applied mathematics thesis topics

Recent Master's Theses - Applied Mathematics

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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 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

Models, Techniques, and Metrics for Managing Risk in Software Engineering , Andriy Miranskyy

Thermodynamics, Hydrodynamics and Critical Phenomena in Strongly Coupled Gauge Theories , Christopher Pagnutti

Molecular Dynamics Studies of Interactions of Phospholipid Membranes with Dehydroergosterol and Penetrating Peptides , Amir Mohsen Pourmousa Abkenar

Socially Responsible Investment in a Changing World , Desheng Wu

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©1878 - 2016 Western University

Applied Mathematics Research

In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.

Applied Mathematics Fields

• Combinatorics
• Computational Biology
• Physical Applied Mathematics
• Computational Science & Numerical Analysis
• Theoretical Computer Science
• Mathematics of Data

Applied Math Committee

Graduate Theses

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Seminar for Applied Mathematics

Student projects and theses, student projects.

If interested please contact the lecturer offering the project.

Note: Most projects are suitable for both students of mathematics and computational science and engineering.

Our research group focuses on the study of stability and regularization of ill-posed problems which arise in various applications. For such problems conventional solvers yield unreliable outputs, so that regularization techniques are necessary to produce trustworthy solutions. Research topics include medical imaging, phase retrieval (with application in coherent diffraction imaging and audio processing) and the vulnerability of deep neural networks. Theses projects on these topics are available, with possible emphasis on either implementation or analysis.

Our goal is to develop new mathematical models and methods of broad utility to science and engineering and to make fundamental advances in the mathematical and physical sciences themselves. We have been developing mathematical and computational frameworks to achieve super-resolution in biomedical imaging. Our work on biomimetics focuses on elucidating mechanisms exploited by bats and weakly electric fish for imaging. Nanophotonics is the study of electromagnetic wave phenomena in media structured on the same lengthscale as the wavelength, and is also a very active area of study in our group. Thesis projects on these current topics of research are available on request.

List of projects see here

The research of the group of S. Mishra focuses on the design, analysis and efficient implementation on state of the art high performance computing platforms, of robust numerical methods for nonlinear partial differential equations, particularly of the hyperbolic type, and their application in fluid dynamics, plasma physics, astrophysics, climate science and geophysics. We also address fundamental mathematical questions of well-posedness of nonlinear hyperbolic PDEs, particularly in the context of novel solution frameworks such as statistical solutions. Numerical methods, of the finite volume, finite difference, spectral and discontinuous Galerkin finite element type are developed in the group. Another focus area is on computational uncertainty quantification i.e efficient calculation of uncertainties in the solutions of PDEs that are driven by stochastic initial/boundary conditions, parameters and chaotic dynamics. Student projects for Bachelor, semester and Masters thesis are available on the whole range of topics from addressing fundamental mathematical questions to the design of efficient algorithms, HPC implementation and interesting applications.

Stu­dent pro­jects are avail­able in Math­em­at­ical Ana­lysis (er­ror es­tim­ates) and Com­puter Im­ple­ment­a­tion of ef­fi­cient dir­ect and in­verse prob­lem solu­tion for de­term­in­istic and stochastic Par­tial Dif­fer­en­tial Equa­tions with either many (sev­eral hun­dred) para­met­ers, or with solu­tions on very high di­men­sional state-​ and phase spaces. Mathematical techniques comprise (but are not limited to): Numerical Analysis of Partial Differential Equations (Finite Element Galerkin discretizations) see, e.g. https://math.ethz.ch/sam/research/reports.html?id=1031 https://math.ethz.ch/sam/research/reports.html?id=2020-67 Sparse Grid and Polynomial Chaos techniques Mathematics of Deep Learning (neural network approximation theory, deep neural network training, etc.), for numerical PDE approximation see, e.g. https://math.ethz.ch/sam/research/reports.html?id=2021-40 https://math.ethz.ch/sam/research/reports.html?id=2022-11 Monte-Carlo and Quasi-Monte Carlo integration in high dimensions see, e.g. https://math.ethz.ch/sam/research/reports.html?id=2022-10 external page J. Dick and M. Longo and Ch. Schwab: Extrapolated Lattice Rule Integration in Computational Uncertainty Quantification, SIAM/ASA Journ. Uncertainty Quantification, 10/2 (2022), pp. 651-686 call_made All Projects are closely related to current research topics, and can be extended to MSc and PhD thesis projects.

Selection of completed theses

• Yanchen He , Download Analytic regularity and hp-Discontinuous Galerkin approximation of viscous, incompressible flow in a polygon (PDF, 844 KB) vertical_align_bottom , 2021, supervisors Prof. Dr. Christoph Schwab and Dr. Carlo Marcati
• Marcello Longo , Download Higher order QMC integration with scrambling for elliptic PDEs with random coeffcients (PDF, 1.3 MB) vertical_align_bottom , 2019, supervisor Prof. Ch. Schwab
• Joost Opschoor, Download ReLU DNN expression of sparse gpc expansion in uncertainty quantification (PDF, 1 MB) vertical_align_bottom , 2018, supervisor Prof. Ch. Schwab
• Simon Etter, Download Parallel Tensor-Formatted Numerics for the Chemical Master Equation (PDF, 2 MB) vertical_align_bottom , 2015, supervisors Robert Gantner and Prof. Dr. Christoph Schwab
• Oded Stein, Download A Boundary Element Method for Eddy Currents (PDF, 2.6 MB) vertical_align_bottom , 2015, supervisor Prof. Ralf Hiptmair
• Ingmar Getzner, Download Examination of Measure Valued Solutions for the Magnetohydrodynamic Equations (PDF, 2.6 MB) vertical_align_bottom , 2014, supervisors Prof. Siddhartha Mishra and Dr. Roger Käppeli
• Samuel Lanthaler, Download Computation of Measure Valued Solutions of the Incompressible Euler Equations (PDF, 3.3 MB) vertical_align_bottom , supervisor Prof. Siddhatha Mishra
• Simon Laumer, Download Finite Difference Approach for the Measure Valued Vanishing Dispersion Limit of Burgers’ Equation (PDF, 1.9 MB) vertical_align_bottom , 2014, supervisor Prof. Siddhartha Mishra
• Jakob Zech, Download A Posteriori Error Estimation of hp-DG Finite Element Methods for Highly Indefinite Helmholtz Problems (PDF, 4.4 MB) vertical_align_bottom , 2014, supervisor Prof. Dr Stefan Sauter
• Lukas Herrmann, Download Isotropic Random Fields on the Sphere - Stochastic Heat Equation and Regularity of Random Elliptic PDEs (PDF, 1.4 MB) vertical_align_bottom , 2013, supervisors Dr. Annika Lang, Prof. Dr. Christoph Schwab 
• Yann Poltera, Download MLMC-FD method for 2D statistical solutions of the Navier-Stokes equations (PDF, 1.4 MB) vertical_align_bottom , 2013, supervisor Prof. Dr. Christoph Schwab
• Helga Thum, Download Numerical Simulations of the Weak Approximation Error for Parabolic Stochastic Partial Differential Equations (PDF, 706 KB) vertical_align_bottom , 2013, supervisor Prof. Dr. Arnulf Jentzen
• Yulia Smirnova, Download Calderon Preconditioning for Higher Order Boundary Element Method (PDF, 1.9 MB) vertical_align_bottom , 2013, supervisor Prof. Ralf Hiptmair
• Raffael Casagrande, Download Sliding Interfaces for Eddy Current Simulations (PDF, 7.1 MB) vertical_align_bottom , 2013, supervisor Prof. Ralf Hiptmair
• Simon Pintarelli, Download Local Multi-trace Boundary Element Formulation for Diffusion Problems (PDF, 2.9 MB) vertical_align_bottom , 2013, supervisor Prof. Ralf Hiptmair
• Michel Verlinden, Download Adaptive Galerkin Methods for Infinite Dimensional Parabolic Equations (PDF, 580 KB) vertical_align_bottom , 2012, supervisor Prof. Christoph Schwab
• Severin Thaler, Download The Criticality Spectral Problem in Neutron Transport (PDF, 1.4 MB) vertical_align_bottom , 2012, supervisor Prof. Christoph Schwab
• Robbin Tops, Download Numerical Pricing of American Options for gerneral Bivariate Lévy Models (PDF, 3.8 MB) vertical_align_bottom , 2012, supervisor Prof. Christoph Schwab
• Elke Spindler, Download Second Kind Single Trace Boundary Element Methods (PDF, 5.4 MB) vertical_align_bottom , 2012, Prof. Ralf Hiptmair
• D. Bernhardsgrütter, Download Multi-Level Monte Carlo Methods for Stochastic Parabolic and 2nd Order Hyperbolic PDEs (PDF, 3.7 MB) vertical_align_bottom , 2011, supervisor Prof. Dr. Christoph Schwab
• Daniel Kövi, Download hp Finite Element Method pricing algorithms for lookback options in Lévy Markets (PDF, 1.3 MB) vertical_align_bottom , 2011, supervisor Prof. Christoph Schwab
• Barry Thornton, Download Electricity Spot Price Modelling and Derivatives Pricing (PDF, 5.3 MB) vertical_align_bottom , 2010, supervisor Prof. Christoph Schwab
• Nathaniel Zollinger, Download Multi-Level Monte Carlo Finite Element Method for Elliptic Partial Differential Equations with Stochastic Data (PDF, 720 KB) vertical_align_bottom , 2010, supervisor Prof. Christoph Schwab
• Alberto Paganini, Download Efficient Convolution Based Impedance Boundary Conditions (PDF, 731 KB) vertical_align_bottom , 2011, supervisor Prof. Ralf Hiptmair
• Michael Spreng, Download Resolution of Skin Layer in EM Simulation (PDF, 865 KB) vertical_align_bottom , 2010, supervisor Prof. Ralf Hiptmair
• Stefan Siebenmann, Download A Scalable Eddy-Current Solver for ANSYS (PDF, 1.3 MB) vertical_align_bottom , 2010, supervisor Prof. Ralf Hiptmair
• Lisa Powers, Download Numerical Study of Small-Jump Regularization on Exotic Contracts in Lévy Markets (PDF, 1.4 MB) vertical_align_bottom , 2008, supervisor Prof. Christoph Schwab 
• Franz Piehler, Download Boundary element discretisation of asymptotic layer models (PDF, 879 KB) vertical_align_bottom , 2008, supervisor Prof. Ralf Hiptmair
• Claude Gittelson, Download Plane wave discontinuous Galerkin methods (PDF, 1.6 MB) vertical_align_bottom , 2008, supervisor Prof. Ralf Hiptmair
• Chris Bardgett, Download Pricing Convertible Bonds using Finite Elements (PDF, 400 KB) vertical_align_bottom , 2007, supervisor Prof. Christoph Schwab
• Simone Riva, Download Computation of electrostatic forces by the virtual work method (PDF, 1.4 MB) vertical_align_bottom , 2007, supervisor Prof. Ralf Hiptmair
• Jan Kayatz, Download Cone Strategies for Formal Deformations of Non-Collapsible Simplicial Complexes (PDF, 412 KB) vertical_align_bottom , 2006,supervisor Prof. Ralf Hiptmair
• Oliver Pfeifer, Download Asymptotische Methode zur Berechnung elektrostatischer Kräfte (PDF, 489 KB) vertical_align_bottom , 2006, supervisor Prof. Ralf Hiptmair
• Julien Renggli, Download Quadtree techniques for the construction of structured auxiliary meshes (PDF, 429 KB) vertical_align_bottom , 2006, supervisor Prof. Ralf Hiptmair
• Gisela Widmer, Download Auxiliary Space Method for Edge Elements (PDF, 706 KB) vertical_align_bottom , 2003/04, supervisor Prof. Ralf Hiptmair
• Benjamin Guélat, Download Régularité des solutions des problèmes d'élasticité et d'écoulement de Stokes dans un polygone (PDF, 2.3 MB) vertical_align_bottom , 2001, supervisor Prof. Christoph Schwab
• Thomas Haener, Download Numerical Solution of a Coefficient Identification Problem for the Poisson Equation (PDF, 3.9 MB) vertical_align_bottom , September 2014, supervisor Prof. Ralf Hiptmair
• Elke Spindler, Download A Posteriori Error Estimates for hp-FEM: Comparison and Implementation (PDF, 545 KB) vertical_align_bottom , 2010, supervisor Prof. Ralf Hiptmair
• Robert Gantner, Download Rayleigh Quotient Multigrid (PDF, 4.2 MB) vertical_align_bottom , 2011, supervisor Prof. Ralf Hiptmair
• Simon Pintarelli,  Download Duality based error estimation for electrostatic force computation (PDF, 13.6 MB) vertical_align_bottom , 2010, supervisor Prof. Ralf Hiptmair
• Julia Slipantschuk, Download Numerical Validation of Emergent Behavior in Flocks (PDF, 4.5 MB) vertical_align_bottom , 2008, supervisors Prof. Christoph Schwab, Claude Jeffrey Gittelson
• Sabine Elmiger, Download Convergence of Binomial Tree Methods for European/American Path-Dependent Options (PDF, 5.8 MB) vertical_align_bottom , 2008, supervisors Prof. Christoph Schwab
• Claude Gittelson, Download Non-equidistant approximate DFT based on Z-Splines (PDF, 382 KB) vertical_align_bottom , 2006, supervisor Prof. Ralf Hiptmair
• Nitya Afambo,  Download Generalized Tensor Models for Recurrent Neural Networks (PDF, 1.2 MB) vertical_align_bottom , 2020, supervisors Dr.  Maksim Rakhuba,  Prof. Christoph Schwab
• Simon Etter, Download MPI-Based Tensor Network Library (PDF, 528 KB) vertical_align_bottom , 2014, supervisors Robert Gantner, Vladimir Kazeev, Prof. Christoph Schwab (RW/CSE)
• Jakob Zech, Download Nonlinear n-term approximation for the solution of the dirichlet problem (PDF, 288 KB) vertical_align_bottom , 2013, supervisors Dr. Markus Hansen, Prof. Christoph Schwab
• Simon Härdi, Download Parallelization of a radiative transfer solver (PDF, 444 KB) vertical_align_bottom , 2012, supervisor Prof. Christoph Schwab
• Yulia Smirnova, Download Dual Mesh Calderon Preconditioning for the Single Layer Boundary Integral Operator (PDF, 5 MB) vertical_align_bottom , 2012, supervisor Prof. Ralf Hiptmair
• Raffael Casagrande, Download Implementation of impedance boundary conditions in HADAPT (PDF, 1.3 MB) vertical_align_bottom , 2012, supervisor Prof. Ralf Hiptmair
• Anders Rosero, Download Spurious Solutions for transient Maxwell equations in 2D (PDF, 1.1 MB) vertical_align_bottom , 2011, supervisor Prof. Ralf Hiptmair
• Yavor Stoev, Download Variance-optimal hedging error in geometric Lévy models (PDF, 530 KB) vertical_align_bottom , 2010, supervisor Prof. Christoph Schwab
• Jonas Sukys, Download Discontinuous Galerkin discretization of magnetic convection (PDF, 2.5 MB) vertical_align_bottom , 2010, supervisor Prof. Ralf Hiptmair
• Andreas Hiltebrand, Download Fast solvers for Eulerian convection schemes, (PDF, 328 KB) vertical_align_bottom 2010, supervisor Prof. Ralf Hiptmair
• Christoph Bossard, Download Hash Based Data Structures for Tetrahedral Meshes (PDF, 152 KB) vertical_align_bottom , 2005, supervisor Prof. Ralf Hiptmair
• Mathias Hack, Download Angle conditions for face and edge elements (PDF, 427 KB) vertical_align_bottom , 2005, supervisor Prof. Ralf Hiptmair
• Manuel Guidon, Download Transient Simulation of Eddy Currents in Ferromagnets (PDF, 3.7 MB) vertical_align_bottom , 2003/04, supervisor Prof. Ralf Hiptmair
• Philippe Corboz, Download Micromagnetism (PDF, 3.7 MB) vertical_align_bottom , 2003, supervisor Prof. Ralf Hiptmair

• Senior Thesis

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

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

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

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

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

Thesis Timeline

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

Mid to late August:

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

Early December:

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

Mid-January:

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

Early February:

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

On the thesis due date:

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

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

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

Thesis Readers

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

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

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

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

Thesis Examples

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

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

Recent thesis titles

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

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

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

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

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

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Ph.D. Program

The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is an advanced degree designed for those who wish to pursue a career involving applied mathematics research. It 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 Ph.D. program is designed to guide students, year-by-year , toward becoming researchers in applied mathematics. Typically the program takes four or five years to complete, including the dissertation (although it can be completed in less time, depending on the student).

There are several stages to the Ph.D. program. The first, which is centered on the course requirements and the Written Preliminary Exam, is designed to help the student acquire a broad background in applied mathematics and computational methods. The second stage includes the Ph.D. Oral Exam, and participation in seminars. Depth is one of the goals of this second stage, but the main objective at this point is to assist the student in choosing a field of specialization and in obtaining sufficient knowledge of this specialized field, including recent research developments, to begin to do independent research. Ph.D. students also have an opportunity to earn a masters degree at this stage. The third and key stage of the Ph.D. program is the dissertation (or "Ph.D. thesis"), in which the student will make an original contribution to applied mathematics and computational science. The entire Ph.D. program is designed to help students move toward taking this significant step in creating new mathematics for applications or new applications of mathematics. Along the way, the students are strongly encouraged to acquire some teaching experience, this skill being essential for those entering an academic Mathematics or Applied Mathematics career. As statistics is the language of experimental data analysis, students in the AMCS Ph.D. program are encouraged to satisfy and develope a proficiency in statistics and the analysis of data .  This can be accomplished through successful completion of a statistics course, at the level of STAT 915 or 970.

The program leading to this degree is described below, and may include work completed at the University of Pennsylvania for a Masters degree. (Up to eight courses taken at other universities, while a candidate for a graduate degree, can also be counted toward the Ph.D. requirements.)

Detailed requirements:

• Admission to candidacy: Admission to Ph.D. candidacy is achieved by passing the Ph.D. Oral Examination. Students must previously have passed the Written Preliminary Exam , and have taken at least six graduate  courses approved by the chair of the graduate group (including those taken elsewhere). 
• The Ph.D. Oral Examination: 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.  It is something of a hybrid between the subject-oriented oral exam administered by the Math department and the thesis proposal used in many fields of science and engineering. As part of this process, the student will choose, with the advice of the Graduate Group Chair, a Thesis Committee to help supervise his/her dissertation research. A detailed description of the exam can be found on the Ph.D. Oral Exam web-page.
• This PhD Thesis committee is appointed by the Graduate Group Chair after consultation with the student. It consists of three or more faculty members, at least two of whom are full members of the graduate group. 
• The PhD Oral Exam has two aspects:  
• The student must prepare a written research proposal, outlining the problem they plan to pursue for their dissertation research. This proposal should be between 10 and 20 double-spaced pages. In any case, not to exceed 20 pages. The proposal should explain the mathematical significance of the proposed research.
• The student must prepare a syllabus of background material, which is needed to pursue research in their chosen field. The syllabus of background material should be prepared about six months before the exam, and must be approved by the Graduate Group Chair.
•  The exam itself will consist of a presentation by the student of their thesis proposal, followed by an oral examination covering both the thesis proposal as well as  background material germaine to that proposal.
• The Graduate Group Chair notifies the AMCS faculty of the exam (date, time, place, committee members, reading lists). All affiliated faculty are to be invited, and are permitted to ask questions, however, only appointed members of the committee will vote on the candidate performance. 
• If the student has elected to write a Masters Thesis related to the topic of their PhD dissertation research (which is not common), then the oral defense of the Masters thesis may be combined with the  Ph.D. Oral Exam.
• Scheduling the Ph.D. Oral Exam: To take this exam, the student should have passed the Masters Preliminary Exam and be in good standing. The student also should have taken at least six approved graduate courses (including those taken elsewhere). The student discusses in advance the topics, syllabi and the composition of the oral exam committee with the Graduate Group Chair, whose written approval is needed. Normally, the exam is to be taken by the end of the first semester of the student's third academic year in the program. A one or two semester extension may be requested from the Graduate Group Chair. If the Ph.D. Oral Exam is not passed on the first try, it may be taken just once more, and this must occur before the end of the following semester. Passing the Ph.D. Oral Exam on the second try, at the latest, is a requirement for remaining in the Ph.D. program.
• Course Requirements: Twenty units of graduate courses, numbered 500 and above (or the equivalent), are required for the Ph.D. degree, including at least twelve courses taken at the University of Pennsylvania.  The bulk of these courses should be drawn from the list of approved courses.  (Independent study courses at Penn may be counted toward the twenty course requirement.) Among the courses, every student must take at least two semesters of graduate courses at the 600 level in each of applied algebra, and applied analysis, at least one semester of probability and stochastic processes, and one semester of computational science.  In general, eight of the courses should be taken in AMCS itself or in the Mathematics department.  After passing the oral exam/thesis proposal requirement, PhD students should register for 3CUs of dissertation research (AMCS 999) until they have accumulated the required 20 CUs. Once they have fulfilled this require they can register for AMCS 995, which carries no credits. To receive the Ph.D. degree a student must have at least a 3.0 cumulative grade point average. Sample programs of study in a range of fields can be found under the Academics menu bar. The Graduate Group Chair may, in exceptional cases, modify the requirement that at least 10 of the 20 graduate courses for the Ph.D. be in AMCS or mathematics. A maximum of 6 of these 20 courses may be reading courses (independent studies).
• Seminar Requirement: It is expected that all advanced graduate students will regularly attend and participate in at least one seminar series each semester.  First and second year students are required to attend the AMCS colloquium talks, and all students are strongly encouraged to do so.  It is expected that students will give at least one, and hopefully a number of seminar talks to audiences of students and faculty. Guidance in the preparation of these lectures is provided by faculty members in the graduate group. The intention is for the student to gain experience in digesting and presenting advanced material and in fielding questions about it before an audience of scientists, as well as actively participating in research interactions and being a part of the  community of graduate students in the AMCS graduate group.
• Teaching: In order to gain experience in classroom teaching, students are strongly encouraged  to serve as a teaching assistant or instructor for at least two semesters. Teaching for more than two semesters is encouraged, especially for those students who plan to teach after their Ph.D. Graduate students must participate in a TA training program offered by the Mathematics department before they begin their teaching.
• The Dissertation: The dissertation, also known as the "Ph.D. thesis", is the heart of the Ph.D. program. It must be a substantial original investigation in a field of applied mathematics and computational science, done under the supervision of a faculty advisor.
• The Ph.D. Thesis Committee: This committee is appointed by the Graduate Group Chair after consultation with the student, at the time of the PhD Oral Exam. It consists of, at least, three faculty members, including the thesis advisor, and meets at least once a year with the student to discuss his or her progress and to offer guidance.
• Dissertation Examination: 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.
• The Dissertation Exam Committee: This committee is appointed by the Graduate Group Chair after consultation with the student, and consists of three or more faculty members, at least one of whom is a full member of the AMCS graduate group, and at least one of whom is from the area of specialization of the thesis. It will normally include the Thesis committee appointed at the time of the student's PhD Oral Exam.  All AMCS faculty are to be invited to attend the Final Disseration Exam, however only those appointed by the Graduate Group Chair are voting members of the Exam Committee.
• The student must deliver a finished copy of the Ph.D. thesis to the graduate secretary at least two weeks before the Final Dissertation Exam, so that it will be available for reading by the AMCS faculty.
• Timing for the Final Dissertation Exam: This must be successfully completed no later than six years after entering the graduate program. It should occur no later than the end of the third academic year after admission to Ph.D. candidacy. In exceptional situations, the Graduate Group Chair may, after consultation with the Graduate Advising Committee, provide an extension.
• Satisfaction of Requirements: When not otherwise specified, this is determined by the Graduate Group Chair, in consultation with the Graduate Advising Committee and involved faculty members and (in the case of the teaching requirement) the Undergraduate Chair.