchers to create or request a copy of any thesis in whole or in part. Students who wish to place additional restrictions on the record copy in the Archives must contact the Archives  directly, independent of the online submission system. 

Students interested in commercializing ideas in their theses may wish to consult Dr. Fawwaz Habbal , Senior Lecturer on Applied Physics, about patent protection. See Harvard's policy for information about ownership of software written as part of academic work.

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Guidelines for Senior Theses in the Mathematics Department

A senior thesis can form a valuable part of a student's experience in the Mathematics Major . It is intended to allow students to cover significant areas of mathematics not covered in course work, or not covered there in sufficient depth. The work should be independent and creative. It can involve the solution of a serious mathematics problem, or it can be an expository work, or variants of these. Both the process of doing independent research and mathematics exposition, as well as the finished written product and optional oral presentation, can have a lasting positive impact on a student's educational and professional future.

Recent Senior Theses

Supervision

Supervision by a qualified member of the field of mathematics at Cornell is the normal requirement for a senior thesis. Other arrangements are possible, however, provided they are made with the assistance of the student's major advisor, and with the approval of the Mathematics Major Committee .

Finding a supervisor/Encouraging students. It should be emphasized that both the writing and the supervising of a senior thesis are optional activities, both for students and faculty. Students interested in doing this will need to find a suitable supervisor — perhaps with the aid of their major advisor or another faculty member whom they know. Advisors and other faculty who encounter students whom they think would benefit from this activity are invited to mention this option to them and assist them in finding a supervisor.

Standard venues for senior theses. One obvious way in which a senior thesis can be produced is through an independent research course (MATH 4900); another way is through an REU experience, either at Cornell or elsewhere. (If the REU work was accomplished or initiated elsewhere, a "local expert" will still be needed to supervise or "vouch for" the work as a senior thesis.) In yet a third way, a student may present a faculty member with a solution or partial solution to an interesting problem. In such cases, this could form the core of a senior thesis. Faculty are invited to encourage such work from their students.

Public Lecture

A public lecture in which the results of the senior thesis are presented is welcome but optional. This should be arranged by the thesis supervisor in conjunction with the undergraduate coordinator and adequately advertised. Department faculty and graduate students are encouraged to attend these presentations.

Submitting the Completed Thesis

The supervisor must approve the student's thesis. No later than April 15th, the student must submit a completed thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student has until April 30th to do so. By April 30th, the student must give the supervisor two paper copies and an electronic copy of the thesis in final form. The electronic copy will be posted on the department's web site. [Students who expect to graduate in January must submit a completed thesis by November 15th and the final form by November 30th.]

Form of the Thesis

Ideally, the final document should be TeXed or prepared in some equivalent technical document preparation system. The document must have large left margins (one and one-half inches or slightly larger). The title page should contain:

• The student's name and graduating class.
• The title of the senior thesis.
• The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)
• The date of completion of the thesis.

This information will be used to produce a standard frontispiece page, which will be added to the document in its library copies.

Merit of the Senior Thesis

Judgment as to the merit of a senior thesis will be based largely on the recommendation of the faculty member supervising the thesis. The Mathematics Major Committee will use this recommendation both in its determination of honors and in its decision on whether to place the thesis in our permanent library collection.

Honors Consideration

The senior thesis will automatically be considered by the Mathematics Major Committee as one of the ingredients for deciding on an honors designation for the student. Students may receive honors without a thesis and are not guaranteed honors with one. However, an excellent senior thesis combined with an otherwise excellent record can elevate the level of honors awarded.

Mathematics Library Collection of Senior Theses

Meritorious senior theses will be catalogued, bound, and stored in the Mathematics Library.

Home > Arts and Sciences > Mathematics > MATHEMATICSHONORS

Mathematics Undergraduate Honors Theses

Honors theses from 2024 2024.

Estimating the Payoffs of Variance Swaps using GARCH(1,1) and COGARCH(1,2) , Nicholas Zehnle

Improved Bounds for the Index Conjecture in Zero-Sum Theory , Andrew Pendleton

Honors Theses from 2023 2023

Automorphisms of a Generalized Quadrangle of Order 6 , Ryan Pesak

Demographic Noise and Fragmentation in Stochastic Extinction , Cameron Curtis

Design and Application of Surrogate Models for Hypersonic Inlet Physics , Owen Guch

Examining Factors Using Standard Subspaces and Antiunitary Representations , Paul Anderson

Merging Cross-Platform Gene Expression Data , Jiayi Xu

Minimal Network Structure for Turing Instability , Brendan Millis

Modeling the Effects of Seasonal Births and Predation on Disease Spread , Ally Introne

The Probability Distribution of the Kaplan-Meier Product-Limit Estimator and its Application to Bias and Interval Estimation , Yuxin Qin

Honors Theses from 2022 2022

Approximating Star-Discrepancy with a Genetic Algorithm , Isabel Agostino

Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics - , Sage Stanish

Enumerating Switching Isomorphism Classes of Signed Graphs , Nathaniel Healy

Investigating Text Mining Techniques Within the Context of Politicized Social Media Data , Grace Smith

Investigating the Effectiveness of GARCH(1,2) and COGARCH(1,2) Models in Estimating Volatility in the S&P500 Index , Ethan Hackett

Modeling and Analyses of Mechanisms Underlying Network Synaptic Dynamics in Two Neural Circuits , Linda Ma

Modern Theory of Copositive Matrices , Yuqiao Li

Period Doubling Cascades from Data , Alexander Berliner

Schur Class Power Series over the Quaternions , Rongbiao Wang

The Enumeration of Minimum Path Covers of Trees , Merielyn Sher

The Minimum Number of Multiplicity 1 Eigenvalues Among Real Symmetric Matrices Whose Graph is a Tree , Jacob Zimmerman

Voting Rules and Properties , Zhuorong Mao

Honors Theses from 2021 2021

A Survey of Methods to Determine Quantum Symmetry of Graphs , Samantha Phillips

Blockchain in Healthcare: a New Perspective from Social Media Data , Andrew Caietti

Determining Quantum Symmetry in Graphs Using Planar Algebras , Akshata Pisharody

Reality and Strong Reality in Finite Symplectic Groups , Spencer Schrandt

The Minimum Number of Multiplicity 1 Eigenvalues among Real Symmetric Matrices whose Graph is a Tree , Wenxuan Ding

Toward a Holographic Transform for the Quantum Clebsch-Gordan Formula , Ethan Shelburne

Using Machine Learning to Track the Location of the Shock Train in Hypersonic Engines , Alison Reynolds

Honors Theses from 2020 2020

A Mathematical Model for the Trend and Prediction of Movie Revenue , Yuxin Shang

Analysis of Modelling Deficiencies that Contributed to the High Unanticipated Loan Losses Incurred During the Housing Price Collapse of the Great Recession , Jennifer Shulman

Dynamics of Sensory Integration of Olfactory and Mechanical Stimuli Within the Response Patterns of Moth Antennal Lobe Neurons , Harrison Tuckman

Learning & Planning for Self-Driving Ride-Hailing Fleets , Jack Morris

Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost , Kaidi Wang

Nonnegative Matrix Factorization Problem , Junda An

RMSE-Minimizing Confidence Intervals for the Binomial Parameter , Kexin Feng

Stage-structured Blue Crab Population Model with Fishing, Predation and Cannibalism , Fangming Xu

Honors Theses from 2019 2019

A General Weil-Brezin Map and Some Applications , Benjamin Bechtold

Continuous Opinion Dynamics on an Adaptive Network , Xinyu Zhang

Disentanglement of Whisker Deflection Velocity and Direction , Srijan Bhasin

Eventually Positive Matrices and Tree Sign Patterns , Madellyne Waugh

Minimal Principal Series Representations of SL(3,R) , Jacopo Gliozzi

Partial Difference Sets in Nonabelian Groups and Strongly Regular Cayley Graphs , Gabrielle Tauscheck

Rankin-Cohen Brackets and Fusion Rules for Discrete Series Representations of SL(2,R) , Emilee Cardin

Spectrogram Analysis of Blood Pressure on Neonates with Hypoxic Ischemic Encephalopathy (HIE) , Tianrui Zhu

Totally Positive Completable Matrix Patterns and Expansion , David Allen

Honors Theses from 2018 2018

A Mathematical Study of Competition and Adoption of Two Consumer Products , Chengli Huang

A New Upper Bound for the Diameter of the Cayley Graph of a Symmetric Group , Hangwei Zhuang

Counting Real Conjugacy Classes in Some Finite Classical Groups , Elena Amparo

Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups , Yoongbok Lee

Modeling Social Interactions of Yeast Biofilms with a Stochastic Spatial Simulation , Aparajita Sur

Potential Stability of Matrix Sign Patterns , Christopher Hambric

Strongly Real Conjugacy Classes in Unitary Groups over Fields of Even Characteristic , Tanner N. Carawan

The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach , John Wilkes and Charles Royal Johnson

TP Matrices and TP Completability , Duo Wang

Ultra-High Dimensional Statistical Learning , Yanxin Xu

Honors Theses from 2017 2017

A Mathematical Model of Economic Growth of Two Geographical Regions , Xin Zou

Center Manifold Theory and Computation Using a Forward Backward Approach , Emily E. Schaal

Involutions and Total Orthogonality in Some Finite Classical Groups , Gregory K. Taylor

Saving Babies Using Big Data , Evan Dienstman

Spatial Analysis with Applications on Real Estate Market Price Prediction , Yujing Zheng

TP and TN Completability of Border Patterns , Haoge Chang

Honors Theses from 2016 2016

Computing All Isolated Invariant Sets at a Finite Resolution , Martin Salgado-Flores

Graph packing with constraints on edges , Fangyi Xu

Growing Networks with Positive and Negative Links , Corynne Smith Dech

Normal Matrices Subordinate to a Graph , Morrison Turnansky

Relaxed Coloring of Sparse Graphs , Michael C. Kopreski

Row and Column Distributions of Letter Matrices , Xiaonan Hu

(Un)Stable Manifold Computation via Iterative Forward-Backward Runge-Kutta Type Methods , Dmitriy Zhigunov

Honors Theses from 2015 2015

On the Non-Symmetric Spectra of Certain Graphs , Owen Hill

Relaxation of Planar Graphs With d∆≥2 and No 4-Cycles , Heather A. Hoskins

Honors Theses from 2014 2014

Basins of Attraction for Pulse-Coupled Oscillators , Ryan Gryder

Combinatorially Derived Properties of Young Tableaux , James R. Janopaul-Naylor

Linear and Nonlinear Trees: Multiplicity Lists of Symmetric Matrices , Eric Wityk

Local Zeta Functions over p-Adic Fields , Stephen P. Cameron

Nonlinear Models of Zooplankton Communities , Catherine King

Honors Theses from 2013 2013

A Population Density Model of Domain Calcium-Mediated Inactivation of L-Type Ca Channels , Kiah Hardcastle

Finding Open Locating Dominating Sets on Infinite and Finite Graphs , Allison Oldham

On Almost Normal Matrices , Tyler J. Moran

Statistical Inference Based on Upper Record Values , Daniel J. Luckett

Honors Theses from 2012 2012

A Model for Blue Crab Population in the Chesapeake Bay , Timothy J. Becker

Analysis and Simulation of an Optimal Control Model of an Oyster Population Displaying an Allee Effect , Timothy Raymond McDade

Circadian Oscillations of the Intestinal Stem Cell Lineage , Brian Waldman

Finding the Minimum Randic Index , Sarah Joyce Kunkler

Fixed Points of Pick and Stieltjes functions: A Linear Algebraic Approach , Nicholas Andrew Woods

Global Dynamics of Pulse-Coupled Oscillators , Allison Leslie Corish

Perfect Partitions of Some (0,1)-Matrices , Jeffrey Soosiah

Permutations with Extremal Routings on Cycles , Luis Alejandro Valentin

Strongly Real Conjugacy Classes of the Finite Unitary Group , Zach Gates

Synchronous Oscillatory Solutions in a Two Patch Predator-Prey Model , Matthew H. Becker

The Laplacian on Isotropic Quantum Graphs: Solutions and Applications , Patrick King

Honors Theses from 2011 2011

A New Lower Bound on the Minimum Density of Vertex Identifying Codes for the Infinite Hexagonal Grid , Ariel J. Cukierman

Basins of Attraction in Stage Structured Populations , Georgia Waite Pfeiffer

Critical Exponents: Old and New , Olivia J. Walch

Factoring Banded Permutations and Bounds on the Density of Vertex Identifying Codes on the Infinite Snub Hexagonal Grid , Chase A. Albert

Persistent Activity in Assortative Networks of Integrate and Fire Neurons , Matthew D. Peppe

Poles and Zeros of Generalized Carathéodory Class Functions , Yael Gilboa

Solution Theory for Systems of Bilinear Equations , Dian Yang

Topological Characterization of Extinction in a Coupled Ricker Patch Model , Benjamin Robert Holman

Honors Theses from 2010 2010

Bistability in Differential Equation Model of Oyster Population and Sediment Volume , William Crowell Jordan-Cooley

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Department of Mathematics

The honors program is a two-semester sequence (Math 99a, "Senior Research" in fall, followed by Math 99b, "Senior Research" in spring) during which senior mathematics majors carry out independent research and the  writing and oral presentation of a senior thesis. Only students who major in the BS in Mathematics or BS in Applied Math may choose the option of writing a thesis in order to be considered for Honors, High Honors or Highest Honors in mathematics. View university resources for undergraduate research support here .

Rules for Senior Honors Thesis

•  A committee of two faculty members, one of whom will be the official instructor, will supervise the work.
• A written thesis proposal must be prepared at the beginning of the first semester, and be approved and signed by both the committee and the Undergraduate Advising Head (UAH), prior to registration for the course. In order to register for the course, the student must requests to take the course in Work Day (see "Request Prerequisite or Permission to Enroll" section under Planning and Registration) .
• A mid-year evaluation must be done by the committee by the end of the first semester, and a written report submitted to the UAH. Students judged to have made insufficient progress will not be permitted to continue in the second semester.
• A thesis in a department-approved format must be submitted to the committee by the last day of classes in the second semester or by a deadline set by the committee members. At a minimum, the thesis must have a title page , a signature page , and an abstract, description of the work performed and the conclusions reached, and references. Students are encouraged to learn the Latex typesetting system ( this repository holds a LaTeX file that serves as a template for senior honors theses in the Brandeis University Department of Mathematics, developed by Chami Lamelas, '22).  We also encourage you to submit your thesis electronically to the library using the following link: Submitting your Thesis to the Library
• The student must defend their thesis in a public oral examination of at least 30 minutes duration by the end of the second semester exam period. The talk should take place in the Math Department and should be accessible to junior math majors. A list of thesis defense talks will be published on the website.
• Written evaluations of the thesis and of the defense must be submitted by the committee to the UAH by the Friday preceding the department degree meeting.
• The level of distinction will be determined by the UAH from evaluation of both the thesis and the student’s academic record.
• Students wishing to graduate in seven semesters must start their thesis research in the spring semester of their junior year, and follow the same rules moved forward one semester.
• The required forms for items (2), (3), and (6) are available on the department website.
• Supervisors outside of the Math Department are acceptable, either in other Brandeis departments or outside of the university. All the rules above apply, including the deadlines. The defense must take place in the Brandeis Math Department. The outside advisor may be an ex officio member of the supervising committee, and advise the committee on the evaluation of the work performed. The grade for Math 99a/b will be determined by the Brandeis instructor of the course. 

Student and Committee Forms for Senior Honors Research

• Student Proposal for Honors Thesis . This form is to be prepared by the student at the beginning of the first semester, and approved and signed by the committee and UAH, prior to registration for the course. You will also need your Instructor to sign an additional form, the  Course Change Form  (see #2) so that you can register.
• In order to register for the course--Course Change Form : This form is to be prepared by the student and signed by both the student and the Instructor. The student then sends the signed form to "[email protected]".

Mid-term Assessment Form . This form is to be prepared by the committee by the end of the first semester, and then submitted by the committee to the UAH.

• Committee Report on Senior Honors Thesis . This form is to be prepared by the committee after the thesis defense and is due to the UAH the Friday before Degree Meetings.

Resources and LATEX Template

View university resources for undergraduate research support.

View funding resources and deadlines for undergraduate research support.

View  how to submit your thesis electronically to Scholar Works. View a template   LaTeX  file that students can choose to use to fill in their information (name, thesis title, advisor etc.),  created by Chami Lamelas '22.

Completed Senior Honors Theses

• Ryan Xie '21: " Mathematically Modeling the Neuron Network Involved in Sleep Regulation " Thesis Advisor: Prof. Jonathan Touboul
• Chami Lamelas, '22  “ Vorticity-Stream Solver for Microfluidic Devices and Applications to Blood Cell Sorters ”   Thesis Advisor: Profs. Thomas Fai and An Huang
• Mathematics Placement

Mathematics Honors Program presentations are held each May. These presentations were based on theses submitted for examination to the Mathematics Department Honors Committee.

The Mathematics Department Honors Committee determines the level of departmental honors awarded (Honors with Distinction, Honors with High Distinction, or Honors with Highest Distinction), based on the student's GPA in the major and the quality of the honors work.

If you are interested in attending the Honors Program Presentations, please send an email to [email protected].

9500 Gilman Drive, La Jolla, CA 92093-0112

(858) 534-3590

Home > ARTSCI > MATH > MTH_ETD

Mathematics Department Theses and Dissertations

Theses/dissertations from 2023 2023.

The Global Dynamics of Some Rational Difference Equations Exhibiting Neimark-Sacker Bifurcation , Connor O'Loughlin

High-Speed Cops and Robbers , Nikolas Townsend

DYNAMICS OF NON-AUTONOMOUS DISCRETE SYSTEMS WITH APPLICATIONS TO EVOLUTIONARY DYNAMICS , Susan Trolle

THE TREE-DEPTH AND CRITICALITY OF UNICYCLIC GRAPHS , Lilith Wagstrom

Theses/Dissertations from 2022 2022

GENDER-SPECIFIC EXPERIENCES OF WOMEN UNDERGRADUATE STEM STUDENTS IN ONLINE MATHEMATICS COURSES DURING A PANDEMIC , Erika R. Fiore

Theses/Dissertations from 2020 2020

ON THE HAVEL-HAKIMI RESIDUE OF DEGREE SEQUENCES AND ITS RELATION TO THE INDEPENDENCE NUMBER , Benjamin Lantz

TWO VARIANTS OF COPS AND ROBBERS WITH ASYMMETRIC MOVEMENT RULES , Eric Peterson

Theses/Dissertations from 2019 2019

CLOSURE UNDER THE MAJORIZATION RELATION AND THE DISTINGUISHING CHROMATIC NUMBER OF CIRCULANT GRAPHS , Jean A. Guillame

GLOBAL DYNAMICS OF DISCRETE MONOTONE MAPS IN THE PLANE AND IN R N , James Marcotte

Global Dynamics of Some Discrete Dynamical Systems in Mathematical Biology , Sarah Van Beaver

Theses/Dissertations from 2018 2018

Global Dynamics of Some Competitive and Cooperative Discrete Dynamical Systems , Elliott J. Bertrand

Identifications in Escape Regions of the Parameter Space of Cubic Polynomials , Chad Estabrooks

On Possible Limit Functions on a Fatou Component in Non-Autonomous Iteration , Christopher Staniszewski

Theses/Dissertations from 2017 2017

Bifurcations of Some Planar Discrete Dynamical Systems with Applications , Toufik Khyat

Global Dynamics and Boundedness of Discrete Population Models , David T. McArdle

Theses/Dissertations from 2016 2016

Degree-Limited Defective Three Colorings of Planar Graphs Containing No 4-Cycles or 5-Cycles , Addie Armstrong

Global Dynamics of Some Discrete Dynamical Systems With Applications , Arzu Bilgin

Minimal Cantor Sets: The Combinatorial Construction of Ergodic Families and Semi-Conjugations , Erin Denette

Global Dynamics of Some Quadratic Difference Equations , Mark Dipippo

Theses/Dissertations from 2015 2015

PLANAR DIFFERENCE EQUATIONS: ASYMPTOTIC BEHAVIOR OF SOLUTIONS AND 1-1 RESONANT POINTS , William T. Jamieson

THE SPECTRAL CONNECTION MATRIX FOR CLASSICAL REAL ORTHOGONAL POLYNOMIALS , Jenna Reis

Theses/Dissertations from 2014 2014

REAL-TIME DATA DISTRIBUTION , Angela Frolov

THE CYCLE INTERSECTION MATRIX AND APPLICATIONS TO PLANAR GRAPHS AND DATA ANALYSIS FOR POSTSECONDARY MATHEMATICS EDUCATION , Caitlin R. Phifer

IMPLICITLY RESTARTED KRYLOV SUBSPACE METHODS FOR LARGE-SCALE LEAST-SQUARES PROBLEMS , Daniel J. Richmond

NEW RESULTS AND IMPROVEMENTS RELATED TO THE STUDY OF MULTI-SPECIALIZATION WHIST TOURNAMENT DESIGNS , W. Kent Rudasill

TOWARDS STEINBERG'S CONJECTURE , Diana L. Smith

Theses/Dissertations from 2013 2013

Some Results on Graph Representations and Closure Systems , Adam J. Gilbert

Some Results on Graph Representations and Graph Colorings , Arlene Mia Heissan

Hypergraph Colorings, Commutative Algebra, and Gröbner Bases , Michael E. M. Krul

On the Global Behavior of Some Systems of Difference , Evalina G. Lapierre

Unboundedness Results for Rational Difference Equations , Gabriel Lugo

Protein Structure Modeling and Its Application to the Mechanics of Actomyosin Interaction , Cynthia N. Prudence

Theses/Dissertations from 2011 2011

RELAXATIONS OF L(1, 1)-LABELING FOR THE BROADCAST SCHEDULING PROBLEM , Shaun N. Joseph

Theses/Dissertations from 2001 2001

Some Limit Theorems for Szego Polynomials , Michael Joseph Arciero

Theses/Dissertations from 1998 1998

Boundedness, Periodicity and Stability of Some Difference Equations , Amal M. Al-Amleh

Theses/Dissertations from 1965 1965

On Solutions of a Class of Ricatti Equations , Gordon Everett Morrison

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View past winners, 2024 byam shaw-brownstone thesis excellence award winners announced, posted on june 03, 2024 by mals program, amanda watson.

The 2024 Winners of the Thesis Excellence Awards have been announced! These awards are given in recognition of the outstanding thesis in each concentration each year.

James Washington, Jr -  Creative Writing 

Jasmine Shirey -  Cultural Studies 

Karina Madzari -  Globalization Studies 

Graeme Blackman -  General Liberal Studies 

Behishta Sadaat - General Liberal Studies ( Medical Humanities)