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Applied Mathematics Theses and Dissertations

This collection contains theses and dissertations from the Department of Applied Mathematics, collected from the Scholarship@Western Electronic Thesis and Dissertation Repository

Theses/Dissertations from 2024 2024

Osculating Curves , Sepideh Bahrami

Host-Pathogen Co-evolution with Various Transmission Modes of Infection and Density-Dependent Dynamics , bita ghodsi

Impact of fluctuating selection on genetic variation when new mutations are expected to be deleterious , Zahra Shafiei

Impact of Energy Allocation on Fish's Age and Weight at Maturation by Mathematical Models , Siyi Zhang

Theses/Dissertations from 2023 2023

Visual Cortical Traveling Waves: From Spontaneous Spiking Populations to Stimulus-Evoked Models of Short-Term Prediction , Gabriel B. Benigno

Spike-Time Neural Codes and their Implication for Memory , Alexandra Busch

Study of Behaviour Change and Impact on Infectious Disease Dynamics by Mathematical Models , Tianyu Cheng

Series Expansions of Lambert W and Related Functions , Jacob Imre

Data-Driven Exploration of Coarse-Grained Equations: Harnessing Machine Learning , Elham Kianiharchegani

Pythagorean Vectors and Rational Orthonormal Matrices , Aishat Olagunju

The Magnetic Field of Protostar-Disk-Outflow Systems , Mahmoud Sharkawi

A Highly Charged Topic: Intrinsically Disordered Proteins and Protein pKa Values , Carter J. Wilson

Population Dynamics and Bifurcations in Predator-Prey Systems with Allee Effect , Yanni Zeng

Theses/Dissertations from 2022 2022

A Molecular Dynamics Study Of Polymer Chains In Shear Flows and Nanocomposites , Venkat Bala

On the Spatial Modelling of Biological Invasions , Tedi Ramaj

Complete Hopf and Bogdanov-Takens Bifurcation Analysis on Two Epidemic Models , Yuzhu Ruan

A Theoretical Perspective on Parasite-Host Coevolution with Alternative Modes of Infection , George N. Shillcock

Theses/Dissertations from 2021 2021

Mathematical Modelling & Simulation of Large and Small Scale Structures in Star Formation , Gianfranco Bino

Mathematical Modelling of Ecological Systems in Patchy Environments , Ao Li

Credit Risk Measurement and Application based on BP Neural Networks , Jingshi Luo

Coevolution of Hosts and Pathogens in the Presence of Multiple Types of Hosts , Evan J. Mitchell

SymPhas: A modular API for phase-field modeling using compile-time symbolic algebra , Steven A. Silber

Population and Evolution Dynamics in Predator-prey Systems with Anti-predation Responses , Yang Wang

Theses/Dissertations from 2020 2020

The journey of a single polymer chain to a nanopore , Navid Afrasiabian

Exploration Of Stock Price Predictability In HFT With An Application In Spoofing Detection , Andrew Day

Multi-Scale Evolution of Virulence of HIV-1 , David W. Dick

Contraction Analysis of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria and Plasmodium within Mosquitoes. , Nickolas Goncharenko

Phage-Bacteria Interaction and Prophage Sequences in Bacterial Genomes , Amjad Khan

The Effect of the Initial Structure on the System Relaxation Time in Langevin Dynamics , Omid Mozafar

Mathematical modelling of prophage dynamics , Tyler Pattenden

Hybrid Symbolic-Numeric Computing in Linear and Polynomial Algebra , Leili Rafiee Sevyeri

Abelian Integral Method and its Application , Xianbo Sun

Theses/Dissertations from 2019 2019

Algebraic Companions and Linearizations , Eunice Y. S. Chan

Algorithms for Mappings and Symmetries of Differential Equations , Zahra Mohammadi

Algorithms for Bohemian Matrices , Steven E. Thornton

A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals , Jeet Trivedi

Theses/Dissertations from 2018 2018

Properties and Computation of the Inverse of the Gamma function , Folitse Komla Amenyou

Optimization Studies and Applications: in Retail Gasoline Market , Daero Kim

Models of conflict and voluntary cooperation between individuals in non-egalitarian social groups , Cody Koykka

Investigation of chaos in biological systems , Navaneeth Mohan

Bifurcation Analysis of Two Biological Systems: A Tritrophic Food Chain Model and An Oscillating Networks Model , Xiangyu Wang

Ecology and Evolution of Dispersal in Metapopulations , Jingjing Xu

Selected Topics in Quantization and Renormalization of Gauge Fields , Chenguang Zhao

Three Essays on Structural Models , Xinghua Zhou

Theses/Dissertations from 2017 2017

On Honey Bee Colony Dynamics and Disease Transmission , Matthew I. Betti

Simulation of driven elastic spheres in a Newtonian fluid , Shikhar M. Dwivedi

Feasible Computation in Symbolic and Numeric Integration , Robert H.C. Moir

Modelling Walleye Population and Its Cannibalism Effect , Quan Zhou

Theses/Dissertations from 2016 2016

Dynamics of Discs in a Nematic Liquid Crystal , Alena Antipova

Modelling the Impact of Climate Change on the Polar Bear Population in Western Hudson Bay , Nicole Bastow

A comparison of solution methods for Mandelbrot-like polynomials , Eunice Y. S. Chan

A model-based test of the efficacy of a simple rule for predicting adaptive sex allocation , Joshua D. Dunn

Universal Scaling Properties After Quantum Quenches , Damian Andres Galante

Modeling the Mass Function of Stellar Clusters Using the Modified Lognormal Power-Law Probability Distribution Function , Deepakshi Madaan

Bacteria-Phage Models with a Focus on Prophage as a Genetic Reservoir , Alina Nadeem

A Sequence of Symmetric Bézout Matrix Polynomials , Leili Rafiee Sevyeri

Study of Infectious Diseases by Mathematical Models: Predictions and Controls , SM Ashrafur Rahman

The survival probability of beneficial de novo mutations in budding viruses, with an emphasis on influenza A viral dynamics , Jennifer NS Reid

Essays in Market Structure and Liquidity , Adrian J. Walton

Computation of Real Radical Ideals by Semidefinite Programming and Iterative Methods , Fei Wang

Studying Both Direct and Indirect Effects in Predator-Prey Interaction , Xiaoying Wang

Theses/Dissertations from 2015 2015

The Effect of Diversification on the Dynamics of Mobile Genetic Elements in Prokaryotes: The Birth-Death-Diversification Model , Nicole E. Drakos

Algorithms to Compute Characteristic Classes , Martin Helmer

Studies of Contingent Capital Bonds , Jingya Li

Determination of Lie superalgebras of supersymmetries of super differential equations , Xuan Liu

Edge states and quantum Hall phases in graphene , Pavlo Piatkovskyi

Evolution of Mobile Promoters in Prokaryotic Genomes. , Mahnaz Rabbani

Extensions of the Cross-Entropy Method with Applications to Diffusion Processes and Portfolio Losses , Alexandre Scott

Theses/Dissertations from 2014 2014

A Molecular Simulation Study on Micelle Fragmentation and Wetting in Nano-Confined Channels , Mona Habibi

Study of Virus Dynamics by Mathematical Models , Xiulan Lai

Applications of Stochastic Control in Energy Real Options and Market Illiquidity , Christian Maxwell

Options Pricing and Hedging in a Regime-Switching Volatility Model , Melissa A. Mielkie

Optimal Contract Design for Co-development of Companion Diagnostics , Rodney T. Tembo

Bifurcation of Limit Cycles in Smooth and Non-smooth Dynamical Systems with Normal Form Computation , Yun Tian

Understanding Recurrent Disease: A Dynamical Systems Approach , Wenjing Zhang

Theses/Dissertations from 2013 2013

Pricing and Hedging Index Options with a Dominant Constituent Stock , Helen Cheyne

On evolution dynamics and strategies in some host-parasite models , Liman Dai

Valuation of the Peterborough Prison Social Impact Bond , Majid Hasan

Sensitivity Analysis of Minimum Variance Portfolios , Xiaohu Ji

Eigenvalue Methods for Interpolation Bases , Piers W. Lawrence

Hybrid Lattice Boltzmann - Molecular Dynamics Simulations With Both Simple and Complex Fluids , Frances E. Mackay

Ecological Constraints and the Evolution of Cooperative Breeding , David McLeod

A single cell based model for cell divisions with spontaneous topology changes , Anna Mkrtchyan

Analysis of Re-advanceable Mortgages , Almas Naseem

Modeling leafhopper populations and their role in transmitting plant diseases. , Ji Ruan

Topological properties of modular networks, with a focus on networks of functional connections in the human brain , Estefania Ruiz Vargas

Computation Sequences for Series and Polynomials , Yiming Zhang

Theses/Dissertations from 2012 2012

A Real Options Valuation of Renewable Energy Projects , Natasha Burke

Approximate methods for dynamic portfolio allocation under transaction costs , Nabeel Butt

Optimal clustering techniques for metagenomic sequencing data , Erik T. Cameron

Phase Field Crystal Approach to the Solidification of Ferromagnetic Materials , Niloufar Faghihi

Molecular Dynamics Simulations of Peptide-Mineral Interactions , Susanna Hug

Molecular Dynamics Studies of Water Flow in Carbon Nanotubes , Alexander D. Marshall

Valuation of Multiple Exercise Options , T. James Marshall

Incomplete Market Models of Carbon Emissions Markets , Walid Mnif

Topics in Field Theory , Alexander Patrushev

Pricing and Trading American Put Options under Sub-Optimal Exercise Policies , William Wei Xing

Further applications of higher-order Markov chains and developments in regime-switching models , Xiaojing Xi

Theses/Dissertations from 2011 2011

Bifurcations and Stability in Models of Infectious Diseases , Bernard S. Chan

Real Options Models in Real Estate , Jin Won Choi

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Digital Commons @ USF > College of Arts and Sciences > Mathematics and Statistics > Theses and Dissertations

Mathematics and Statistics Theses and Dissertations

Theses/dissertations from 2024 2024.

The Effect of Fixed Time Delays on the Synchronization Phase Transition , Shaizat Bakhytzhan

On the Subelliptic and Subparabolic Infinity Laplacian in Grushin-Type Spaces , Zachary Forrest

Utilizing Machine Learning Techniques for Accurate Diagnosis of Breast Cancer and Comprehensive Statistical Analysis of Clinical Data , Myat Ei Ei Phyo

Quandle Rings, Idempotents and Cocycle Invariants of Knots , Dipali Swain

Comparative Analysis of Time Series Models on U.S. Stock and Exchange Rates: Bayesian Estimation of Time Series Error Term Model Versus Machine Learning Approaches , Young Keun Yang

Theses/Dissertations from 2023 2023

Statistical Analysis of Ribonucleotide Incorporation in Human Cells , Tejasvi Channagiri

Matrix Models of 2D Critical Phenomena , Nathan Hayford

Data-Driven Learning Algorithm Via Densely-Defined Multiplication Operators and Occupation Kernels. , John Kyei

Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani

Applied Analysis for Learning Architectures , Himanshu Singh

Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze

Recovering generators of principal ideals using subfield structure and applications to cryptography , William Youmans

Theses/Dissertations from 2022 2022

Application of the Riemann-Hilbert method to soliton solutions of a nonlocal reverse-spacetime Sasa-Satsuma equation and a higher-order reverse-time NLS-type equation , Ahmed Ahmed

New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana

Advances and Applications of Optimal Polynomial Approximants , Raymond Centner

Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty

On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly

Methods in Discrete Mathematics to Study DNA Rearrangement Processes , Lina Fajardo Gómez

Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He

Adversarial and Data Poisoning Attacks against Deep Learning , Jing Lin

Exploring the Vulnerability of A Neural Tangent Generalization Attack (NTGA) - Generated Unlearnable CIFAR-10 Dataset , Gitte Ost

Statistical Methods for Reliability Test planning and Data Analysis , Oluwaseun Elizabeth Otunuga

Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias

Effective Statistical and Machine Learning Methods to Analyze Children's Vocabulary Learning , Houston T. Sanders

Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi

A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman

Theses/Dissertations from 2021 2021

Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri

Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi

Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou

Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando

Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu

Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang

Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang

Theses/Dissertations from 2020 2020

Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi

Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun

Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu

On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman

Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek

Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen

Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan

Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop

On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink

Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang

Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala

Theses/Dissertations from 2019 2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian

Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar

Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil

Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter

Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz

Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi

Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi

Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos

The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva

Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak

Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich

An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado

Power Graphs of Quasigroups , DayVon L. Walker

Theses/Dissertations from 2018 2018

Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed

Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai

A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah

Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa

Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields

Generalizations of Quandles and their cohomologies , Matthew J. Green

Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu

Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou

Human Activity Recognition Based on Transfer Learning , Jinyong Pang

Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham

Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel

Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova

Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang

Theses/Dissertations from 2017 2017

Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack

Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon

On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill

Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill

Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly

Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera

Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao

Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati

Dynamics of Multicultural Social Networks , Kristina B. Hilton

Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi

Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally

Patterns in Words Related to DNA Rearrangements , Lukas Nabergall

Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na

Schreier Graphs of Thompson's Group T , Allen Pennington

Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya

Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo

Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi

Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou

Theses/Dissertations from 2016 2016

A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea

Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery

Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman

On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr

Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim

Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano

Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure

Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru

Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park

Leonard Systems and their Friends , Jonathan Spiewak

Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun

Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu

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Ph.D. Program

The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is conferred in recognition of marked ability and high attainment in advanced applied and computational mathematics, including the successful completion of a significant original research project. The program typically takes four to five years to complete, although this length may vary depending on the student. Below, we describe the requirements and expectations of the program. All graduate students require a 3.0 GPA to graduate (no exceptions).

Written Preliminary Exam

Upon entry into the Ph.D. program, students are required to take the Written Preliminary Exam, typically scheduled the week before classes start in the Fall semester. The coverage of the exam is in Linear Algebra, Advanced Calculus, Complex Variables, and Probability at the undergraduate level. Details of the exam can be found here: Preliminary Exam Details

The student must pass the exam to continue as a Ph.D. student. The Written Exam is offered in April and August. If the student fails on the first attempt, two more attempts are granted (three attempts total).

Course Requirements

The student must take the following six core courses:

• Analysis: AMCS 6081/6091 (MATH 6080/6090)
• Numerical Analysis: AMCS 6025/6035
• Probability and Stochastic Processes: AMCS 6481/6491 (MATH 6480/6490)

These six core courses are to be completed in the first and second years of graduate studies.

Ten elective courses (a total of 14 courses) are required for graduation. These elective courses should be chosen according to the interests and/or research program of the student and must contain significant mathematical content. Whether a given course can be counted toward AMCS elective course credit will be decided in consultation with the Graduate Chair. Recent courses approved for elective credit can be discussed with your advisor and the Graduate Group Chair.

Deviations from the above may be necessary or recommended depending on the individual student; such decisions are made with the approval of the graduate chair.

Choosing an Advisor

In the first two years of graduate studies, students must choose their thesis advisor. Some students already have an advisor to whom they have committed upon entry to the program. Other students will typically start working with their prospective advisors in the latter half of the first year or the summer between the first and second year.

The purpose of the oral exam is to assess a student’s readiness to transition into full-time research and eventually write his or her dissertation. This exam will be taken by the end of the third year of graduate study.

First, an oral exam committee must be formed, consisting of three faculty members, two of whom must belong to the AMCS graduate faculty. The student must then produce a document of up to about 20 pages describing the research proposal and background material, which is then approved by the oral exam committee before the exam. In the exam, the student will give an oral presentation to the committee. A discussion with the committee follows this. In the oral exam, the committee may ask the student about the presentation as well as about necessary background material as seen fit by the committee. If the student fails this exam, the student will have one more attempt.

Dissertation and Defense

The dissertation must be a substantial original investigation in the field of applied mathematics and computational science, done under the supervision of a faculty advisor. A Ph.D. Thesis Committee consists of at least three faculty members, including the thesis advisor. When the dissertation is complete, it must be defended in a Dissertation Exam, at which the student will be expected to give a short public exposition of the results of the thesis and to satisfactorily answer questions about the thesis and related areas.

Teaching Assistant

Full-time students admitted to our Ph.D. program who are offered a financial support package for four years of study are required to be teaching assistants during the second year. Students for whom English is not their native language are required to pass a test the “Speak Test” (IELTS) demonstrating proficiency in English. More information can be found on the English Language Programs  web page.

https://www.elp.upenn.edu/institute-academic-studies/requirements

Applied Mathematics

Faculty and students interested in the applications of mathematics are an integral part of the department of mathematics; there is no formal separation between pure and applied mathematics, and the department takes pride in the many ways in which they enrich each other. we also benefit tremendously from close collaborations with faculty and students in other departments at uc berkeley as well as scientists at  lawrence berkeley national laboratory  and visitors to the  mathematical sciences research institute.

The Department regularly offers courses in ordinary and partial differential equations and their numerical solution, discrete applied mathematics, the methods of mathematical physics, mathematical biology, the mathematical aspects of fluid and solid mechanics, approximation theory, scientific computing, numerical linear algebra, and mathematical aspects of computer science. Courses in probability theory, stochastic processes, data analysis and bioinformatics are offered by the Department of Statistics, while courses in combinatorial and convex optimization are offered by the Department of Industrial Engineering and Operations Research. Our students are encouraged to take courses of mathematical interest in these and many other departments. Topics explored intensively by our faculty and students in recent years include scientific computation and the mathematical aspects of quantum theory, computational genomics, image processing and medical imaging, inverse problems, combinatorial optimization, control, robotics, shape optimization, turbulence, hurricanes, microchip failure, MEMS, biodemography, population genetics, phylogenetics, and computational approaches to historical linguistics. Within the department we also have a  Laboratory for Mathematical and Computational Biology .

Chair:   Per-Olof Persson

Applied Mathematics Faculty, Courses, Dissertations

Senate faculty, graduate students, visiting faculty, meet our faculty, mina aganagic, david aldous, robert m. anderson, sunčica čanić, jennifer chayes, alexandre j. chorin, paul concus, james w. demmel, l. craig evans, steven n. evans, f. alberto grünbaum, venkatesan guruswami, ole h. hald, william m. kahan, richard karp, michael j. klass, hendrik w. lenstra, jr., lin lin (林霖), michael j. lindsey, c. keith miller, john c. neu, beresford n. parlett.

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College of Arts and Sciences

Mathematics, ph.d. in mathematics and applied mathematics.

The plan of work for the Ph.D. degree includes the comprehensive exam and qualifying examinations. Ph.D. in Mathematics students will all take the qualifying examination in the same two areas, Algebra and Real Analysis, within two years. Students in the Ph.D. in the Applied Program will follow a parallel policy and tested on two different areas, Statistics and Applied Probability for students in the Statistics track and Analysis and Differential Equations for students in the Applied Mathematics track.

In addition, each student will be required to prepare a written plan for additional advanced course work and substantial reading of research articles. An advanced topic examination will also be required in the third year. A general exam, in which the candidate describes the thesis program, and the doctoral dissertation and its defense complete the work for the Ph.D. degree. A student entering Lehigh without a masters degree must take 72 credits including at least 48 regular course credits (i.e. not dissertation credits). These students typically earn as Masters degree during the process of their work. A student entering Lehigh with a masters degree must take 48 credits including at least 18 regular course credits (i.e. not dissertation credits).

Program Requirements

View a list of recent phd graduates.

• Princeton University Doctoral Dissertations, 2011-2024

Applied and Computational Mathematics

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• News & Events
• Organizations
• Past PhD Dissertations
• Nicholas Barendregt Adaptive Decision-Making in Dynamic Environments Using Sequential Bayesian Inference
• Abe Ellison Gyroscopic Polynomials

Shay Gilpin A New Perspective on Covariance Propagation for Data Assimilation Applications

Evan Gorman On the Three-dimensional, Quadratic Differomorphism: Anti-integrability, Attractors, and Chaos

• Amanda Hampton On the Three-dimensional, Quadratic Differomorphism: Anti-integrability, Attractors, and Chaos
• Yifeng Mao Two-phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics
• Ruyu Tan Methods for Change Points Detection and Model Selection in State-Space Models
• Kris Tucker Analyzing Properties of Driven-Dissipative Quantum Systems from the Mean Field to Machine Learning
• Subekshya Bidari Models of Foraging Decisions in Social Animal Groups

Richard Clancy Mathematical Formulations with Uncertain Data in Optimization and Inverse Problems

Ellen Ellefsen Nonlocal Models with Applications in Ecology

• Daniel Ferguson Inference of Multiple Diffusion Coefficients from Single Particle Trajectories
• Mingyu Hu Micromagnetic modeling and waves in magnetic materials
• Nicholas Landry Contagion on Complex Systems: Structure and Dynamics
• Allen Alvarez Loya High-Order Methods for Wave Phenomena
• Daniel Messenger Weak-form Sparse Identification of Differential Equations from Noisy Measurements
• Liam Madden First-order Methods for Online and Stochastic Optimization, and Approximate Compiling
• Graham Kesler O'Connor Source Localization on Infection Networks
• Samuel Ryskamp Line Soliton Interactions and Dispersive Magnetoelastic Waves
• Lyndsey Wong Mathematical Models of Wealth Distribution Through An Amenities-Based Theory
• Kiera van der Sande Contributions to Computational Techniques and Machine Learning for Applied Science
• Sabina Altus Analysis of Multi-Structured Population Models
• Lewis Baker Inference of Multiple Diffusion Coefficients from Single Particle Trajectories
• Alec Dunton Matrix Methods for Low-Rank Compression in Large-Scale Applications
• Fortino Garcia Numerical Methods for Wave Phenomena
• David Gunderman High-order Spatial Discretization and Numerical Integration Schemes for Curved Geometries
• Erik Johnson Measuring image resolution in super-resolution microscopy and Bayesian estimation of population size and overlap and vaccine effectiveness
• Osman Asif Malik Topics in Matrix and Tensor Computations
• Nathaniel Mathews Computational Modeling for 3D Data Reconstruction of Solar Coronal Magnetic Fields
• Caleb Miller Monte Carlo Methods with Space Domain Applications
• Joy Mueller Perfectly Simulated and Exact Analytic Solutions for Chemical Reaction Networks and a Level Set Inspired Image Segmentation Algorithm
• Zofia Stanley Applications of Mathematics to Climate Modeling: Analysis and Development of Ocean Parameterizations and Multivariate Localization Functions
• Jeremy Thompson Local Fourier Analysis of Domain Decomposition and Multigrid Methods for High-Order Matrix-Free Finite Elements
• Lucia Minah Yang Numerical Analysis of Mixed Precision Algorithms and Time-steppers for Wave Turbulence, and Generative Modeling for Analogs in Data Assimilation
• Dylan Abrahamsen Space-time Evolution with Radial Basis Functions and Hermite-based Finite Difference Methods
• Joshua Aurand Optimal Control of Epstein-Zin Utility on Random Time Horizons
• Harry Dudley Dynamical System Analysis and Data-Driven Model Selection for Differential-Algebraic Equation Models of Microbial Electrolysis

Zhishen Huang Randomization in Statistical Machine Learning

• Mitchell Krock Some Models for Large Spatial Data
• Antony Pearson On Hidden Structures in Contaminated Symbolic Data
• Peter Shaffery Understanding the Variance Reduction Effect and Bayesian Structural Time Series for Behind-the-Meter Disaggregation
• Wenqi Zhang Statistical Approaches to Assess High Frequency Variability of Solar Irradiance
• Jacqui Wentz Spatial-temporal Effects of Diffusion in Complex Biochemical Networks
• Ashton Wiens Using Gaussian Processes for Registration and Nonstationarity Emulation
• Hao Xu Qualitative Analysis of Some Elliptic Differential Equations
• Tracy Babb Accelerated Time-Stepping of Parabolic and Hyperbolic PDEs via Fast Direct Solvers for Elliptic Problems
• Anna Broido Describing the Tails of Degree Distributions in Real-World Networks
• Jessica Gronski Non-Convex Optimization and Applications to Bilinear Programming and Super-Resolution Imaging
• Nathan Heavner Building Rank-Revealing Factorizations with Randomization
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Zachary Alexander A Topology-based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis

David Biagioni Numerical Construction of Green's Functions in High-dimensional Elliptic Problems with Variable Coefficients and Analysis of Renewable Energy Data via Sparse and Separable Approximations

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Daniel Larremore Critical Dynamics in Complex Excitable Networks

Douglas Lipinski Efficient Ridge Tracking Algorithms for Computing Lagrangian Coherent Structures in Fluid Dynamics Applications

Kuo Liu Hybrid First-Order System Least-Squares Finite Element Methods with the Application to Stokes and Navier-Stokes Equations

Matthew Reynolds Nonlinear Approximations in Tomography, Quadrature Construction, and Multivariate Reductions

Yuqi Wu Parallel Scalable Domain Decomposition Method for Simulating Blood Flows in Three-dimensional Compliant Arteries

Erin Byrne The Post-fragmentation Probability for Bacterial Aggregates

Adrianna Gillman Fast Direct Solvers for Elliptic Partial Differential Equations

Ian Grooms Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow

Sean Nixon Development and Applications of Soliton Perturbation Theory

Kristine Snyder Tuning and Control in Human Locomotion

Kye Taylor Modeling and Analysis of the Low-dimensional Geometry of Signal and Image Patch-sets

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Patrick Young Numerical Techniques for the Solution of Partial Differential and Integral Equations on Irregular Domains with Applications to Problems in Electrowetting

James Adler Nested Iteration and First Order Systems Least Squares on Incompressible Resistive Magnetohydrodynamics

Andrew Barker Parallel Monolithic Fluid-structure Interaction Algorithms with Application to Blood Flow Simulation

Benjamin Jamroz Reduced Modeling of the Magnetorotational Instability

Christian Ketelsen Least-squares Finite Element Methods for Quantum Electrodynamics

Michael Levy A High-order Element-based Galerkin Method for the Global Shallow Water Equations

Si Liu Parallel Fully Coupled Domain Decomposition Algorithm for Some Inverse Problems

Gregory Norgard Shock regularization of conservation laws through use of spatial averaging in nonlinear terms

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Seth Claudepierre Solar Wind Driving of Magnetospheric Ultra-Low Frequency Pulsations

Terry Haut Nonlocal Formulations of Ideal Fluids and Applications

Christopher Kurcz Fast Convolutions with Helmoholtz Green's Functions and Radially Symmetric Band-Limited Kernels

Joshua Nolting Efficiency-Based Local Adaptive Refinement for FOSLS Finite Elements

Cecile Piret Analytical and Numerical Advances in Radial Basis Functions

Geoffrey Sanders Extensions to Adaptive Smooth Aggregation (alphaSA) Multigrid: Eigensolver Initialization and nonsymmetric Problems

Michael Watson  A Study of Rotationally Constrained Convection in Tall Aspect Ratio Annular Geometries

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Julia Zuev Recent Advances in Numerical Partial Differential Equations

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Chad Westphal First-Order System Least Squares for Geometrically-Nonlinear Elasticity in Nonsmooth Domains

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Adriana Gómez-Hoyos (Dept. of Mathematics) Conservative Maps: Reversibility, Invariants and Approximation

Luke Olson Multilevel Least-Squares Finite Element Methods for Hyperbolic Partial Differential Equations

Cristina Perez Simulating the Interaction Between Intraseasonal and Interannual Variability in the Tropical Pacific with a Coupled System of Nonlinear Ordinary Differential Equations

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• Eric S. Wright Modeling and Analysis of Aqueous Chemical Reactions in a Diffusive Environment

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Brian Bloechle On the Taylor Dispersion of Reactive Solutes in a Parallel-Plate Fracture-Matrix System

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• Markus Berndt Adaptive refinement and the Treatment of Discontinuous Coefficients for Multilevel First-Order System Least Square (FOSLS)
• David Sterling Anti-integrable continuation and the destruction of chaos
• Lora Billings Dynamical Systems Methods Applied to Polynomial Factorization Families: a Study of Chaotic Attractors
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• Barry Lee First-Order Systems least Squares for Electromagnetics
• Alejandro Spina Confined States in Large Aspect Ratio Thermohaline Convection
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Ph.D. in Applied Mathematics

See the catalog copy of the description of the Ph.D. in Applied Mathematics program.

1. Overview

A student in the Ph.D. in Applied Mathematics degree program must maintain satisfactory academic progress towards completion of the degree. Student satisfactory academic progress is primarily assessed by: (a) satisfactory coursework performance, (b) the Qualifying Examination, (c) the Dissertation Topic Approval Defense, and (d) the Dissertation Defense. Courses and the Qualifying Examination are used to ensure that the student has the breadth as well as the depth of knowledge needed for research success. The Dissertation Topic Approval Defense is used to ensure that the scope of dissertation research is important, that the plan is well thought out, and that the student has sufficient skills and thoughtfulness needed for success. The Dissertation Defense is used to assess the outcomes of the dissertation research, and whether or not the plan agreed upon by the Dissertation Committee has been appropriately followed.

The key requirements and milestones for the Ph.D. in Applied Mathematics degree are provided below. Failure to satisfy the requirements can result in suspension or dismissal from the program.

• Minimum Hours
• Interdisciplinary Minor
• Core Courses
• Additional “Core” Courses
• Qualifying Examination
• Dissertation Committee
• Dissertation Topic Approval Defense
• Dissertation Defense

2. Minimum Hours

To earn a Ph.D. in Applied Mathematics degree, a student must complete at least 56 approved post baccalaureate credit hours. This includes 2 hours of Responsible Conduct of Research (GRAD 8302), at least 18 hours of dissertation research and reading (MATH 8994), and the hours for the interdisciplinary minor. Graduation requirements mandate that students must achieve a minimum grade point average of 3.0 to graduate. Receiving more than two grades of C or a single grade of U in any graduate course will result in a suspension from the program.

A limited amount of transfer credit is allowed. In accordance with rules of the UNC Charlotte Graduate School, students are allowed to transfer up to 30 semester hours of graduate credit earned at UNC Charlotte or other recognized graduate programs. Only courses with grades A or B may be accepted for transfer credit. To receive transfer credit, students must file an online request (and submit all necessary documents including copies of transcripts and course syllabi if requesting to transfer non-UNC Charlotte courses).

File an online request to transfer post-Baccalaureate credits at http://gpetition.uncc.edu .

3. Interdisciplinary Minor

The interdisciplinary minor may be satisfied by 9 hours of graduate work outside the mathematics department, by 6 credit hours for a directed project in an area of application (MATH 8691/8692), or by a combination of external coursework and a directed project in an area of application totaling 9 credit hours.

It is expected that interdisciplinary minor courses shall in general be in STEM disciplines, but if there are applications in the student’s dissertation work towards the social sciences, courses in those fields are allowed too. The following is a non-exhaustive list of interdisciplinary minor courses allowed for several fields.

Physics: PHYS 5222, 5232, 5242, 5271, 6101 through 6201, 6203 through 6211, 6221 through 6271. A common example is PHYS 6210, but 5242 and 5271 would also be along the same lines.

Optics: OPTI 8101, 8102, 8104, 8105, 8211 with 8102, 8104, and 8211 being particularly relevant.

Molecular Biophysics: PHYS 6108/OPTI 8000, PHYS 6204, PHYS 6610 ( https://mbp.charlotte.edu/ )

Mechanical Engineering: MEGR 6116, 7113, 7164 for students who have specialized in math of fluids, while 6141, 6125, 7102, 7142, and 7143 for those specializing in continuum mechanics and elasticity.

Computer Science: ITCS 6111, 6114, 6150, 6153, 6155, 6165, 6170, 6171, 6220, 6226 with 6114 commonly taken.

Finance and Economics: Any of FINN or ECON courses listed under the MS Mathematical Finance program. Common examples include FINN 6203, 6210, 6211, and ECON 6206, 6113, 6219.

Mathematics Education: Any graduate level MAED courses such as MAED 6122, 6123, 6124.

4. Core Courses

All students in the Ph.D. in Applied Mathematics degree program must take the following courses, regardless of their intended area of study:

• GRAD 8302 Responsible Conduct of Research (2 hours, usually required to take within the first year in the program)
• MATH 8143 Real Analysis I (3 hours)
• MATH 8144 Real Analysis II (3 hours)
• MATH 8994 Doctoral Research and Reading (at least 18 hours)

Students whose intended area of study is statistics or mathematical finance are also required to take

• MATH 8120 Theory of Probability I (3 hours)

5. Additional “Core” Courses

The following courses, though not explicitly required, are strongly recommended for each area of study.

Statistics: STAT 5123, 5124, 5126, 5127, 6115, 8127, 8133, 8135, 8137, 8139, 8122, 8123, 8027 (at least once)

Computational Math: MATH 5165, 5171, 5172, 5173, 5174, 5176, 8172, 8176

PDE and Mathematical Physics: MATH 5173, 5174, 8172

Probability: MATH 5128, 5129, 8120, 8125

Dynamical Systems: MATH 5173, 5174, 7275, 7276, 7277

Topology: MATH 5181, 8171, 8172 and independent study

Algebra: MATH 5163, 5164, 8163, 8164, and 8065 and/or independent study

Mathematical Finance: MATH 6202, 6203, 6204, 6205, 6206

6. Qualifying Examination

After being admitted to the Ph.D. program, a student is expected to take the qualifying examination within three semesters. This time limit may be extended up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination consists of two parts: the first part is a written examination based on Real Analysis I and II (MATH 8143/8144) or Theory of Probability I and Real Analysis I (MATH 8120/8143), the latter intended for a student with intended area of study in statistics or mathematical finance . The second part is a written examination based on two other courses chosen by the student to be specifically related to the student’s intended area of study and approved by the Graduate Coordinator. Typical choices for Part II are STAT 5126/5127, MATH 5173/5174, MATH 5172/5176, MATH 5163/5164, MATH 6205/6206, etc. The student may be allowed to retake a portion of the qualifying examination a second time if the student does not pass that portion on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. A student who does not complete the qualifying examination as per the regulations of the Graduate School will be terminated from the Ph.D. program.

Complete and submit the following form after taking the Qualifying Examination. (Qualifying Exam Report Form) -> Graduate School form.

7. Dissertation Committee

After passing the Qualifying Examination, the student must set up a Dissertation Committee of at least four graduate faculty members, which must include at least three graduate faculty members from the Department of Mathematics and Statistics and one member appointed by the Graduate School. The committee is chaired by the student’s dissertation advisor. If the dissertation advisor is a graduate faculty member from an outside department or institution, a graduate faculty member from the Department of Mathematics and Statistics must be a co-chair of the committee. The Dissertation Committee must be approved by the Graduate Coordinator. After identifying and obtaining the signatures of the Dissertation Committee faculty, the Appointment of Doctoral Dissertation Committee Form must be sent to the Graduate School for the appointment of the Graduate Faculty Representative.

The Dissertation Committee should be appointed as soon as it is feasible, usually within a year after passing the Qualifying Examination.

Complete and submit the following form within a year of passing the Qualifying Examination. (Appointment of Doctoral Dissertation Committee Form) -> Graduate School form.

8. Dissertation Topic Approval Defense

Each student must present and orally defend a Ph.D. dissertation proposal after passing the Qualifying Examination and within ten semesters of entering the Program. The Dissertation Topic Approval Defense will be conducted by the student’s Dissertation Committee, and will be open to faculty and students. The dissertation proposal must address a significant, original and substantive piece of research. The proposal must include sufficient preliminary data and a timeline such that the Dissertation Committee can assess its feasibility.

The student should provide copies of the written dissertation proposal to the Dissertation Committee at least two weeks prior to the oral defense. At the discretion of the Dissertation Committee, the defense may include questions that cover the student’s program of study and background knowledge and techniques in the research area. The Dissertation Committee will unanimously grade the Dissertation Topic Approval Defense as pass/fail according to the corresponding rubrics. A student may retake the Dissertation Topic Approval Defense if he/she fails the first time. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program. It is expected that the student first take the proposal defense by the ninth semester after enrollment to provide time for a second try should the first one fail. A doctoral student advances to Ph.D. candidacy after the dissertation proposal has been successfully defended. Candidacy must be achieved at least six months before the degree is conferred (so if you plan to graduate in a spring semester with the commencement on May 14, then you would need to successfully defend your dissertation topic by November 13 the prior year.)

The student must follow the following procedure in order to defend the dissertation proposal.

• Communicate with the Dissertation Committee to set up a date/time for the oral defense, and reserve a defense room for at least two hours .
• Send an electronic or written copy of the dissertation proposal to each member of the Dissertation Committee at least two weeks prior to the oral defense.
• Inform the Graduate Coordinator the schedule at least one week prior to the oral defense.

Complete and submit the following form only after successfully passing the Dissertation Topic Approval Defense. (Petition for Topic Approval Form) -> Graduate School Form.

9. Dissertation

Each student must complete and defend a dissertation based on a research program approved by the student’s dissertation advisor which results in a high quality, original and substantial piece of research. The student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. The Dissertation will be unanimously graded as pass/fail based on the corresponding rubrics by the Dissertation Committee and must be approved by the Dean of the Graduate School. Two attempts of the Dissertation Defense are permitted. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program.

The student must follow the following procedure in order to defend the dissertation.

• Communicate with the Dissertation Committee to set up a date/time for the public defense, and reserve a defense room for at least two hours with the help of the Graduate Coordinator.
• Send an electronic or written copy of the dissertation to each member of the Dissertation Committee at least three weeks prior to the public defense.
• Send an electronic copy of the dissertation in PDF as well as an abstract in a separate word file to the Graduate Coordinator at least two weeks prior to the public defense. The abstract is limited to 200 words, and does not have to be the same as the abstract included in the dissertation.
• Prepare a presentation that should be at least 45 minutes long.

Complete and submit the following forms after defending your Dissertation. (Dissertation Report for Doctoral Candidates Form) -> Graduate School Form.

Also, submit the Dissertation Title Page with Original Committee Signatures.

In addition, submit ETD Signature Form with original committee and student signatures to the Graduate School within 24 hours after defense.

10. Graduation

Detailed information about graduation including the dissertation manual can be found on the Graduate School’s Graduation website . The Graduation process consists of the following steps and all three are required to complete the graduation process.

• Complete the online graduation application – directions below – deadlines in the academic calendar.
• Submit an approved candidacy application to the Graduate School – directions below – deadlines in the academic calendar.
• Register for the term of graduation – deadlines in the academic calendar.

How to Apply for Graduation: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Online Graduation Application. Read the directions. Click “Continue” if this is the first time you have applied for graduation or “Create a New Application” if you have applied previously. After you complete all sections, remember to click the “Submit” button.

How to Access the Electronic Candidacy Application: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Apply for Candidacy for Graduate Students. Carefully read and follow all directions for each section. The total number of credit hours selected must be at least the minimum required for your degree or certificate. After you complete all sections, click the “Print” button. Do not change the page layout or formatting in any way. Take the printed document to your department for the Graduate Coordinator’s approval signature and then submit it to the Graduate School. Electronically submitted forms are not accepted.

Pay attention to the various deadlines in the official UNC Charlotte academic calendar , in particular, the following deadlines if you are planning to graduate.

• Deadline for graduate students to file candidacy form
• Deadline for graduate students to apply for graduation
• Doctoral dissertation pre-defense formatting consultation deadline
• Doctoral dissertation defense deadline
• Doctoral dissertation post-defense formatting consultation deadline
• Last day to submit doctoral dissertations to Graduate School

In addition, complete and submit the following forms to the graduate school.

• Complete Survey of Earned Doctorates at https://sed.norc.org/doctorate . Print the Certificate of Completion and submit to the Graduate School within 24 hours after defense.
• Contact Information Form
• Copyright and Open Access Publishing Payment Form (optional)

Finally, a sample graduation checklist for doctotal graduates can be found here . Make sure

• All courses with In Progress grades have been assigned grades; check with your advisor to ensure this happens. This must be completed 10 days prior to the commencement.
• All courses in the current term have been assigned grades; check with your advisor or instructor to ensure this happens. This must be completed 10 days prior to the commencement.

Applied and Computational Mathematics

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• Caltech Theses & Dissertations Includes all Caltech theses since 2002 (except for a few that are restricted) and many theses from before 2002.
• Caltech Theses All Caltech theses (print or electronic) can also be found in the library catalog.

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• URL: https://library.caltech.edu/ACM

Dissertations and Placements 2010-Present

Emily Dautenhahn Thesis: Heat kernel estimates on glued spaces Advisor: Laurent Saloff-Coste First Position:  Assistant Professor at Murray State University

Elena Hafner Thesis: Combinatorics of Vexillary Grothendieck Polynomials Advisor: Karola Meszaros First Position: NSF Postdoctoral Fellow,, at University of Washington

Sumun Iyer Thesis: Dynamics of non-locally compact topological groups Advisor: Slawomir Solecki First Position: NSF Postdoctoral Fellow at Carnegie Mellon University in Pittsburgh

Sebastian Junge Thesis: Applications of Transferring the Ramsey Property between Categories Advisor: Slawomir Solecki First Position: Lecturer at Texas State University

Nicki Magill Thesis: Infinite Staircases for Hirzebruch Surfaces Advisor: Tara Holm First Position: NSF Postdoctoral Fellow at UC Berkeley

Prairie Wentworth-Nice Thesis: Finite Groups, Polymatroids, and Error-Correcting Codes Advisor: Edward Swartz First Position: Postdoctoral Teaching Fellow at Johns Hopkins University

Fiona Young Thesis: Dissecting an Integer Polymatroid Advisor: Edward Swartz First Position: Pursuing her own start-up in the math education technology space

Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton

Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology

Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group  Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies

Andrew Melchionna Thesis: Opinion Propagation and Sandpile Models  Advisor: Lionel Levine First Position: Quantitative Researcher at Trexquant

Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University

Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington

Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC

Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University

Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington

Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University

Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University

Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University

Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine

David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky

Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université

Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute

Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota

Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal

Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa

Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology

Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine

Aleksandra Niepla Thesis:  Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross

Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group

Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania

Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College

Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University

Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz

Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria

Beihui Yuan Thesis:  Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University

Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago

Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management

Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance

Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University

Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota

Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs

Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia

Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign

Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading

Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA

Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One

Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison

Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University

Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com

Ian Pendleton Thesis:  The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm

Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft

Yujia Zhai Thesis:  Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes 

Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis

James Barnes Thesis:  The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College

Jeffrey Bergfalk Thesis:  Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico

TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna

Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba

Eduard Einstein Thesis:  Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)

Balázs Elek Thesis:  Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto

Kelsey Houston-Edwards Thesis:  Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College

My Huynh Thesis:  The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.

Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position:  Postdoctoral Associate at UFT (University Toronto)

Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute

Aliaksandr Patotski Thesis:  Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft

Ahmad Rafiqi Thesis:  On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil

Ying-Ying Tran Thesis:  Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher

Drew Zemke Thesis:  Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University

Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties  Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group

Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft

Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo

Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes

Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey

Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky

Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University

Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg

Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut

Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma

Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University

Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology

Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University

Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up

Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia 

Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas

Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of

David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore

Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France

Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore

Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC

Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University

Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University

Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher

Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland

Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs

Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense

Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University

Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy

Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft

Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan

Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago

Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University

Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network

Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto

Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine

Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario

Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow

Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track

Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto

Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College

Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft

Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs

Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis 

Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan

Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University

Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology

Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University

Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University

Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University

Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University

Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester

Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP

Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto

Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto

Mihai Bailesteanu  Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester

Owen Baker  Thesis:  The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University

Jennifer Biermann  Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University

Mingzhong Cai  Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison

Ri-Xiang Chen  Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China

Denise Dawson  Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University

George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind

Samuel Kolins  Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College

Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind

Ho Hon Leung  Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai

Benjamin Lundell  Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington

Eyvindur Ari Palsson  Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester

Paul Shafer  Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University

Michelle Snider  Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland

Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand

Russ Thompson  Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute

Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College

Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College

Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University

Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University 

Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard

Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University

• 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 2025 graduates is Friday, March 28, 2025 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 at 2:00PM. 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 2024.

Theses submitted in 2023

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.

In Applied Mathematics

• First-Year Exploration
• Areas of Application
• AM & Economics
• How to Declare
• Who are my Advisors?
• Secondary Field
• Research for Course Credit (AM 91R & AM 99R)
• AB/SM Information
• Peer Concentration Advisors (PCA) Program
• Student Organizations
• How to Apply
• PhD Timeline
• PhD Model Program (Course Guidelines)
• Oral Qualifying Examination
• Committee Meetings
• Committee on Higher Degrees
• Research Interest Comparison
• Collaborations
• Cross-Harvard Engagement
• Clubs & Organizations
• Centers & Initiatives
• Alumni Stories
• Graduate student stories
• Undergraduate Student Stories

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COLLEGE OF LIBERAL ARTS AND SCIENCES

Department of Mathematics

• Applied Mathematics
• Actuarial Science
• Algebra and Number Theory
• Geometry and Topology
• Mathematics Education
• Mathematical Finance
• Mathematical Logic
• Numerical Analysis
• Partial Differential Equations
• Probability Theory

Research Activity

• There is activity in the area of differential equations, particularly those arising in applications in science and engineering. Research is conducted in both the qualitative theory and the numerical solution of these equations on modern high speed computers. Particular emphasis is on equations arising from continuum mechanics.
• In the area of applied functional analysis, work is done on the application of analysis to problems in tomography and remote sensing.
• In the area of applied and numerical linear algebra the main emphasis is on the solution of large scale problems, computations in stochastic processes, and nonnegative matrices. In particular, there is interest in the development and analysis of new algorithms and their implementation on parallel and vector processing machines.
• Implementation of the Mountain Pass Theorem.
• PDE problems from material science.
• Other areas that are represented include mathematical physics and space-time structure.

Jeffrey Connors

Maksym Derevyagin

Dmitriy Leykekhman

Vadim Olshevsky

Alexander Teplyaev

Xiaodong Yan

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Mathematics PhD theses

A selection of Mathematics PhD thesis titles is listed below, some of which are available online:

2023   2022   2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Reham Alahmadi - Asymptotic Study of Toeplitz Determinants with Fisher-Hartwig Symbols and Their Double-Scaling Limits

Anne Sophie Rojahn –  Localised adaptive Particle Filters for large scale operational NWP model

Melanie Kobras –  Low order models of storm track variability

Ed Clark –  Vectorial Variational Problems in L∞ and Applications to Data Assimilation

Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes  

Chiara Cecilia Maiocchi –  Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems

Samuel R Harrison – Stalactite Inspired Thin Film Flow

Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability

Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions  

Jennifer E. Israelsson –  The spatial statistical distribution for multiple rainfall intensities over Ghana

Giulia Carigi –  Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics

André Macedo –  Local-global principles for norms

Tsz Yan Leung  –  Weather Predictability: Some Theoretical Considerations

Jehan Alswaihli –  Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations

Jemima M Tabeart –  On the treatment of correlated observation errors in data assimilation

Chris Davies –  Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems

Birzhan Ayanbayev –  Some Problems in Vectorial Calculus of Variations in L∞

Penpark Sirimark –  Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation

Adam Barker –  Path Properties of Levy Processes

Hasen Mekki Öztürk –  Spectra of Indefinite Linear Operator Pencils

Carlo Cafaro –  Information gain that convective-scale models bring to probabilistic weather forecasts

Nicola Thorn –  The boundedness and spectral properties of multiplicative Toeplitz operators

James Jackaman  – Finite element methods as geometric structure preserving algorithms

Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics

Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface

Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations

Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)

Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)

Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)

Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)

Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)

Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)

Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)

Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)

Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)

Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)

Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)

Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)

Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)

Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)

Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)

Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)

Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)

Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)

Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)

Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)

Mark Parsons - Mathematical Modelling of Evolving Networks

Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring

David Gilbert - Analysis of large-scale atmospheric flows

Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)

Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)

Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)

Cassandra A.J. Moran - Wave scattering by harbours and offshore structures

Ashley Twigger - Boundary element methods for high frequency scattering

David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)

Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)

Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)

Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)

Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)

Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)

Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)

Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)

R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)

G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)

C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.

P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)

L. Bennetts - Wave scattering by ice sheets of varying thickness

M. Preston - Boundary Integral Equations method for 3-D water waves

J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)

D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)

S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)

J.M. Morrell - A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF-7.7MB)

L. Watkinson - Four dimensional variational data assimilation for Hamiltonian problems

M. Hunt - Unique extension of atomic functionals of JB*-Triples

D. Chilton - An alternative approach to the analysis of two-point boundary value problems for linear evolutionary PDEs and applications

T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill

C. Hughes - On the topographical scattering and near-trapping of water waves

B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems

D.A. Bailey - A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows

M. Henderson - Extending the edge-colouring of graphs

K. Allen - The propagation of large scale sediment structures in closed channels

D. Cariolaro - The 1-Factorization problem and same related conjectures

A.C.P. Steptoe - Extreme functionals and Stone-Weierstrass theory of inner ideals in JB*-Triples

D.E. Brown - Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling

S.J. Fletcher - High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction

C. Johnson - Information Content of Observations in Variational Data Assimilation

M.A. Wakefield - Bounds on Quantities of Physical Interest

M. Johnson - Some problems on graphs and designs

A.C. Lemos - Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts

R.K. Lashley - Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems

J.V. Morgan - Numerical Methods for Macroscopic Traffic Models

M.A. Wlasak - The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling

M. Martin - Data Assimilation in Ocean circulation models with systematic errors

K.W. Blake - Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations

J. Hudson - Numerical Techniques for Morphodynamic Modelling

A.S. Lawless - Development of linear models for data assimilation in numerical weather prediction .

C.J.Smith - The semi lagrangian method in atmospheric modelling

T.C. Johnson - Implicit Numerical Schemes for Transcritical Shallow Water Flow

M.J. Hoyle - Some Approximations to Water Wave Motion over Topography.

P. Samuels - An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.

M.J. Martin - Data Assimulation in Ocean Circulation with Systematic Errors

P. Sims - Interface Tracking using Lagrangian Eulerian Methods.

P. Macabe - The Mathematical Analysis of a Class of Singular Reaction-Diffusion Systems.

B. Sheppard - On Generalisations of the Stone-Weisstrass Theorem to Jordan Structures.

S. Leary - Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.

I. Sciriha - On Some Aspects of Graph Spectra.

P.A. Burton - Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.

J.F. Goodwin - Developing a practical approach to water wave scattering problems.

N.R.T. Biggs - Integral equation embedding methods in wave-diffraction methods.

L.P. Gibson - Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.

A.K. Griffith - Data assimilation for numerical weather prediction using control theory. .

J. Bryans - Denotational semantic models for real-time LOTOS.

I. MacDonald - Analysis and computation of steady open channel flow .

A. Morton - Higher order Godunov IMPES compositional modelling of oil reservoirs.

S.M. Allen - Extended edge-colourings of graphs.

M.E. Hubbard - Multidimensional upwinding and grid adaptation for conservation laws.

C.J. Chikunji - On the classification of finite rings.

S.J.G. Bell - Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems.

D.J. Staziker - Water wave scattering by undulating bed topography .

K.J. Neylon - Non-symmetric methods in the modelling of contaminant transport in porous media. .

D.M. Littleboy - Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .

M.P. Dainton - Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .

M.H. Mawson - The shallow-water semi-geostrophic equations on the sphere. .

S.M. Stringer - The use of robust observers in the simulation of gas supply networks .

S.L. Wakelin - Variational principles and the finite element method for channel flows. .

E.M. Dicks - Higher order Godunov black-oil simulations for compressible flow in porous media .

C.P. Reeves - Moving finite elements and overturning solutions .

A.J. Malcolm - Data dependent triangular grid generation. .

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Department of Mathematics

Senior theses.

An undergraduate thesis is a singly-authored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research.  

To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project. The advisor will almost surely be a faculty member of the pure math department, though on occasion we have accepted theses written by people with applied math advisors. In these rare cases, the theses have been essentially pure math theses.

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