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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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• Senior Theses

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]
• Suzy Borgschulte  A mathematical approach to the panting of dogs  (2004) [with M. Reed]
• Lauren M. Childs  Scaling population dynamics from the macroscopic to the microscopic  (2004) [with T. Kepler]
• Ryan Letchworth  Wavelet methods for numerical solutions of differential equations  (2004) [with S. Roudenko]
• David Marks  Coadjoint orbits and geometric quantization  (2004) [with M.R. Plesser]
• Lori Peacock  Distributions of the small eigenvalues of Wishart matrices  (2004) [with B. Rider]
• Lindsay C. Piechnik  Smooth reflexive 4-polytopes have quadratic triangulations  (2004) [with C. Haase]
• Matthew Toups  A solution to the D0-D4 system of equations  (2004) [with M. Stern]
• Jenna VanLiere  Mathematically modelling the growth and diversification of T-cell populations  (2004) [with T. Kepler]
• Matthew J. Atwood  Evaluating singular and nearly singular integrals numerically  (2003) [with J.T. Beale]
• Marie Guerraty  Controlling alternans in a cardiac map model  (2003) [with M. Romeo]
• Meredith C. Houlton  Classification of critical curves and preliminary analysis of caustics  (2003) [with A. Petters]
• Steven R. Nicklas  Envy and satisfaction in the public goods game  (2003) [with D. Kraines]
• Dane R. Voris  A numerical approach to the M t /M t /N t  queue with abandonment  (2003) [with B. Rider]
• Melanie Wood  Invariants and relations of the action of the absolute Galois group on dessins d’enfants and the algebraic fundamental group of the punctured sphere  (2003) [with R. Hain]
• Thomas W. Finley  Efficient Myrinet routing  (2002) [with W. Allard]
• Samuel W. Malone  Alternative Price Processes for Black-Scholes: Empirical Evidence and Theory  (2002) [with A. Petters]
• Carl Miller  Exponential Iterated Integrals and the Solvable Completion of Fundamental Groups  (2001) [with R. Hain]
• Daniel Neill  Optimality under Noise: Higher Memory Strategies for the Alternating Prisoner’s Dilemma  (2001) Computer Science [with D. Kraines]
• Luis Von Ahn  Models of the language of set theory and Zermelo Frankel axioms  (2000) [with R. Hodel]
• Christopher Beasley  Superconformal theories from Branes at Singularities  (1999) Physics [with R. Plesser]
• Alexander Brodie  Measurable Cardinals  (1999) [with R. Hodel]
• Jeffrey DiLisi  The Biology and Mathematics of the Hypothalamic-Pituitary-Testicular Axis  (1999) [with M. Reed]
• Garrett Mitchener  Lattices and Sphere Packing  (1999) [with R. Hain]
• Andrew O. Dittmer  Generalized Formulas for Circular Polygons  (1998) [with R. Hain]
• Richard R. Schneck  Set Theory and Cardinal Arithmetic  (1997) [with R. Hodel]
• Tung T. Tran  Counting Independent Subsets in Nearly Regular Graphs  (1997) [with G. Lawler]
• Paul A. Dreyer  Knot theory and the human pretzel game  (1995) [with J. Harer]
• Paul J. Koss  Effects of noise on the iterated prisoner’s dilemma  (1995) [with D. Kraines]
• Jeff Vanderkam  Eigenfunctions of an acoustic system  (1994) [with T. Beale]
• Linie Chang  Mathematics and immunology: Modeling antigen and antibody interactions  (1993) [with M. Reed]
• Sang H. Chin  Action of the Torelli group on the 3-fold cover of G-hole torus  (1993) [with R. Hain]
• Jennifer Slimowitz  Transitions of gaps between the integers N satisfying N q < j (1993) [with M. Reed]
• David Jones  Primality testing, factoring and continued fractions  (1992) [with C. Schoen]
• Will Schneeberger  The axiom diamond  (1992) [with J. Shoenfield]
• Jeanne Nielsen  Triply periodic minimal surfaces in  R 3  (1991) [with R. Bryant
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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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Department of Mathematics - UC Santa Barbara

Senior Thesis Options

To enter the honors program in mathematics, a student must have completed 120 units of coursework with an overall grade-point average of at least 3.5 and at least 24 upper-division mathematics and statistics units with a grade-point average of at least 3.5 (excluding Mathematics 100A-B, 193, 195A-B, and PSTAT 133A-B-C and 193).

To complete the honors program, the student must maintain a grade-point average of at least 3.5 in all upper-division and graduate mathematics and statistics courses (excluding Mathematics 100A-B, 193, 195A-B, and PSTAT 133A-B-C and 193) and as well as complete one of the following: (a) a senior thesis, Math 197A-B; (b) a two-quarter graduate sequence; or (c) together with an advisor, submit a Distinction in the Major proposal for an interdisciplinary program of three mathematically oriented courses outside the math department to the undergraduate committee for its approval. Option C does not apply to economics/mathematics or financial mathematics majors.

Distinction in the Major for each option will be awarded at graduation pending final approval by the Department of Mathematics Undergraduate Committee. Written projects will be submitted to the committee, and grades will be evaluated for coursework options. To apply for the Honors Program in Mathematics, please email the Mathematics Undergraduate Advisors at  [email protected] .

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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.

St Andrews Research Repository

•   St Andrews Research Repository
• Mathematics & Statistics (School of)
• Pure Mathematics

Pure Mathematics Theses

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Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.

For more information please visit the School of Mathematics and Statistics home page.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

Recent Submissions

Groups defined by language theoretic classes , rearrangement groups of connected spaces , modern computational methods for finitely presented monoids , finiteness conditions on semigroups relating to their actions and one-sided congruences , on constructing topology from algebra .

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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

Quick Links +

Undergraduate research.

Undergraduate Research is an great opportunity to get more involved in the Math Department while working directly with faculty to expand the bounds of existing knowledge. There are many benefits to conducting undergraduate research, including the opportunity to:

• Explore an area of interest more deeply
• Learn first-hand about research to determine if you would like to pursue advanced study after your bachelor's degree
• Gain experience that is often highly valued by graduate school admissions committees
• Present your findings at the UC Davis Undergraduate Research Conference or other symposia, and possibly co-author a published paper
• Build relationships with faculty, which can lead to personalized letters of recommendation

MAT 099/199: Research Credit

Students completing undergraduate research (MAT 99/199) will receive lower/upper division credit toward graduation requirements (180 unit requirement) but will not receive credit toward their major. Every 1 unit of credit corresponds to 3 hours of work a week, or 30 hours of work per quarter.

MAT 099 : Undergraduates students who have 83 units or less completed (lower division credit)

MAT 199 : Undergraduate students who have 84 units or more completed (upper division credit)

Academic Year Research Projects

Each quarter, a list of advertised research projects (along with a link to apply to these projects) can be found on the Quarterly Research Projects webpage .

Undergrad Research Conference 2021

The following are presentations held during the annual conference: 

Research in Ramsey Theory and Automatic Theorem Proving

One-Dimensional range restrcited C^2 Interpolation Algorithm

Approximating K-Means using an ADMM Approach

Recovering Individual Based Model Outcomes on Spatiotemporally Coarsened Data

Summer Research Projects

We have research projects happening each summer. For a list of summer projects (and to apply, if they are taking new students), see the Summer Research webpage .

Undergraduate Research Advisor

The undergraduate research advisor is a faculty member who has agreed to help students with all details related to a Research Experience for Undergraduates (REU). Primary responsibilities include helping students on finding a mentor, selecting students for available fellowships, and advertising other REU programs and fellowships outside of UC Davis.

Contact him for help!

Prof. Bob Guy! [email protected]

Undergraduate Senior Thesis in Mathematics

The Department of Mathematics at UC Davis offers undergraduate students the opportunity to participate in original mathematical research that will culminate in a senior undergraduate thesis. A student taking advantage of this opportunity would work under the guidance of a faculty mentor, pursuing original research.

Eligibility

To be eligible to write a senior thesis, advanced undergraduate students must

• Have a GPA of 3.5 or above in upper level courses in Mathematics OR be in the Honors Program .
• Find an appropriate research mentor willing to supervise their research project. Research supervisors can be faculty from the Mathematics Department or faculty from the Graduate Group in Applied Mathematics (GGAM) .
• Students that do not meet the GPA requirement may also be permitted to write a senior thesis. However, they must be nominated by a faculty member who is willing and able to supervise them in a research project, and the nomination must be approved by Undergraduate Research Committee.

Requirements for completion of an undergraduate thesis

• Students must complete two full quarters of research prior to graduation.
• While pursuing their research, students must complete MAT 199 (Special Studies for Advanced Undergraduates) and/or MAT 194 (Undergraduate Thesis) for a total of at least 6 units of credit over two quarters.
• Students must complete a thesis of sufficient quality and substance. Both the research supervisor and the Undergraduate Program Committee Chair (UPC) will evaluate a student's thesis.
• The UPC must receive a draft of the thesis no later than the beginning of the eighth week of the quarter in which the student plans to graduate. The UPC must also receive the supervisor's evaluation of the thesis at this time. The final copy of the thesis must be submitted to the department by the end of finals week.

Students who have a cumulative GPA that exceeds a College of Letters & Science requirement, complete at least 6 units of credits of MAT 199 and/or 194 over two quarters, and complete theses may be considered for graduation with High Honors or Highest Honors. All students completing theses will be recognized at the June Graduation Reception and in the Fall Department Newsletter.

Undergraduate Senior Thesis - Archived Submissions

Research programs at uc davis.

UC LEADS is a comprehensive two-year program designed to prepare economically or educationally disadvantaged students for success in doctoral degree programs in science, engineering, technology, or mathematics. Students are assigned individual faculty mentors, who guide them in academic year and summer research experiences. Scholars receive stipends and housing for their summer research and participate in extensive academic enrichment activities, including presenting their research at the annual UC LEADS Symposium.

MURPPS is a UC Davis undergraduate mentoring program designed to increase the number of disadvantaged students who pursue graduate studies in the physical and mathematical sciences by offering students the chance to work with professors on research projects relevant to their major. The goal of MURPPS is to help create a diverse post-graduate population in the Physical and Mathematical Sciences. Students are paid a quarterly stipend. MURPPS also runs seminars which introduce students to faculty and research projects, offers academic guidance, and access to the tutoring at the Academic Assistance and Tutoring Centers .

The Mentorships for Undergraduate Research in Agriculture, Letters, and Science (MURALS) is a two-quarter program that encourages students to further their education beyond the baccalaureate degree by providing opportunities to participate in academic research with a faculty mentor. MURALS welcomes students from all academic disciplines. For application information, please go to their "How to Apply" webpage.

Online Research Search Engines

The following are just a few suggested links that may prove helpful when you begin your research endeavors at UC Davis. Each site — or search engine — offers a wide variety of research aides including published articles and reviews, mathematical documents for specific phrases, or membership listings.

• Undergraduate Research Opportunities at UC Davis A comprehensive site relative to undergraduate research related to UC Davis, both on and off campus. Includes a link to the Undergraduate Research Center.
• eScholarship The publication listings for the entire University of California. This includes all research topics, but also mathematics.
• Front for the Mathematics ArXiv A front end to assist in searching the mathematics articles archive maintained by Cornell University.
• MathSciNet American Mathematical Society's listing of math reviews on the web.
• American Mathematical Society
• Society for Industrial and Applied Mathematics
• Combined Membership List A searchable database of the combined membership listings of the American Mathematical Society (AMS), Mathematical Association of America (MAA), Society for Industrial and Applied Mathematics (SIAM), American Mathematical Association of Two-Year Colleges (AMATYC), and the Association for Women in Mathematics (AWM).

• 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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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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Mathematics thesis and dissertation collection

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This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

Recent Submissions

Spencer cohomology, supersymmetry and the structure of killing superalgebras , higher triangulated categories and fourier-mukai transforms on abelian surfaces and threefolds , investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by stack , estimation and application of bayesian hawkes process models , novel statistical learning approaches for open banking-type data , statistical and machine learning approaches to genomic medicine , using markov chain monte carlo in vector generalized linear mixed models: with an application to integral projection models in ecology , symmetries of riemann surfaces and magnetic monopoles , kan extensions in probability theory , regression analysis for extreme value responses and covariates , categorical torelli theorems for fano threefolds , laplacians for structure recovery on directed and higher-order graphs , efficient interior point algorithms for large scale convex optimization problems , solving sampling and optimization problems via tamed langevin mcmc algorithms in the presence of super-linearities , algebraic combinatorial structures for singular stochastic dynamics , stochastic modelling and inference of ocean transport , convergence problems for singular stochastic dynamics , classification of supersymmetric black holes in ads₅ , bps cohomology for 2-calabi—yau categories , quantitative finance informed machine learning .

Why do the requirements take this form?

Calculus represents the beginning of modern mathematics and is one of the most profound applications of mathematics to the physical and social sciences.  Thus, the major begins with the study of calculus in one and several variables, as well as with linear algebra, which will teach you how to manipulate linear equations in many variables and how to connect them to geometry.  Starting in the second year, you will begin to gain experience in the three main branches of mathematics, algebra, analysis, and geometry, as well as in some of their subdivisions and hybrids, e.g., number theory, complex analysis, and differential geometry.  As you continue in your studies, the courses will become increasingly less computational and more proof-oriented.  Aside from the courses offered by the Mathematics Department, cognate courses in physics, probability, logic, and computer science are often part of the major, and are examples of the wealth of mathematical thinking present in other disciplines.

Whom do I speak to about this major? How does the department structure its faculty for advising purposes?

Any questions you have about majoring in mathematics should be addressed to the Director of Undergraduate Studies for the department or to one of the designated Departmental Advisors.

You are welcome to approach any of them with your questions about the major. While the department does not have a system of assigning individual advisors to students, you may consult the bulletin page for a list of our undergraduate advisors.

The department also organizes a series of information sessions and events in the fall and spring terms. The presentation slides from the virtual Math Open House Spring 2022  can be found here .

When should I declare my major?

Although most students generally declare their major during the major declaration period in the second semester of their sophomore year, you should definitely begin a calculus sequence in your first year if you are seriously considering majoring in mathematics.

What research opportunities exist in or through the department?

The department runs several undergraduate research programs aimed at math majors. Opportunities are available during the academic year and summer terms.

Will study abroad enhance this major?

Although study abroad is not an integral part of your studies in mathematics, it can provide you with exposure to a different culture and a different educational system, and, as such, can be very fulfilling.  You may also want to participate in the Budapest Mathematical Seminar or similar programs in your junior year.  Keep in mind, however, that study abroad requires careful planning.  If you are seriously considering studying abroad, you should consult with the Director of Undergraduate Studies as early in your program as possible in order to plan your major accordingly and to incorporate study abroad courses that are compatible with your major in mathematics.

How might a sample track or course of study look?

In the sample tracks listed below courses required for the major are listed in bold face. You should understand that these sample tracks are just models and that your program might look quite different.

1. Starting with Calculus I

If you start with Calculus I-II your first year, you may either continue with Calculus III – IV, or, ideally, switch to Honors Math A and B in your sophomore year. Junior year you should either take the Introduction to Modern Algebra or the Introduction to Modern Analysis. Some students find it preferable to substitute other analysis courses for Introduction to Modern Analysis. The following is a possible program if you were to choose to complete the entire Calculus I sequence and substitute Partial Differential Equations (PDE) and Complex Variables for the Modern Analysis sequence:

Your program might look something like this if you were to choose to switch to Honors Math in your second year (note that Linear Algebra is not required):

2. Starting with Honors Math A

If you begin with Honors Math A, your program will be a very accelerated one, and you will not need to take Linear Algebra, as the material is covered in Honors Math. Because you will receive six points of advanced credit and because Honors Math A and B are worth 4 points each, you will need only 10 additional math and cognate courses to complete the major.

3. Starting with Calculus III

If you start with Calculus III and take Linear Algebra in your sophomore year, your program might look something like this:

You can accelerate this program by taking Linear Algebra in the first year, an option that will allow you to sample graduate courses in your senior year and/or to take more mathematics courses than required by the major.

How does one receive departmental honors?

To be recommended to the College Committee on Honors, Awards, and Prizes, which makes the final decisions on all honors’ recipients, you must have a GPA of 3.63 in the major and have completed a senior thesis of merit.  For more information on researching and writing the senior thesis and on departmental honors, you should consult with the Director of Undergraduate Studies.

What awards and prizes are sponsored by the department?

The following cash prizes are awarded annually to students with the highest score on a special departmental exam:

• Professor Van Amringe Mathematical Prize

John Dash Van Buren Jr. Prize in Mathematics

Are there any student clubs, committees, and/or activities offered within or through the department?

Yes. The Undergraduate Mathematics Society is the department’s undergraduate club.  Detailed information on membership, Society-sponsored seminars and activities, and archival resources are available on the Society’s Web site . The department also sponsors workshops and   weekly seminars in mathematics, and posts information about special lectures, conferences, and seminars at nearby schools .

In addition, the Association for Women in Mathematics Columbia Chapter connects students and professors interested in mathematics at Columbia University and Barnard College as part of a broader effort to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment of women and girls in the STEM fields.

What career opportunities follow upon study in this field?

If you graduate with a bachelor’s degree in mathematics you will have the foundation for a broad range of positions in business, industry, government, and education. Companies in the computer and communications industries employ many mathematicians, as do oil companies, banks, insurance companies, and consulting firms. Almost every bureau and branch of the federal government, including the Department of Health and Human Services, the General Accounting Office, the Department of Energy, the Department of Defense, the National Aeronautics and Space Administration, and the National Security Agency, employ mathematicians in various capacities.  Your Columbia College foundation in general education combined with your major in mathematics will qualify you for a vast array of employment opportunities in nearly any field.  You may also decide to continue your study of mathematics at the graduate level, especially if you are interested in research and/or teaching at the college level.

Whom should I contact about graduate study in this field?

Departmental advisors can offer advice about and help with graduate school applications. The Mathematics department also runs a Master’s degree program in mathematical finance and a Ph.D. program in mathematics .

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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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Department of Mathematics, University of California San Diego

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Thesis Defense

Patrick girardet, automorphisms of hilbert schemes of points of abelian surfaces.

Given an automorphism of a variety $X$, there is an induced ''natural'' automorphism on $X^{[n]}$, the Hilbert scheme of $n$ points of $X$. While unnatural automorphisms of $X^{[n]}$ are known to exist for certain varieties $X$ and integers $n$, all previously known examples could be shown to be unnatural because they do not preserve multiplicities. Belmans, Oberdieck, and Rennemo thus asked if an automorphism of a Hilbert scheme of points of a surface is natural if and only if it preserves the diagonal of non-reduced subschemes.

We give an answer in the negative for all $n\ge 2$ by constructing explicit counterexamples on certain abelian surfaces $X$. These surfaces are not generic, and hence we prove a partial converse statement that all automorphisms of the Hilbert scheme of two points on a very general abelian surface are natural for certain polarization types (including the principally polarized case).

Advisor: Dragos Oprea

May 16, 2024

9500 Gilman Drive, La Jolla, CA 92093-0112

(858) 534-3590

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2024 english and creative writing honors thesis presentations.

Please join the Department of English and Creative Writing for this year's English and creative writing honors thesis presentations, Tuesday, May 28 - Thursday, May 30, 2024, in Sanborn Library.

Please join the Department of English and Creative Writing for this year's English and creative writing honors thesis presentations, Tuesday, May 28 - Thursday, May 30, 2024, in Sanborn Library. These presentations will also be available virtually. Please register at dartgo.org/engl-cw-honors .

Tuesday, May 28, 2024

12:30 p.m. Introduction   12:45 p.m. Elle Muller Haunted Halls and Misnamed Monsters: Displacement and Erasure in Hrólfs Saga Kraka and Beowulf   1:00 p.m. Kennedy Hamblen Soft Mechanics: Hallucinogenic Media from De Quincey to Burroughs   1:15 p.m. Jea Mo Letters from Hanseong Street   1:30 p.m. Elizabeth Lee Grooves of Enactment: Bob Dylan's Planet Waves and the Philosophy of Recording   1:45 p.m. Isabella Macioce Everything Is a Love Poem   2:00 p.m. Ophelia Woodland Landmarks: A First Approach

Wednesday, May 29, 2024

1:00 p.m. Introduction   1:15 pm. Eliza Holmes The Madwoman Reimagined: Narration and the Diagnostic Process in Victorian Gothic Fiction   1:30 p.m. Maria Amador The Museum of Everyday Life   1:45 p.m. Kat Arrington Please Watch Me When I'm Alone So I Don't Stop Existing   2:00 p.m. Elijah Oaks A Paralytic History: Narratives of the Late South   2:15 p.m. Edgar Morales Out in the Field, There Are No More Fences   2:30 p.m. Zhenia Dubrova What Remains: Stories

Thursday, May 30, 2024

10:00 a.m. Introduction   10:15 a.m. Grace Schwab Counsel and Consequence: Intergenerational Models of Womanhood in the Novels of Jane Austen   10:30 a.m. Arielle Feuerstein "Remember who the enemy is": Liminality as a Tool for Revolution in The Hunger Games   10:45 a.m. Laurel Lee Pitts Good Neighbors   11:00 a.m. Heather Damia In a Woman's Hide: Supernatural Gender in Shakespeare's History Plays   11:15 a.m. Jiyoung Park Post Office 4640   11:30 a.m. Michaela Benton Wounded Lives: Trauma, Survival, and Slavery in Toni Morrison's Beloved and Octavia Butler's Kindred .