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Applied Mathematics Department

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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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.

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Mathematics PhD theses

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

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

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. .

applied mathematics phd thesis

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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.
  • Submit dissertation defense announcement to the general public at least 10 days prior to the scheduled defense date through https://graduateschool.charlotte.edu/current-students/graduation-clearance/submit-dissertation-defense-announcement.
  • 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 .

Please 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 apply for graduation
  • Doctoral dissertation pre-defense formatting consultation deadline (may no longer be required)
  • Doctoral dissertation defense deadline
  • Doctoral dissertation post-defense formatting consultation deadline (may no longer be required)
  • Last day to submit doctoral dissertations to Graduate School

Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right. 

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the  Graduate Policies  pages. 

General Ph.D. Requirements

  • 10 semester-long graduate courses, including at least 8 disciplinary.   At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses.  Undergraduate-level courses cannot be used.  For details on course requirements, see the school's overall PhD course requirements  and the individual program pages linked therein.
  • Program Plan (i.e., the set of courses to be used towards the degree) approval by the  Committee on Higher Degrees  (CHD).
  • Minimum full-time academic residency of two years .
  • Serve as a Teaching Fellow (TF) in one semester of the second year.
  • Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
  • Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing.  For details see the "G3+ Committee Meetings" section of the Policies of the CHD  and the individual program pages linked therein.
  • Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself.  For details of arranging your final oral exam see the  Ph.D. Timeline  page.
  • Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

  • a Secondary Field (which is similar to a "minor" subject area).  SEAS offers PhD Secondary Field programs in  Data Science and in  Computational Science and Engineering .   GSAS  lists  secondary fields offered by other programs.
  • a Master of Science (S.M.) degree conferred  en route to the Ph.D in one of several of SEAS's subject areas.  For details see here .
  • a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the  Health Sciences and Technology graduate program  with Harvard Medical School and MIT.  Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

In Applied Mathematics

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Ph.D. Program

Introduction.

These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the  Graduate Student Resources  page and the  Doctoral Degree Policies  of the graduate school. Students are expected to be familiar with these procedures and regulations.

The Doctor of Philosophy program

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions that are relevant to a significant area of application.

Course requirements for the Ph.D. program

  • AMATH 561, 562, 563
  • AMATH 567, 568, 569
  • AMATH 584, 585, 586
  • AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year.
  • Students must take a minimum of 15 numerically graded courses. At most two of these can be at the 400 level or be cross listed with courses at the 400 level. Graduate level courses previously taken at UW (e.g., during a Master's program) count toward this requirement. Graduate level courses taken outside of UW may count toward the requirement for 15 numerically graded courses with the approval of the Graduate Program Coordinator. The entire course of study of a student and all exceptions to this list must be approved by the Graduate Program Coordinator and the student’s advisor or faculty mentors.

For students who entered the doctoral program autumn 2017 or autumn 2018, please see these degree requirements. For students who entered the doctoral program prior to autumn 2017, please see these degree requirements.  

Faculty mentoring

Upon arrival, incoming students will be assigned two faculty mentors. Until a student settles on an advisor, the faculty mentors aid the student in selecting courses, and they each guide the student through a 2-credit independent reading course on material related to the student’s research interest. The faculty mentors are not necessarily faculty in the Department of Applied Mathematics.

Faculty advisor

By the end of a student’s first summer quarter, an advisor must be determined.  T he advisor provides guidance in designing a course of study appropriate for the student’s research interests, and in formulating a dissertation topic.

A full Supervisory Committee should be formed four months prior to the student’s General Exam. The full Supervisory Committee should have a minimum of three regular members plus the Graduate School Representative , and will consist of at least two faculty members from Applied Mathematics, one of whom is to be the Chair of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chair. The dissertation advisor may be from another department,  or may have an  affiliate  (assistant, associate, full) professor appointment with the Applied Mathematics department  and is then also a member of the Supervisory Committee.

The Dissertation Reading Committee , formed after the General Exam,  is a subset of  at least   three members from the Supervisory Committee   who are appointed to read and approve the dissertation.  Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty. At least one of the committee members must be a member of the core  Applied Mathematics faculty. It is required that this member is present for both the general and final examination, and is included on the reading committee.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of the Supervisory Committee. It is suggested that the student meet with the Supervisory Committee at least once a year to discuss their progress until the doctoral thesis is completed.

Examination requirements for the Ph.D. program

Students in the Ph.D. program must pass the following exams:

  • The  qualifying exam
  • The  general exam
  • The  final exam  (defense)

Satisfactory performance and progress

At all times, students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.4/4.0 or better. Satisfactory progress on the examination requirements consists of passing the different exams in a timely manner. Departmental funding is contingent on satisfactory progress.   The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress .   The Department of Applied Mathematics follows these recommended guidelines of the Graduate School including an initial warning, followed by a maximum of three quarters of probation and one quarter of final probation, then ultimately being dropped from the program.    We encourage all students to explore and utilize the many available  resources  across campus.

Expected academic workload

A first-year, full-time student is expected to register for a full course load, at least three numerically graded courses, typically totaling 12-18 credits. All other students are expected to consult with their advisor and register for at least 10-18 credits per quarter.  Students who do not intend to register for a quarter must seek approved  academic leave  in order to maintain a student status.   Students who do not maintain active student status through course registration or an approved leave request need to request reinstatement to rejoin the program. Reinstatement is at the discretion of the department. Students approved for reinstatement are required to follow degree requirements active at time of reinstatement. 

Annual Progress Report

Students are required to submit an Annual Progress Report to the Graduate Program Coordinator by the second week of Spring Quarter each year. The annual progress report should contain the professional information related to the student’s progress since the previous annual report. It should contain information on courses taken, presentations given, publications, thesis progress, etc., and should be discussed with the student's advisor prior to submission. Students should regard the Annual Progress Report as an opportunity to self-evaluate their progress towards completing the PhD. The content of the Annual Progress Report is used to ensure the student is making satisfactory progress towards the PhD degree.

Financial assistance

Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student’s thesis supervisor, to the Graduate Program Coordinator.

Master of Science program

Students in the Ph.D. program obtain an M.Sc. Degree while working towards their Ph.D. degree by satisfying the  requirements for the M.Sc. degree.  

Additional Ph.D. Degree Options and Certificates

Students in the Applied Mathematics Ph.D. program are eligible to pursue additional degree options or certificates, such as the  Advanced Data Science Option  or the  Computational Molecular Biology Certificate .  Students must be admitted and matriculated to the PhD program prior to applying for these options. Option or certificate requirements are in addition to the Applied Mathematics degree requirements. Successful completion of the requirements for the option or the certificate leads to official recognition of this fact on the UW transcript.

Career resources, as well as a look at student pathways after graduation, may be found   here.

FAQs |  Contact the Graduate Program  |  Apply Now

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  • PhD Step-by-Step Guide

These are the general steps to obtain your PhD in Applied Mathematics at CU Boulder.

Schedule for obtaining your PhD

  • 18 credit hours must be from APPM at 5000+ level.
  • The 18 hours of APPM credits must include 5600 & 5610 (numerics I & II), 5440 & 5450 (analysis I & II), and one more approved \sequence" (see supplement for a list of approved sequences).
  •  6 credit hours must be a two-course out-of-department sequence. This sequence needs approval (pre-approval recommended!) from graduate chair. Must be at 5000+ level, and not duplicate material taught by APPM.
  • Two 1 credit seminar courses are required. Must be taken after the rst year.
  • You must maintain a GPA of 3.0 or better, and earn at least a B- in each class.
  • Doctoral students must take and pass two preliminary exams by August at the end of their first year.
  • In January, first-year PhD students can choose to take either PDEs or Statistics.
  • In May, first-year PhD students can choose to take either Applied Analysis or Numerical Analysis.
  • Make-up exams are offered in August.
  • You may take any one exam no more than two times. 

The Graduate Chair will be the advisor for all incoming students.  Once the student has selected an area of specialization and found an Advisor who will take them on, they will inform the Graduate Chair and the Graduate Coordiator.  This usually happens after the students passes their Preliminary Exams and start to focus of their dissertation.

If you are planning on using transfer credits from another accreditied University.  Please review this form below and submit the appropriate paperwork.

​ Request for Transfer of Credit

The purpose of the comprehensive exam is to ensure that the student has a sufficient grasp of the fundamentals of the chosen thesis area to begin research, the ability to exchange ideas and information with the members of the examining board (thesis committee), and a broad base of knowledge in applied mathematics. 

Before the comprehensive exam, the Ph.D. student must submit a 5-10 page thesis proposal, complete with motivation for the topic and references to key papers, to each member of the thesis committee.  This proposal should be written in consultation with the chair of the thesis committee.

The exam will consist of a presentation by the student on his/her research proposal for a maximum of one hour in length, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program. 

Students will need to be registered in classes for the semester they are going to complete their examination for it to count towards that semester. This includes the summer semester.

  • Select Committee (see rules on Exam Report)
  • Schedule Comprehensive date and location with Graduate Coordinator
  • Get Graduate Chair signature/approval
  • Make copy for Graduate Coordinator
  • Submit original to Graduate School
  • Submit Title and Abstract to Graduate Coordinator to post in department (at least 2 weeks prior to Comp date) See example  or .tex file
  • Have Committee Chair pick up Exam folder from Graduate Coordinator prior to Comp Exam. (Graduate Coordinator will have it ready at least 48 hrs. prior to Exam time)
  • Turn original and copy to Graduate Coordinator
  • This needs to be submitted with the Completed Comprehensive Exam Report. Your Comprehensive final will not be submitted to the Graduate School without your Candidacy Application.

The exam will consist of a presentation by the student on his/her research proposal, followed by a questioning period of up to one additional hour.  The presentation portion is open to all faculty and students in the program. 

  • Submit Title of Thesis to Graduate School – see doctoral deadlines  for dates
  • Print a copy of Thesis Signature page, get original signatures and submit the form directly to the Graduate School. 
  • Have Committee Chair pick up Exam Report from Graduate Coordinator prior to Thesis Defense. (Graduate Coordinator will have it ready at least 48 hrs. prior to Exam time)
  • Submit Thesis to Graduate School electronically - see doctoral deadlines  for dates and instructions.
  • One copy must be printed single sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight.
  • The other two copies can be printed double sided, on 8.5 x 11 watermarked paper of at least 25 % cotton and 20# weight. 
  • Submit Thesis to CU Electronic Scholars Depository - see instructions .
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applied mathematics phd thesis

Doctoral Program (PhD)

complex equations.

UB's doctoral program in mathematics aims toward generating career options for our students. Additionally, the program guides students toward being prepared for research by the end of third year of coursework.

As reported by the American Mathematical Society, mathematician was the #1 rated career in CareerCast’s Job Rated 2014 report. Individual who have demonstrated a high level of mathematical acumen by obtaining a PhD in mathematics are highly prized in both the academic and private sector job markets.

The requirements below are for students admitted in Fall 2016 and later. The main steps in completing a PhD are:

(A) First Year's Coursework and Evaluation exams— Successfully completing the first year's 6 core courses and passing at least 4 out of 6 evaluation exams attached to these courses. For students interested in pursuing research in pure mathematics the 6 core courses are in algebra, analysis and geometry/topology. For students interested in pursuing research in applied mathematics the 6 core courses are in analysis, numerical analysis and methods in applied mathematics.

(B) Oral Examination and Advancing to Candidacy— An oral examination covering material in advanced topics and research ideas in the student's chosen area of research. This oral examination is also the final requirement for advancement to candidacy and should be taken before the end of the student's third year.

(C) PhD Thesis and Final Oral Examination— Writing a dissertation and passing an oral defense.The dissertation must consist of original research of sufficient quality for publishing in a respectable mathematics journal.

After the 1st year's course work, the student will take more advanced courses at the 600 level and 700/800 level topics course. Entering their 3rd year, students will focus on their preferred area of research. Advancement to candidacy and dissertation work requires passing an oral exam. Students should pass their oral examination prior to the end of the 3rd year of the program.

In addition to these primary steps, the program offers a 1st year mentoring seminar meant to help students in their career development and management. Topics covered include: study mathematics; using LaTex; media in research mathematics; documenting your achievements; writing, editing and publishing mathematics; seminars, conferences and workshops; and, job options for PhD's in mathematics.  

This mentoring seminar will also include faculty talks directed at graduate students, presenting their area of research.

Both the MA and the PhD degrees have residency requirements: one year for the MA and two years for the PhD.

On this page

Phd program requirements.

The main steps in obtaining a PhD in mathematics are: (A) Satisfactory completion of first year's coursework and evaluation exams; (B) Passing oral exam in intended area of research and advancing to candidacy; and, (C) Writing the dissertation and successfully defending it in a final oral exam. The aspects of each step are more fully discussed on this page.

(A) First Year's Coursework and Evaluation exams

The course schedule outlined below is for students in the PhD program who are supported by a teaching assistantship and tuition fellowship. It is 9-credits per semester. For students who do not have support an additional 3-credit course is require so as to be a full time student. 

Learning mathematics is a shared enterprise. Thus, all members of an entering doctoral class advance through the first year coursework as a cohort.

Fall semester:

  • MTH 534, Basic Measure Theory.
  • MTH 519, Introduction to Abstract Algebra.
  • MTH 527, Introduction to Topology I.  
  • MTH 539, Methods of Applied Mathematics.
  • MTH 537, Introduction to Numerical Analysis I.
  • One of:  MTH 534, Basic Measure Theory; or MTH 519, Introduction to Abstract Algebra; or MTH 527, Introduction to Topology I.

Spring semester offering:

  • MTH 625, Complex Variables.
  • MTH 520, Advanced Linear Algebra.
  • MTH 528, Introduction to Topology II.  
  • MTH 540, Methods of Applied Mathematics II.
  • MTH 538, Introduction to Numerical Analysis II.
  • One of:  MTH 639 Fourier Analysis; or, MTH 625, Complex Variables. MTH 520, Advanced Linear Algebra. MTH 528, Introduction to Topology II.

Evaluation Exams: Attached to each first year course is an evaluation exam. This exam will be given during the regularly scheduled final exam time. All first year evaluation exams are pass/fail.  To continue in the PhD program a student needs to achieve at least 4-out-of-6 exam passes. To continue in the MA program a student needs to achieve at least a 3-out-of-6 exam passes. To be in good standing in any graduate program a student needs a GPA of B or above.

Deficiency:  Students whose performance at the end of their 1st year is judged to be significantly insufficient by the Graduate Director will be dismissed from the program before the beginning of their 2nd year. Students who are marginally below the mark (e.g., pass 2 out of 4 exams or better at PhD level) and/or are marginally below the required B-GPA level, so that they can still advance with their original cohort, have an opportunity to retake the relevant exams in the final exam week of the Fall and Spring semesters in their 2 nd  year. If the student passes these “make ups’’ (i.e., pass 4-out-of-6 in total for PhD and 3-out-of-6 for MA), then the student will be allowed to advance through the program along with their original cohort. If not, then the student will be dismissed from the program.

(B) Oral Examination and Advancing to Candidacy

After the first year's course work, the student will take more advanced courses at the 600 level and 700/800 level topics course. Students also typically arrange individual reading courses with professors and participate in area seminars.

Entering their third year, students will be focusing on their preferred area of research and the faculty with whom they would like to work. Students will be required to form an oral examination committee of two or three faculty members chaired by a potential thesis advisor.

Students will work with their committee to prepare a syllabus outlining topics to be covered in the oral examination including a bibliography of books and/or articles. Typically the topics to be covered in the oral examination should be at the level of 600 to 800 level courses and include material that the student learned individually.

The syllabus must be approved by the Graduate Director’s office and the student’s committee members. Students should pass their oral examination prior to the end of the third year of the program.

(C) PhD Thesis and Final Oral Examination

The final departmental steps in attaining the degree is completion of a dissertation that must consist of original research of sufficient quality for publishing in a respectable mathematics journal. It is not unusual for the mathematics in a single dissertation to generate two or three published manuscripts.

PhD Thesis Template

Student resources and related links.

Jenny Russell

Assistant to the Graduate Director

Department of Mathematics

227 Mathematics Building, Buffalo, NY 14260-2900

Phone: 716-645-8782; Fax: 716-645-5039

Email: [email protected]

For those students admitted to the program in 2015, the prior requirements remain in effect.

The main steps in completing a PhD are: passing qualifying examinations; and, writing a dissertation.

The qualifying examinations are taken in several parts. During the first year of full-time study, the student must pass the First Qualifying Examination, an exam on basic material from undergraduate algebra and analysis. During the second year, the student must pass a more advanced, but quite flexible Second Qualifying Examination based on courses at the 600 level and above. By the end of the third year, the student must pass another exam, the nature of which will vary from student to student, and depends primarily on the student's area of study and thesis advisor.

The dissertation must consist of original research of sufficient quality to be published in a respectable mathematics journal. Upon completion of the second qualifying exam, the student will choose (in consultation with the director of graduate studies) a doctoral committee, the chair of which will direct the thesis research. Upon completion of the thesis, the student must pass a final oral examination administered by the department.

The week before classes begin in August, all new M.A. and Ph.D. students must take the First Qualifying Examination . The syllabus for this exam is based on undergraduate analysis and algebra (including linear algebra). This exam is given before classes begin to enable the student and the director of graduate studies to refer to its results while deciding the most appropriate courses for the student.

The main steps in obtaining a PhD are passing the qualifying examinations, writing a thesis, and passing a final oral examination on this thesis. The departmental regulations concerning each of these are given below. The regulations are interpreted by the graduate studies committee which, on written petition from a student, may permit deviations from the rules, provided there are exceptional circumstances. In addition to the departmental regulations, there are university requirements which must also be satisfied.

Admission with Advanced Standing At the time of admission to UB's Graduate School, the director of graduate studies may decide that certain students have advanced standing of one or two semesters of graduate work, depending on UB Graduate School requirements. This will be done after examining the graduate records of the students and taking account of his previous courses, the institutions where he studied, his proficiency in English (TOEFL), etc. It will be clear from what follows that such students will have to fulfill various requirements more quickly than normally admitted students.

Definition of Total Semesters of Graduate Work The sum of the semesters of graduate work as defined by (i) and (ii) below yields the total semesters of graduate work which will simply be called "semesters of graduate work".

(i) A student admitted with graduate coursework may credited with one or two semesters of graduate work, according to Graduate School requirements.

(ii) For every semester at SUNYAB that a student is registered for fewer than nine credit hours, the credit hours are to be totaled and divided by nine. The result, rounded down to the next integer, will also be counted as semesters of graduate work. In no event will a student be said to have completed more than two semesters of academic work in one calendar year.

Deficiency A student is considered to have a deficiency if in the first semester as a graduate student at UB,  the student officially enrolls in, and completes, Math 519 (introductory algebra) or Math 531 (introductory real variables). The student should base her/his decision on whether to take these courses on advice from the director of graduate studies and on evaluation of the student's knowledge in algebra and analysis by the relevant area committees.

First Qualifying Examination

The First Qualifying Exam is a three-and-a-half-hour written examination based on a syllabus covering introductory real variables at the level of MTH 431-432, introductory abstract algebra at about the level of MTH 419, and linear algebra at about the level of MTH 420. The examination is given twice a year, during the week prior to the beginning of each semester.

The purpose of the first examination is to assist the director of graduate studies and the student in deciding soon after the student's entry into the UB Graduate School, whether or not the student will be admitted to the the PhD program in mathematics.

Normally, to remain in the PhD program, a student is required to pass this examination within the first two years of graduate work. A student who entered with a deficiency is not required to pass this examination until the first opportunity after completiing two semesters of graduate work. See the Syllabus for the First Qualifying Examination (Revised 04/25/13) attached as a pdf, below.

Second Qualifying Exam This consists of two three-hour area examinations, selected by each student from the following four choices: ALGEBRA; ANALYSIS; GEOMETRY/TOPOLOGY; and DIFFERENTIAL EQUATIONS. It is the purpose of the second qualifying examination to insure that each student has a rudimentary command of at least two "core" areas of mathematics.

To remain in the PhD program a student is required to obtain a grade of A or B for one of the area examinations no later than the beginning of his fourth semester of graduate work and an average of at least B for both of the area exams no later than the beginning of his fifth semester. Students may repeat the examinations, within the time limit, without penalty and are encouraged to take at least one of the examinations as early as possible. See Information on the Second Quaifying Examination, attached as a pdf, below.

Doctoral Committee During the semester in which he completes the Second Qualifying Examination, each student will select a major professor, who is a member of the graduate faculty, in consultation with the director of graduate studies. The latter and the major professor will then choose the student's doctoral committee, consisting of at least three members of the faculty with the major professor as chair.

Admission to Candidacy The student's doctoral committee will set the requirements for admission to candidacy. These are subject to the approval of the director of graduate studies and may include, but are not restricted to, any of the following: an oral examination on "research level" material, a project, a series of lectures on "research level" mathematics, or a written qualifying examination in another department. These requirements must be satisfied by the end of the sixth semester of graduate work.

Language Requirements There are no language requirements.

Additional Course Work Before the final oral exam, each student should pass, with a grade of A, B , or S , two one-semester graduate course in subjects other than those of his or her second qualifying exam. These courses are to be approved by the director of graduate studies. Each PhD student must complete 72-credit hours from: (a) selected 500 level mathematics courses; (b) 600-800 level Mathematics courses, with the exception of thesis guidance, seminar courses, and other courses of this nature; (c) courses designated by his/her major professor.

PhD Thesis and Final Oral Examination

The final departmental steps in attaining the degree of Doctor of Philosophy are:

1. Completion of a thesis satisfactory to the major professor and the student's doctoral committee;

2. Approval by the UB Graduate School that the student proceed to examination on his/her thesis at a final oral examination;

3. Submission of the thesis to each member of the doctoral committee at least three weeks prior to the final oral examination;

4. Passing the final oral examination.

Program Requirements for students admitted Fall 2015 and earlier

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Applied Mathematics - Doctor of Philosophy (PhD)

With internationally recognized faculty and a strong commitment to its graduate program, the Department of Applied Mathematics at CU Boulder strives to provide graduate students a high-quality education and training in applied mathematics while preparing them for careers in industry, laboratories and the academic professions. 

The department fosters extensive interaction between students and faculty to provide a tailored educational experience in applied mathematics. Currently, the department has both faculty and  affiliated faculty  from other academic departments and colleges. A PhD student can be advised by core faculty or co-advised by an affiliate involved in applied mathematics which creates a definitively unique learning experience in many areas of physical, biological, computational or engineering sciences. With the breadth of such a diverse faculty, a student can explore their academic and research interests through the investigation of numerous ongoing faculty projects.

Many of our PhD students have had the opportunity to conduct their research at world-class institutes located right here in Boulder such as the National Center for Atmospheric Research, National Institute of Standards and Technology, and the National Oceanic and Atmospheric Administration. Our students have the opportunity to not only work directly with organizations here in Boulder but also the National Renewable Energy Lab and the Laboratory for Atmospheric and Space Physics, along with many other national research laboratories. 

The Department of Applied Mathematics offers coursework and research leading to the PhD degree in applied mathematics. The aim of the department is to train graduate students to perform independent research on the methods and applications of applied mathematics. Research areas represented in the department include:

  • computational mathematics
  • mathematical biology
  • mathematical geosciences
  • applied nonlinear PDEs and dynamics
  • statistics and data science
  • stochastic processes and applications 

For more information on the department and degree requirements, download the supplement to the catalog or visit the Applied Mathematics website.

PhD with Certificate in Interdisciplinary Quantitative Biology

Applied mathematicians interested in collaborations with bioscientists will need a breadth of knowledge in quantitative bioscience to be successful. The interdisciplinary quantitative biology (IQ biology) graduate certificate program emphasizes training at the intersection of biochemistry, biology, computer science, engineering, applied mathematics and physics. The PhD in applied mathematics with a certificate in IQ biology will strengthen this training with additional foundations in numerical and mathematical analysis, probability and statistics, mathematical biology and network analysis.

Candidates interested in this program should apply directly to IQ biology and select applied mathematics as one of their graduate programs of interest. In addition to satisfying the requirements for the PhD in applied mathematics, students in this program must take 12 credit hours in three IQ biology core courses (Quantitative Biology Foundations, Statistics and Computations for Genomes and Meta-Genomes and Forces in Biology), which can serve as the out-of-department sequence for the PhD, as well as three 10-week rotations in labs associated with the IQ biology program.

For more information, visit the BioFrontiers Institute's IQ Biology PhD Program website.

Requirements

Required courses and credits, preliminary exams, comprehensive exams, dissertation defense.

A minimum of 60 credits is required for the degree, including 30 credits in courses numbered 5000 or above ( APPM 5350 ,  APPM 5360 , APPM 5570 and APPM 5720 generally do not count toward this requirement) and 30 credits of applied math dissertation credit.

A grade of B -  or higher must be attained in each course. PhD students must maintain a grade point average of 3.0 or better each semester.

  • Preliminary exams are offered in four areas: Applied Analysis and Numerical Analysis are mandatory. Students can choose either Partial Differential Equations or Probability & Statistics.
  • Exams are offered in January and in August.
  • Possible "grades" on a prelim are "Research Pass," "Pass" and "Fail." Students need to pass all three exams, and need a research pass in either Applied Analysis or Numerical Analysis. 
  • Students may take any one exam no more than two times.
  • To be considered to make good progress towards the degree (for purposes of getting TAs renewed, etc.), students should normally have at least one pass before their third semester, and one pass and one research pass before their fourth semester.

The purpose of the comprehensive exam is to ensure that the student has a sufficient grasp of the fundamentals of the chosen thesis area to begin research, the ability to exchange ideas and information with the members of the examining board (thesis committee), and a broad base of knowledge in applied mathematics. 

Before the comprehensive exam, the PhD student must submit a 5–10 page thesis proposal, complete with motivation for the topic and references to key papers, to each member of the thesis committee. This proposal should be written in consultation with the chair of the thesis committee.

The exam will consist of a presentation by the student on his/her research proposal for a maximum of one hour in length, followed by a questioning period of up to one additional hour. The presentation portion is open to all faculty and students in the program. 

Students will need to be registered in classes for the semester they are going to complete their examination for it to count toward that semester. This includes the summer semester.

  • Select committee (see rules on Exam Report) and schedule comprehensive date and location. Then inform Graduate Coordinator ( [email protected] ). 
  • Complete  Doctoral Comprehensive Exam form for committee approval (select comprehensive; at least 3 weeks prior to Comp Date).
  • Submit title and abstract to  [email protected] to post in department (at least 2 weeks prior to comp date) See example or  .tex file.
  • Complete Candidacy application  to PhD.

The exam will consist of a presentation by the student on his/her research proposal, followed by a questioning period of up to one additional hour. The presentation portion is open to all faculty and students in the program. 

Students will need to be registered in classes for the semester they are going to complete their examination for it to count towards that semester. This includes the summer semester.

  • Select committee members (see rules on Exam form) and inform the Graduate Coordinator.
  • Complete  Doctoral Exam f orm  for committee approval (at least 2 weeks prior to Defense Date).
  • Submit a Thesis Approval Form  (TAF) to ensure that the final copy has been accepted by the thesis committee. The TAF must be uploaded as a supplemental file with the thesis in order for the submission to be complete. 
  • One copy must be printed single-sided, on 8.5" x 11" watermarked paper of at least 25 percent cotton and 20# weight.
  • The other two copies can be printed double-sided, on 8.5" x 11" watermarked paper of at least 25 percent cotton and 20# weight. 
  • Submit thesis to CU Electronic Scholars Depository (see instructions on the About Institutional Repositories webpage).
  • Complete the Survey of Earned Doctorates (contact Graduate Coordinator for details).

Plan of Study

The track below is a sample curriculum for students who are interested in focusing on partial differential equations.

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Mathematical Modeling Doctor of Philosophy (Ph.D.) Degree

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The mathematical modeling Ph.D. enables you to develop mathematical models to investigate, analyze, predict, and solve the behaviors of a range of fields from medicine, engineering, and business to physics and science.

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Overview for Mathematical Modeling Ph.D.

Mathematical modeling is the process of developing mathematical descriptions, or models, of real-world systems. These models can be linear or nonlinear, discrete or continuous, deterministic or stochastic, and static or dynamic, and they enable investigating, analyzing, and predicting the behavior of systems in a wide variety of fields. Through extensive study and research, graduates of the mathematical modeling Ph.D. will have the expertise not only to use the tools of mathematical modeling in various application settings, but also to contribute in creative and innovative ways to the solution of complex interdisciplinary problems and to communicate effectively with domain experts in various fields.

Plan of Study

The degree requires at least 60 credit hours of course work and research. The curriculum consists of three required core courses, three required concentration foundation courses, a course in scientific computing and high-performance computing (HPC), three elective courses focused on the student’s chosen research concentration, and a doctoral dissertation. Elective courses are available from within the School of Mathematics and Statistics as well as from other graduate programs at RIT, which can provide application-specific courses of interest for particular research projects. A minimum of 30 credits hours of course work is required. In addition to courses, at least 30 credit hours of research, including the Graduate Research Seminar, and an interdisciplinary internship outside of RIT are required.

Students develop a plan of study in consultation with an application domain advisory committee. This committee consists of the program director, one of the concentration leads, and an expert from an application domain related to the student’s research interest. The committee ensures that all students have a roadmap for completing their degree based on their background and research interests. The plan of study may be revised as needed. Learn more about our mathematical modeling doctoral students and view a selection of mathematical modeling seminars hosted by the department.

Qualifying Examinations

All students must pass two qualifying examinations to determine whether they have sufficient knowledge of modeling principles, mathematics, and computational methods to conduct doctoral research. Students must pass the examinations in order to continue in the Ph.D. program.

The first exam is based on the Numerical Analysis I (MATH-602) and Mathematical Modeling I, II (MATH-622, 722). The second exam is based on the student's concentration foundation courses and additional material deemed appropriate by the committee and consists of a short research project.

Dissertation Research Advisor and Committee

A dissertation research advisor is selected from the program faculty based on the student's research interests, faculty research interest, and discussions with the program director. Once a student has chosen a dissertation advisor, the student, in consultation with the advisor, forms a dissertation committee consisting of at least four members, including the dissertation advisor. The committee includes the dissertation advisor, one other member of the mathematical modeling program faculty, and an external chair appointed by the dean of graduate education. The external chair must be a tenured member of the RIT faculty who is not a current member of the mathematical modeling program faculty. The fourth committee member must not be a member of the RIT faculty and may be a professional affiliated with industry or with another institution; the program director must approve this committee member.

The main duties of the dissertation committee are administering both the candidacy exam and final dissertation defense. In addition, the dissertation committee assists students in planning and conducting their dissertation research and provides guidance during the writing of the dissertation.

Admission to Candidacy

When a student has developed an in-depth understanding of their dissertation research topic, the dissertation committee administers an examination to determine if the student will be admitted to candidacy for the doctoral degree. The purpose of the examination is to ensure that the student has the necessary background knowledge, command of the problem, and intellectual maturity to carry out the specific doctoral-level research project. The examination may include a review of the literature, preliminary research results, and proposed research directions for the completed dissertation. Requirements for the candidacy exam include both a written dissertation proposal and the presentation of an oral defense of the proposal. This examination must be completed at least one year before the student can graduate.

Dissertation Defense and Final Examination

The dissertation defense and final examination may be scheduled after the dissertation has been written and distributed to the dissertation committee and the committee has consented to administer the final examination. Copies of the dissertation must be distributed to all members of the dissertation committee at least four weeks prior to the final examination. The dissertation defense consists of an oral presentation of the dissertation research, which is open to the public. This public presentation must be scheduled and publicly advertised at least four weeks prior to the examination. After the presentation, questions will be fielded from the attending audience and the final examination, which consists of a private questioning of the candidate by the dissertation committee, will ensue. After the questioning, the dissertation committee immediately deliberates and thereafter notifies the candidate and the mathematical modeling graduate director of the result of the examination.

All students in the program must spend at least two consecutive semesters (summer excluded) as resident full-time students to be eligible to receive the doctoral degree.

Maximum Time Limitations

University policy requires that doctoral programs be completed within seven years of the date of the student passing the qualifying exam. All candidates must maintain continuous enrollment during the research phase of the program. Such enrollment is not limited by the maximum number of research credits that apply to the degree.

National Labs Career Fair

Hosted by RIT’s Office of Career Services and Cooperative Education, the National Labs Career Fair is an annual event that brings representatives to campus from the United States’ federally funded research and development labs. These national labs focus on scientific discovery, clean energy development, national security, technology advancements, and more. Students are invited to attend the career fair to network with lab professionals, learn about opportunities, and interview for co-ops, internships, research positions, and full-time employment.

Students are also interested in: Applied and Computational Mathematics MS

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The College of Science consistently receives research grant awards from organizations that include the National Science Foundation , National Institutes of Health , and NASA , which provide you with unique opportunities to conduct cutting-edge research with our faculty members.

Faculty in the School of Mathematics and Statistics conducts research on a broad variety of topics including:

  • applied inverse problems and optimization
  • applied statistics and data analytics
  • biomedical mathematics
  • discrete mathematics
  • dynamical systems and fluid dynamics
  • geometry, relativity, and gravitation
  • mathematics of earth and environment systems
  • multi-messenger and multi-wavelength astrophysics

Learn more by exploring the school’s mathematics research areas .

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Curriculum for 2023-2024 for Mathematical Modeling Ph.D.

Current Students: See Curriculum Requirements

Mathematical Modeling, Ph.D. degree, typical course sequence

Concentrations, applied inverse problems, biomedical mathematics, discrete mathematics, dynamical systems and fluid dynamics, geometry, relativity and gravitation, admissions and financial aid.

This program is available on-campus only.

Full-time study is 9+ semester credit hours. International students requiring a visa to study at the RIT Rochester campus must study full‑time.

Application Details

To be considered for admission to the Mathematical Modeling Ph.D. program, candidates must fulfill the following requirements:

  • Complete an online graduate application .
  • Submit copies of official transcript(s) (in English) of all previously completed undergraduate and graduate course work, including any transfer credit earned.
  • Hold a baccalaureate degree (or US equivalent) from an accredited university or college.
  • A recommended minimum cumulative GPA of 3.0 (or equivalent).
  • Submit a current resume or curriculum vitae.
  • Submit a statement of purpose for research which will allow the Admissions Committee to learn the most about you as a prospective researcher.
  • Submit two letters of recommendation .
  • Entrance exam requirements: None
  • Writing samples are optional.
  • Submit English language test scores (TOEFL, IELTS, PTE Academic), if required. Details are below.

English Language Test Scores

International applicants whose native language is not English must submit one of the following official English language test scores. Some international applicants may be considered for an English test requirement waiver .

International students below the minimum requirement may be considered for conditional admission. Each program requires balanced sub-scores when determining an applicant’s need for additional English language courses.

How to Apply   Start or Manage Your Application

Cost and Financial Aid

An RIT graduate degree is an investment with lifelong returns. Ph.D. students typically receive full tuition and an RIT Graduate Assistantship that will consist of a research assistantship (stipend) or a teaching assistantship (salary).

Additional Information

Foundation courses.

Mathematical modeling encompasses a wide variety of scientific disciplines, and candidates from diverse backgrounds are encouraged to apply. If applicants have not taken the expected foundational course work, the program director may require the student to successfully complete foundational courses prior to matriculating into the Ph.D. program. Typical foundation course work includes calculus through multivariable and vector calculus, differential equations, linear algebra, probability and statistics, one course in computer programming, and at least one course in real analysis, numerical analysis, or upper-level discrete mathematics.

Recent Master's Theses - Applied Mathematics

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Master's Theses 2024

Master's theses 2023, master's theses 2022, master's theses 2019, master's theses 2018, master's theses 2017, master's theses 2016, master's theses 2015, master's theses 2014, master's theses 2013, master's theses 2012, master's theses 2011, master's theses 2010, master's theses 2009, master's theses 2008, master's theses 2007.

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Department of Applied Mathematics University of Waterloo Waterloo, Ontario Canada N2L 3G1 Phone: 519-888-4567, ext. 32700 Fax: 519-746-4319

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Grad student handbook, general information about your graduate program.

Applied Mathematics

  • Degree Requirements (PDF at Grad Studies) - 2010
  • Degree Checklist (M.S.)
  • Degree Checklist (Ph.D.)
  • Applied, M.S., Master's Plan I (Thesis) Requirements
  • Applied, M.S., Master's Plan II (Comprehensive Examination) Requirements
  • Applied, Ph.D. Requirements
  • List of Faculty

Mathematics

  • Degree Requirements (PDF at Grad Studies) - 2021 , 2019 , 2007
  • Degree Checklist  (M.A. and Ph.D.)
  • Math, M.A., Master's Plan II (Comprehensive Exam) Requirements
  • Math, Ph.D. Requirements

Departmental Forms and Submission (for Current Math Students ONLY)

  • EMAIL Study List & Variable Unit forms to [email protected] .
  • UPLOAD to your Box.com folder by [email protected] at the beginning of the quarter.
  • Upload the signed version to your Box folder, do not change the file name.

Office of Graduate Studies (additional forms/policy)

  • Grad Studies FORMS
  • DATES & DEADLINES

Who's Who in the Department: From Staff to Students to Faculty

Throughout your career here in the Department, you will come into contact with a variety of individuals, from staff to students to faculty. For more information about the people you will encounter and what it is they do, please reference the following:

  • General Departmental Contact Information
  • Faculty Profiles
  • Faculty in the Graduate Group in Applied Mathematics
  • The Graduate Students

Unsure whom to contact? Please start with the Student Services Staff. Their office is located in the administrative office suite (MSB 1130) on the first floor . Or, you may email your questions to [email protected] .

The Galois Group is another resource to whom you can turn. Feel free to contact current Galois Group Officers or email us at [email protected] .

Finding Your Faculty Adviser

Initial Faculty Adviser

Initial faculty advisers are assigned to newly admitted students. All members of the Department's Graduate Program Committee (GPC) and the Graduate Group in Applied Mathematics (GGAM), including the committee chairs, serve in this capacity. The incoming students are equally divided among the serving members and, to the degree possible, distributed in accordance with the student's area of interest.

Selecting a Thesis Adviser

Attending research seminars is an important beginning step toward finding a thesis adviser. For this reason, the Department gives unit credit for attending research seminars (MAT 290s), as well as reading groups (MAT 298s or MAT 290s). To sign up for Individual or Group Reading please use the Variable Unit Form . For more information about our student-run seminars, also look under the Course Information section of this handbook or go to the Seminars/Colloquium web page.

You can find research information on departmental faculty and GGAM faculty , as well links to individual pages. And to view a list of the articles being produced by members of the Department, please check out out our publications page .

A list of advanced students sorted by their thesis adviser is provided on our website, which is helpful for the student who is not quite ready to approach faculty directly. The Department's student-run Galois Group has posted many helpful hints on many topics including how to select a thesis adviser.

Please note that only when you advance to candidacy (via the Candidacy form) and name your thesis committee members, including your chair, is the name of your thesis adviser officially recorded with the Graduate Studies Office. Until that point, when you first arrive here, you are assigned an initial adviser and that is only recorded in your Departmental file. Before advancing to candidacy, you may have a prospective faculty member in mind as a thesis adviser or find that a faculty member other than your initial adviser seems a better "fit" for you. If this faculty member agrees to serve as your unofficial adviser, keep the Student Services staff apprised so that any evaluation paperwork can be directed to him/her instead of your initial adviser.

If you have any questions or concerns about this process, please consult with a Student Services staff member or write to [email protected] .

Mentoring Guidelines

The campus Graduate Council's Mentoring Guidelines are available for further reference about the relationship between you and your thesis adviser.

Course Information

University Catalog

The University provides a UC Davis General Catalog of all courses online. They also provide a PDF version that can be downloaded or printed as desired.

Schedule of Mathematics Courses

Information about our courses, including day, time, instructor, and Course Registration Numbers (CRN), are noted on this web page. Additionally, you can obtain a glimpse of the entire academic year by selecting "All courses for the Academic Year."

Posted Syllabi of Mathematics Courses

These are Departmentally-approved generic syllabi. They are made available on our website and should be viewed as an advisory tool. When taking a course, the instructor's syllabus is the official one for that particular course.

Seminars/Colloquium

You are encouraged to attend several of these; it's a beginning step to finding a thesis adviser. Closer to the start of the quarter, check our web page for details. Not all seminar Course Registration Numbers (CRN) will be noted on our webpage. The organizers decide whether or not to make the CRN public on our website. If, for example, an organizer knows a seminar will not be meeting regularly, it isn't appropriate to give unit credit. If an organizer intends a student to register, he/she will determine the unit allocation plan. In terms of how many units, some might give one unit for simply attending, and perhaps as much as three for special presentations. Organizers will be indicated on our website. If you have any questions about how seminars are organized, contact the organizers.

Registering for Individual Study with a Faculty Member

You may obtain research units when working with individual faculty members. These courses are MAT 298s (Group Study; letter grading), MAT 299s (Individual Study; S/U grading), and MAT 299Ds (Dissertation Research; S/U grading). When registering for these classes, you are required to submit a Variable Unit Course Request form, which is available in the Student Services Office. This form must be completed with the faculty member you intend to work with and filed with the Student Services Office. Quarter-specific Course Registration Numbers (CRN) can be obtained from a Student Services staff member.

If you have any questions or concerns about this process, please consult a Student Services staff member or write to [email protected] .

Registration

General Registration Information: What You Need to Know

Well before the start of each quarter, it is strongly recommended that you register for 12 units of "something" to maintain your full-time student status AND your eligibility to receive financial support. In doing so, please be mindful of the following:

  • Consult your program brochure about specific course requirements.
  • Complete your quarterly study list.
  • Register for no less than 12 units for each and every quarter.

After you have initially registered for your courses, it is then recommended that you make an appointment with your faculty adviser to review your course schedule and discuss your study list.

Graduate students are not assigned appointment times to register for classes and may enroll any time during all registration periods, which can be obtained via the Academic Calendar . If you are a new student to the program, you can find further registration guidelines on the Office of the University Registrar registration page , as well as Preparing to Register .

As mentioned above, you are also required to complete a quarterly study list with your faculty adviser at the start of each quarter. Your study list must include all courses registered for that quarter and be signed by you and your faculty adviser. Once complete and signed, your study list should be returned to the Student Services Office for processing.

Using Schedule Builder and Course Registration Numbers (CRN)

To use Schedule Builder , you will need your UC Davis Login ID (this is NOT your math department account) and password. Graduate students can establish their UC Davis Login ID online at http://computingaccounts.ucdavis.edu/ . Please allow at least 48 hours prior to the day you wish to enroll to ensure your account is active.

To register, you will need the CRN (Course Registration Number), which is available on our courses page or in the Class Schedule and Registration Guide . A number of graduate courses are listed TBA (to be announced) in terms of time and location. Usually, the instructor sends out an email indicating an organizational meeting during which day/time are agreed upon. Or, they might just organize via email.

For CRNs, you may also refer to our courses web page for additional details and options. For example, when known, this is where we will provide the title of a specific MAT 280 or special topics courses, and list which seminars (MAT 290s) are being offered and by whom. In fact, before referring to the Class Schedule and Registration Guide, it may be easier to refer to our courses web page first.

Is the Math class you want closed? Please contact a staff adviser in the Student Services Office.

Be mindful of the last day to add and the last day to drop courses. For these and other important deadlines, as well as fee information, finals schedule, academic calendar, the online catalog, etc., please visit the Registrar's website .

Milestones: Exams, Quals, Candidacy, Dissertation etc.

Please use the links below.

Master's Examination (Mathematics program only)

  • For the Mathematics MA, the candidate must pass the master's comprehensive examination offered each year at the beginning of the Fall and Spring quarters. Typically, this occurs before the start of instruction.
  • This is a written exam that comprises the material covered in 201AB (analysis) and 250AB (algebra).

Preliminary Examinations

Prelim Dates : Preliminary examinations for the PhD degree in Mathematics and Applied Mathematics are offered each year at the beginning of the Fall and Spring quarters. Typically, this occurs before the start of instruction. See the schedule HERE .

Prelim Timeline:

  • Mathematics PhD : the Preliminary Examination is a written examination which comprises of graduate material in Analysis, Algebra, and Topology as covered in the following six graduate courses: 201AB, 250AB, 215A and 239. The exam consists of three parts: Analysis (201AB), Algebra (250AB), and Topology (215A, 239). The exam is written and administered by the GPC. The exam is offered twice yearly, normally at the beginning of the Fall and Spring quarters. Students in the Ph.D. program may take any or all three parts, during a given offering of the exam. Students in the Ph.D. program must pass two of the three parts of the Preliminary Exam by the beginning of the student’s 7th quarter. Passing two of the three parts is considered fulfilling the Preliminary Examination requirement.
  • Applied Mathematics PhD : the preliminary exam is a written exam covering MAT 201AB and MAT 207ABC. The exam is offered at the beginning of Fall and Spring quarters every year. Ph.D. students are required to pass this examination before the end of their second year in the Applied Mathematics program (and if they entered with a Master's, by October of their second year). They may take the examination multiple times; what matters is when they pass, not how many attempts.
  • Please consult your original support letter for additional information about the timing of exams.
  • Mathematics: Workshops, Exam Prep, and Sample Exams
  • Applied Mathematics: Workshops, Exam Prep, and Sample Exams

Qualifying Examinations

The purpose of the qualifying examination is to determine whether you are capable of independent research. Once you pass this examination, you will petition to advance to candidacy. For international students, once they advance to candidacy, the nonresident tuition will be waived for three calendar years. Your thesis adviser should be seen as a valuable resource when preparing for your qualifying examination. In other words, they can help inform you of what to expect during the qualifying examination itself.

More info from UC Davis Graduate Studies  HERE .

Sample Math QE Proposal, for your reference HERE . (Applied Math Students, please see the Applied Math QE proposal on the GGAM website)

QE Timeline:

  • Mathematics PhD timeline: must advance to candidacy by the beginning of their 9th quarter. PhD students entering with an MA or MS or equivalent should advance to candidacy by the beginning of their 7th quarter.
  • Applied Math PhD timeline: must advance to candidacy no later than by the end of the third year in the program. PhD students entering with an MA or MS or equivalent should advance to candidacy by the beginning of their 7th quarter.

QE Committee members:

  • Mathematics - a committee of four examiners. Normally three of the members are members of the Department of Mathematics. Per Graduate Council guidelines, at least one member must be external to the Department. The Dissertation Advisor can be a member of the committee but cannot be the chair.
  • Applied Mathematics - a committee of five examiners. As required by Graduate Council policy, at least one member must be outside of the GGAM and the major professor/proposed. The Dissertation Advisor can be a member of the committee but cannot be the chair.
  • To see policy on who can be on your committee visit: Service on Advanced Degree Committees

QE Process:

  • Consult with your advisor to select a Qualifying Exam Committee.
  • Arrange a time and date with Qual Committee.
  • Reserve room: [email protected].
  • Email 1) Qualifying Exam Proposal AND 2) Qual Exam Application to [email protected] preferable at the same time in order to have approved and submitted on time . This process should be completed approximately SIX weeks prior to the date of your examination.
  • Once your Qualifying Exam Proposal has been approved (by the Graduate Program Committee, for Math; by the executive committee of GGAM, for Applied), your program Chair will recommend the appointment of your qualifying examination and committee to the Dean of Graduate Studies.
  • Only if, the qual is remote or has a remote member, the student is responsible for sending remote link information to the committee.

Qualifying Exam Workshop -Galois Group : the Department participates in quarterly workshops conducted by the student-run Galois Group. These sessions are informal and are intended to provide a generalized overview of the process.

  • Policy on Service on Advanced Degree Committees
  • Qualifying Examination Application (GS319)
  • QE Committee Member Remote Participation Request (GS342)
  • Qualifying Exam Regulations
  • Strategies for Successful QE

Masters (M.A. and M.S. Degree)

MA Degree in Mathematics:

To be considered for the MA degree, you must complete a petition to Advance to Candidacy ( more info on the Grad Studies page ). All course requirements for the MA degree must be completed before submitting your petition to Advance to Candidacy.

You may submit your petition to Advance to Candidacy for the MA degree prior to passing your written examination at the Masters level (or the PhD level if you are a PhD candidate). As soon as you have passed your examinations, please ask the Department to forward to the Office of Graduate Studies a Masters Report form. This form indicates to the Graduate Studies Office that you have met all the requirements for the MA degree and that you are ready to undergo the degree conferral review process.

MA Process:

Email your 1) receipt of payment (see petition for instructions) AND 2) petition to Advance to Candidacy to [email protected] after it is approved by your thesis adviser and the Chair of your graduate program. Once their signatures are secured, a copy of your petition is made for your department file. Then, it is forwarded to the Office of Graduate Studies for final approval.

MS Degree in Applied Mathematics

To be considered for the MS degree, you must complete a petition to Advance to Candidacy ( more info on the Grad Studies page ). It is recommended that you work with your thesis adviser to discuss whom to nominate for your thesis committee. Three members are required, all of whom should be consulted prior to submitting the Candidacy paperwork. Please be sure to have each member initial next to their name on the form as verification that they have agreed to serve on your committee. All course requirements for the MS degree, except for the thesis, must be completed before submitting your petition to Advance to Candidacy.

MS Process:

Masters on Way to Phd:

In order to complete the Master's degree on the way to your Ph.D., students submit the following forms to [email protected]:

  • Petition for Change of Graduate Major, Degree Objective, Multiple Graduate Majors, or Multiple Degree Objectives form to add on the Master’s degree and sequence number: https://ucdavis.app.box.com/v/ PetitionforChange
  • Masters Candidacy Plan II: https://ucdavis.app.box.com/v/ MastersCandidacyII
  • Receipt of the fee stated on the Petition for Change.  Please send the email receipt to me as well as the two forms above.
  • We will fill out and submit - the Master's Report form (completion dates & chair you used for your qual): https://ucdavis.app.box.com/v/ MastersReportII

Advance to Candidacy

After you have passed your qualifying exam you will advance to candidacy. Candidacy is the second and advanced phase of graduate study.  To be eligible for candidacy, students must fulfill certain standards determined by their degree objective and their graduate program requirements.  Students must also demonstrate adequate preparation to begin work on their final requirements (thesis, dissertation, comprehensive exam, capstone) and select an advanced degree committee. 

Instructions:

  • 1) Receipt of Payment
  • 2) Petition to Advance to Candidacy after it is approved by your thesis adviser and the Chair of your graduate program.

Once their signatures are secured, a copy of your petition is made for your department file. Then, it is forwarded to the Office of Graduate Studies for final approval.  Graduat Studies will send you confirmation in about 2 weeks.

  • The Cashiers Office indicates proof of payment by placing a stamp on your petition form PAY HERE.
  • PhD Candidacy Application

Doctoral students are eligible to advance to candidacy when they have:  

  • Completed all required coursework and any other program degree requirements except the dissertation (e.g. language requirement, preliminary exam, etc.).  Including replacement of any incomplete grades .    
  • Earned a cumulative GPA of 3.0 or higher. 
  • Passed the  Doctoral Qualifying Examination .  
  • Secured dissertation committee members who will provide mentorship and evaluate the dissertation.  The committee is proposed through the Candidacy Application , and reviewed for eligibility by Graduate Studies.    
  • Registered full-time in the current or upcoming quarter.  Doctoral students may not be part-time after passing the QE (starting the quarter after the QE).   

PhD Degree in Mathematics and Applied Mathematics

Dissertation/Thesis

MS Thesis in Applied Mathematics

  • A master's thesis on a topic selected under the advice and guidance of your thesis adviser must be completed to earn the MS degree. Your thesis adviser also recommends a program of study in your area of application. You are expected to choose a thesis adviser during your first year. It is very important to choose a thesis adviser as early as possible for timely completion of the degree.
  • Using modern methods of applied mathematics, the master's thesis will normally consist of the solution of a problem or problems, from your area of specialization. The thesis will be read and approved by a committee of three faculty members, which includes the thesis adviser as chair of the committee. The thesis should be completed and submitted to the Graduate Studies Office no later than the end of Summer quarter of your second year. In support of your preparation, the student-run Galois Group has provided some tips to help get you started.

PhD Dissertation

  • The doctoral dissertation is the main part of your program of study. You are to select a topic under the advice and guidance of your thesis committee. A majority of students will be ready to begin some research activity during the first year of the PhD program. A good way to get started is to take a reading course with a faculty member during the Spring quarter of the first year and start research in the Summer after the first year.
  • In support of your preparation, the student-run Galois Group has provided some tips to help get you started.

Exit Seminar

  • Optional Final Oral Examination (at the discretion of the Dissertation Committee) After the exit seminar, the student's dissertation committee may meet privately with the student to discuss the contents of the dissertation and ask additional questions. Satisfaction of this requirement must be verified by the Dissertation Committee Chair.
  • Select the best date for as many committee members to attend. 
  • Schedule room and/or set up the remote link.
  • Send date, location, and title to [email protected].

Filing Dissertation/Thesis

  • Filing your thesis or dissertation with the Graduate Studies Office is the last requirement to be satisfied by candidates for advanced degrees. Deadlines and information for completing this requirement are listed for each quarter on the Graduate Studies Office website under Calendar and Deadlines and Information for Degree Candidates .
  • Please note that a candidate must be a regularly registered student or on Filing Fee status at the time of filing a thesis or dissertation, with the exception of the period between the end of the Spring quarter and the beginning of the Fall quarter, as long as you were either registered or on filing fee during that Spring quarter.

Commencement

  • The Graduate Studies Office, together with the Graduate Council and the Graduate Student Association, hosts graduate commencement. The ceremony is held the evening of the last Thursday of Spring quarter in the Pavillion of the Activities and Recreation Center (ARC). A reception is held immediately following the ceremony for the degree recipients, faculty, family, and friends.
  • If you receive your graduate degree in September, December, March, or June, you are eligible and welcome to participate in the commencement. If you are close to completion and will not be in Davis the following June, you are also eligible and welcome to participate. The Graduate Studies Office will typically send information about commencement in February.
  • Any student who will receive a degree in March, June or September, or who expects to receive a degree in December, and who has not already participated in a June commencement ceremony, is eligible and welcome to participate in a Fall commencement ceremony.
  • For more information about commencement, please reference the "help links" set up by the Graduate Studies Office on their Commencement website.

Becoming a Teaching Assistant (TA)

Teaching Assistant Orientation

The university requires that first-time TAs at UC Davis attend a TA Orientation, conducted by the Teaching Resources Center. This is typically held just prior to the start of the Fall quarter, and announcements of the exact date are distributed by the Student Services staff. You must register on line prior to the orientation at the Center for Educational Effectiveness to receive an email confirmation, which serves as your entry ticket. If a student has an unavoidable time conflict, a department staff member must request that their name be added to a waiting list for the other session.

Additionally, International TAs are required to take a SPEAK test once they arrive here. For more information, test dates, and how to register, please go to the International & Academic English web page .

MAT 390: Teaching Assistantship Training

First-time TAs at UC Davis are required by our Department to take MAT 390. It is only offered during the Fall quarter, therefore, if you're not TA-ing until a later quarter, you still need to plan on taking this course in the Fall. Although this course does not count towards degree requirements, it does count for work load units. If you feel you should not be required to take this course, you can try to appeal this requirement. In other words, some of you may already have extensive teaching experience and thus taking this course might not be the best use of your time. To do this, please contact our Business Office Staff at [email protected].

Teaching Assistant Evaluations

Questionnaires for quarterly student evaluations of teaching assistants in all mathematics discussion classes (without any exceptions) are to be distributed during the last week of classes. If you are not leading a discussion class, a written evaluation of your work is submitted by the instructor teaching the course for which you have been assigned to TA.

Please note that students enrolled in your discussion class must be given notice that evaluations will be distributed, one class meeting prior to distribution. Students will be given a minimum of 15 minutes to complete the evaluation form. Questionnaires for distribution to your students will be put in your mailbox by the Student Services staff, along with guidelines on the proper return of completed forms.

Becoming an Associate-Instructor (AI)

Eligibility to Become an Associate-Instructor

For those interested in obtaining a Summer teaching assignment, a call for Associate-Instructors (AI) is emailed sometime during the Spring quarter. Shortly after that (but also during the Spring quarter), a separate call for those interested in teaching during the academic year will go out. Only those who have advanced to candidacy AND who have met with the approval from the Committee on Courses can be considered for an upper division course.

In the summer, AIs are employed by the Summer Sessions Office . During the academic year, AIs are employed by the Department.

AIs are appointed by the Department's Vice-Chair of Graduate Matters after reviewing preferences, evaluations, teaching assistant experiences, and grade point average. Minimum qualifications for being employed as an AI include:

  • Master's degree or completion of 30 units of graduate work.
  • One year teaching experience, including any time served as a TA.
  • Full-time, registered graduate student.
  • 3.00 GPA (on a 4.00 point scale).
  • Student must be in good academic standing.

Associate-Instructor Orientation

All first-time instructors (graduate students and faculty alike) will be invited to attend an orientation session organized by the Department's Student Services staff. The purpose of this session is to better acquaint you with not only the Department's teaching policies, but also that of the University's. For more information on teaching classes including how to set up your course, grading, student enrollments, etc., please refer to the Instructor Handbook (Math Department login required).

Teaching Mentor

For your first quarter of teaching, a faculty member will be assigned to you as a teaching mentor. The mentor will occasionally visit your class to observe your teaching and will give you feedback on his/her observations. He/she will also be available to critique your exams before they are reproduced and to answer any questions you may have on teaching. The mentor will provide a written evaluation at the end of your teaching assignment which will be included in your personnel file.

Instructor Evaluations

Questionnaires for quarterly student evaluations of instructors in all mathematics classes (without any exceptions) are to be distributed during the last week of classes. Students must be given notice that evaluations will be distributed, one class meeting prior to distribution. Students will be given a minimum of 15 minutes to complete the evaluation form. Questionnaires for distribution to your students will be put in your mailbox by the Student Services staff, along with guidelines on the proper return of completed forms.

Degree Information

Degree Forms

For almost every process or stage of graduate study, there is a corresponding form that needs to be filed with your program and the Graduate Studies Office . Most forms can be found on their Graduate Studies Forms page . If you don't find a form, please consult a staff member with the Student Services Office.

Tracking Your Degree Progress

In consultation with your faculty adviser, you are to design a program of study that will help you progress toward a stated goal. Any changes to the program must have the approval of your adviser. Failure to have such approval may mean that credit toward the degree will not be received for courses taken, and normal progress will therefore be delayed.

Additionally, at the start of each quarter, you are required to complete a quarterly study list which you must review with your faculty adviser. The study list must include all courses registered for that quarter and be signed by you and your faculty adviser. Once complete and signed, your study list should be returned to the Student Services Office for processing.

During the spring quarter of each year, the Department performs a review of each student based on information provided by the student, the faculty adviser, instructors of the core courses, and the student's transcript. The main objective of this evaluation is to determine whether the student is making satisfactory progress and to communicate to the student expectations for future progress. The results of these evaluations are also used in the award process of financial support for the summer months and the following year.

Occasionally it happens that you might not do well in any given quarter. If this should happen, consult with a Student Services staff member, who will then direct you to the appropriate person, as needed.

Please consult your program brochure for more specific information and guidelines about progress toward the degrees in Mathematics or Applied Mathematics.

Probation and Disqualification

Graduate students are subject to probation if at any point their progress is judged unsatisfactory or if their cumulative grade point average is below 3.0, or if they accumulate more than 8 units of incomplete (I) or unsatisfactory (U) grades.

The Dean of Graduate Studies will inform the student he/she is on probation and what must be done to return to regular status. A student is subject to disqualification if he/she cannot meet the requirements to return to regular status. Students cannot be advanced to candidacy if they are on probation. Disqualification of students is at the discretion of the Dean of Graduate Studies.

For more information about academic probation or program disqualification, please reference the Graduate Studies Office's policy and guidelines on Disqualification and Appeal .

Troubleshooting

If you're having mechanical issues registering, send an email to a staff adviser in the Student Services Office to make sure you're properly recorded in the system. If you are correctly in the system, then you should be able to register. If you cannot register, we are unable to problem-solve anything further relative to computer access issues. You will then need to call the Registration Hotline, (530) 752-3639.

Financial Aid and Departmental Support

As long as you are in good academic standing, continue to make progress toward your degree, and perform satisfactorily in an appointed position (such as a Teaching Assistant) you will receive departmental or University financial support of some type. This support consists of a salary or stipend, plus full or partial fee remission. For nonresidents, several fellowships are available to help pay the nonresident tuition.

Please refer to your offer letter regarding your funding package. Funding is currently only offered to Ph.D. applicants. Ph.D. students are typically offered a 5-year financial aid package (4 if coming with a Master's) in the form of fellowships, employment as a Teaching Assistant, or as a Graduate Student Researcher. Teaching Assistants and Graduate Student Researchers are eligible for tuition remissions. You do not have to apply for these positions, they will be appointed to you upon admission.

  • FAFSA:We highly encourage you fill out FAFSA each academic year. There are times when we can apply for funds on your behalf if you qualify through FAFSA. The annual priority filing deadline for State and University grant consideration is March 2. Applying begins with the Free Application for Federal Student Aid (FAFSA) or the California Dream Act Application (CADAA) . Both applications are free.
  • TA/GSR/AI Salary Scale Information: HERE
  • Please visit HERE to learn more about graduate school fees at UC Davis.
  • For more information about student support, please refer to our Graduate Financial Information webpage.

Getting Around

Bicycling: Preparation and Knowledge

The Bicycle Program maintains and encourages the popular and beneficial use of the bicycle as an important mode of transportation to, from and on campus by providing the campus community with a safe, secure, and efficient cycling environment in response to customer needs and expectations.

Transportation Services (TAPS)

Transportation Services (TAPS) facilitates the access and mobility needs of the campus community through the coordination of efforts among TAPS units and with other campus departments and non-university entities, and ensures that services are provided in a professional, efficient, and service-oriented manner.

Unitrans was founded in 1968 as the University Transport System, when the Associated Students of UC Davis purchased two vintage London double decker buses to operate on two routes. In 1972, Unitrans was opened to the general public, with partial funding from the City of Davis. Since that time the ASUCD/City of Davis partnership has continued, and now Unitrans provides public transportation service to the entire city with 49 buses on 14 routes, carrying over 3 million passengers/year (about 20,000 on a typical day).

Anyone can ride Unitrans for a small cash fare, and many types of prepaid discounted tickets and passes are available. More information on fares and passes is available by going online to their Bus Fares and Rates web page or by calling 752-2877.

Getting Started - ID Info - Department Needs

Student Identification Card

Your student ID card or "AggieCard" identifies you as a UC Davis student to all faculty and staff at UC Davis and at other UC campuses. To obtain your AggieCard, reference the AggieCard website . New students can request it online and pick it up at the AggieCard office in 253 Memorial Union. All students must have a valid driver's license, or other form of valid photo ID, to pick up the card.

If you lose your student ID card, you can arrange to have a new card made. To do this, please visit the AggieCard's Office in 253 Memorial Union. You must provide a government-issued ID (valid state driver's license, visa, or passport) and pay a fee of $15.00 toward replacing a lost, stolen or intentionally damaged card.

Student Office and Building Access

At the beginning of each year, the Galois Group president assigns student office space for all new and returning graduate students. A listing showing your assigned room is typically sent via email, which also includes general instructions on when you may move into your space. Keys to your office can be obtained by visiting a staff person with the Student Services Office. If you are a returning student who has been granted new office space, it is very important that you return your old office key in exchange for the new one.

The Mathematical Sciences Building is open to the public during the weekdays from 7:00 a.m. to 7:00 p.m. Overnight access to the building can be granted by using your student identification card (AggieCard), but only after your name and student identification number has been entered into the building's electronic key system. To have this done, please visit a staff person with the Business Office.

Copy Machines and Computer Labs

Copy machines are available for your use as long as the work is either teaching or research related. The machines are in several locations: ( click here for building maps ) MSB 1224, the Department's mailroom, on the first floor; MSB 2201 on the second floor; and MSB 3114 on the third floor.

You have access to both of the Department's computer labs. The graduate lab (room 3114) is located on the third floor and consists of 8 Linux systems and 1 Mac system (this lab is not to be used by undergraduates). If a class is not in session, you may also use the undergraduate lab (room 2118) which is located on the second floor and consists of 32 computers. Before you can begin using any one of our computer systems, you would need to create a computer account with the Department. To have this done, please visit a staff person with the Student Services Office or a systems administrator with the Technical Office, which is located on the third floor in MSB 3117.

Mailroom and Mailboxes

Personal mailboxes are located in the Department's mailroom (MSB 1224) on the first floor . You may access your mailbox in two ways: you may enter through the front door of the administrative office suite during regular business hours ; or you may use your office key to enter from the mailroom's back door. Graduate student mailboxes are arranged in alphabetical order and are alongside personal mailboxes for the faculty and staff. Under no circumstances are undergraduates permitted in this room. Therefore, when you teach, never permit them to return work to your personal mailbox.

Office Supplies

Office supplies such as pens/pencils, dry erase markers, notepads, post-it notes, etc. are available in the mailroom and the second floor copy room.

Room Reservation

Please submit a request to:

Groups - Math Community

Dual Pair Program

The dual pair program informally pairs each incoming student with a "senior level" graduate student in the Department. The purpose of this program is to give "senior level" students an opportunity to welcome and share their experiences and knowledge with an incoming student who is just starting out and who may need that extra helping hand.

Galois Group

The Galois Group is an official organization of the graduate students of the UC Davis Department of Mathematics. All graduate students are automatically members of the Galois Group. This group serves as a voice for the graduate students to the Math faculty and staff. They also coordinate and facilitate various activities, such as Monthly Game Nights, the Departmental Tea, and New Student Welcomes. When referencing the Galois Group's website, take special note of their helpful tips and advice, which have been collected and compiled by the graduate students.

Graduate Student Association (GSA)

The Graduate Student Association (GSA) represents graduate and professional students on the UC Davis campus. As the officially recognized student government, the GSA serves to empower students and build graduate student community through activities and advocacy. The GSA office is located at 253 South Silo. There are typically representatives from each graduate program, graduate group, etc., that meet throughout the year and discuss issues of importance to graduate and professional students.

The SIAM (Society for Industrial and Applied Mathematics) Club at UC Davis is committed to promoting the interests of students interested in all forms of applied mathematics at UC Davis. They plan several events throughout the year including a student research conference. Students from mathematics, physics, computer science, atmospheric science, engineering, and other departments interested in applied mathematics are encouraged to join.

Check our Outreach page for other groups and communities at UC Davis. There are groups for promoting inclusivity and diversity, promoting math across ages, and others!

Health and Well-Being

Student Health Insurance Plan (SHIP)

The University of California requires that all students have health insurance. To help you meet this requirement, UC Davis automatically enrolls all registered students in the Student Health Insurance Plan (SHIP). Fees for SHIP coverage are charged to your student account each school term along with your registration fees. If you have comparable health insurance and do not want to be enrolled in SHIP, you may apply for a SHIP waiver.

SHIP is designed specifically for UC Davis students with both Davis area and worldwide coverage. SHIP includes medical and dental benefits for undergraduate, graduate, and professional students. Beginning in Fall 2008, SHIP will also include vision benefits.

SHIP does not provide health insurance coverage for the dependents of UC Davis students. However, the student health center provides information and counseling for dependents regarding available health insurance options.

Student Health and Counseling Services

UC Davis Student Health and Counseling Services or SHCS provides a wide variety of medical, mental health and wellness services to all registered UC Davis students regardless of insurance coverage. Most services are provided through scheduled appointments, however acute care  (services without appointments) for acute medical and mental health needs are also available. Services are provided at two primary locations: The Student Health and Wellness Center and North Hall

Intramural Sports and Club Sports (Rec Sports)

Campus Recreation Rec Sports (formerly Intramural Sports) program provides students, faculty, staff, alumni and other university affiliates the opportunity to participate in a variety of competitive and recreational sport activities. Rec Sports offers more than 30 different activities (Men’s, Women’s and CoRec) in traditional sports such as basketball, softball, soccer, volleyball and flag football, as well as non-traditional activities such as ultimate frisbee, tube polo, and dodgeball. Rec Sports also presents tournaments and leagues for individuals and two-person teams in such activities as badminton, spikeball, and tennis.

Activities and Recreation Center (ARC)

The Activities and Recreation Center (ARC) offers both informal as well as formal recreation opportunities. From working on your jump shot, practicing your dance steps, trying out the climbing wall, playing table tennis or racquetball with a friend to personal training, group exercise classes, and dietary analysis. The ARC makes it easy for you to keep fit, relax, have fun, and meet your fitness goals.

Outdoor Adventure

California offers some of the most spectacular natural areas in the world from Yosemite, to Mt. Lassen, to Point Reyes, to the American and Klamath Rivers. Outdoor Adventures can take you there. Offering a range of diverse hiking, whitewater, and kayaking opportunities, Outdoor Adventures also features a friendly student staff, a helpful resource center of books and maps, comprehensive first aid training, and a rental center stocked with top quality equipment at reasonable prices.

Child Care and Family Services

UC Davis Student Housing

UC Davis Student Housing operates three types of housing: residence halls, campus apartments, and cooperatives. Each area and its included buildings are unique in character, combining with the residents to create a diverse, exciting community. All Student Housing buildings are located on university property, and all are located on the main campus. As a graduate student, you may want to concentrate your initial search by checking out what is available through campus apartments or cooperatives.

Of course, if off-campus housing is more to your liking, there are many opportunities offered among the many community apartments surrounding the university.

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The Community Housing Listing (CHL) is a service offered to UC Davis students and other Davis community members through the ASUCD Student Services Office. For a nominal fee, anyone can add a listing to the CHL database, and everyone can view their listings either online or at the ASUCD Student Services Office.

Galois Group Housing Information

If you start your housing search well in advance of your arrival on campus, you should be able to find a great place to live. To assist you, the Galois Group has set up this informative web page to explain the difference between leasing and renting. The site also breaks down cost details and shares tips on "what you should look for" when looking for a place to live.

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Services for International Students and Scholars (SISS)

The mission of Services for International Students and Scholars (SISS) is to help promote the internationalization of UC Davis by facilitating the integration of international students and scholars into the campus community. A major role for SISS is to assist international students and scholars with visa and immigration issues while they are at UC Davis. In addition to preparing the necessary documents to apply for a U.S. visa, SISS assists international students and scholars in maintaining their legal status while in the United States. SISS also provides orientation, assistance, information, and referral to international students, faculty, and researchers regarding financial, personal, cultural, and academic concerns.

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Internship and Career Center (ICC)

The Internship and Career Center (ICC) provides career advising services to all UC Davis graduate students and postdoctoral scholars for careers in academia, the public and private sectors. In addition, the ICC provides a variety of workshops and symposia on topics such as CV writing, applying and interviewing for faculty positions, career opportunities beyond academia, and transferable skills among other topics relevant to advanced degree holders.

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The Academic Assistance and Tutoring Centers (AATC) offers free academic assistance to all UC Davis students in: Study Skills, Mathematics/Statistics, Physics, Chemistry, Genetics, Biology, Spanish, Writing and English as a Second Language. They have several resources to help you. Located in Dutton Hall, with space in different buildings for tutoring .

GradPathways

Graduate Studies offers unparalleled opportunities and support for professional and career development.  Over 200 workshops, seminars, and panel discussions are offered throughout the year through partnerships between Graduate Studies and other campus units.

Professors for the Future (PFTF)

Professors for the Future (PFTF) is a year-long competitive fellowship program designed to recognize and develop the leadership skills of outstanding graduate students and postdoctoral scholars who have demonstrated their commitment to professionalism, integrity, and academic service. This unique program sponsored by the Graduate Studies Office focuses on the future challenges of graduate education, postdoctoral training, and the academy. PFTF is designed to prepare UC Davis doctoral students and postdoctoral scholars for an increasingly competitive marketplace and a rapidly changing university environment. PFTF Fellows receive a $3,000 stipend.

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This office includes representatives from various student services units, including the Dean's Offices, Financial Aid, Advising Services, Shields Library, Child Care, and Family Services. Reentry Student Services, in cooperation with the Reentry/Transfer Resource Network and the reentry student club OWLS (Older Wiser Learners), sponsors special programs and activities for reentry students.

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The philosophy of the Student Disability Center (SDC) is to promote independence and integrated participation in campus life for students with disabilities. The SDC is staffed by professional Disability Specialists who specialize in different areas of disability: learning, vision, hearing, medical, psychological, and mobility. These professionals each work with an assigned caseload of students, determining their eligibility for academic accommodations and ensuring the provision of accommodations necessary to allow the students to participate meaningfully in educational opportunities on campus.

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UC Davis is dedicated to helping teachers grow as effective educators in undergraduate and graduate teaching. Through the Office of Undergraduate Education, faculty members are supported by have access to  campus initiatives and units that support instruction.

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The Women's Resources and Research Center seeks to educate the campus community about women's issues and concerns. Its hope is to promote an understanding of the role and impact of gender in our lives and our society while helping women of diverse backgrounds achieve their intellectual, professional and personal goals and realize their full potential.

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The Office of Student Support and Judicial Affairs (OSSJA) supports the University's educational mission by upholding standards of academic honesty and responsible behavior, promoting student development, and assisting students in need. 

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applied mathematics phd thesis

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applied mathematics phd thesis

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applied mathematics phd thesis

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applied mathematics phd thesis

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applied mathematics phd thesis

Soutir Bandyopadhyay Director of Graduate Studies – AMS 303-373-3677 [email protected]

applied mathematics phd thesis

Lisa Maddux Department Manager – AMS Chauvenet Hall 147 303-273-2752 [email protected]

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Planar structure for infinite index subfactors and strongly Markov inclusions of finite von Neumann algebras

Khairul Bashar successfully defended his PhD dissertation . Congratulations!

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Johns Hopkins University Applied Physics Laboratory

2024 phd graduate – guidance, navigation, and control.

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Do you want to join a high performing research team conducting cutting-edge basic and applied research of advanced estimation and control algorithms across a multitude of different weapon systems?

Are you ready to apply your PhD to tackle challenging, novel problems facing the nation’s Air and Missile Defense community?

If you are graduating with a PhD in Engineering or Applied Mathematics and want to do research in control and estimation for autonomous systems, we’d love to have you join our team!

We are interested in candidates who have a broad technical background, a core skillset in control and estimation theory, and a passion for using new theoretic techniques to solve challenging problems. Candidates should have demonstrated experience applying their broad skillset to a diverse array of technical challenges, and show an ability to act independently to identify, learn, develop, implement, and share the techniques needed to solve a wide variety of problems. Our team is also committed to developing exceptional engineering talent and fostering a diverse culture of innovation and collaboration.

As a member of our team…

  • Your primary responsibility will be to research, develop, implement, and assess advanced guidance, navigation, control, and analysis algorithms supporting next-generation weapon systems
  • You will propose, lead, and participate in R&D efforts related to development of new weapon system algorithms and technologies
  • You will share your concepts and findings with other team members, APL management, and external sponsors and research communities
  • You may perform modeling, simulation, and performance assessment of guided missile GNC systems to support conceptual design through flight test

You meet our minimum qualifications for the job if you…

  • Are a current PhD candidate in electrical engineering, mechanical engineering, aerospace engineering, applied mathematics, or a related technical field
  • Have at least two years of relevant academic work (formal dissertation/research) involving control theory AND one or more of the following areas: robotics, guidance algorithms, machine learning, path planning, state estimation, multi-agent systems, SLAM, or optimization.
  • Demonstrate strong interpersonal skills and the ability to work independently and on a team
  • Are proficient in MATLAB, Simulink, and/or C++.
  • Are able to travel occasionally to support flight testing or technical meetings at sponsor or contractor facilities
  • Are able to obtain a Secret security clearance. If selected, you will be subject to a government security clearance investigation and must meet the requirements for access to classified information. Eligibility requirements include U.S. citizenship.

You’ll go above and beyond our minimum requirements if you…

  • Have a PhD in electrical engineering, mechanical engineering, aerospace engineering, applied mathematics, or a related technical field
  • Have professional/internship experience in control theory and one or more of the areas listed above
  • Have experience proposing and leading applied research efforts
  • Have an active Secret or Top Secret security clearance

Why work at APL?

The Johns Hopkins University Applied Physics Laboratory (APL) brings world-class expertise to our nation’s most critical defense, security, space and science challenges. While we are dedicated to solving complex challenges and pioneering new technologies, what makes us truly outstanding is our culture. We offer a vibrant, welcoming atmosphere where you can bring your authentic self to work, continue to grow, and build strong connections with inspiring teammates.

At APL, we celebrate our differences and encourage creativity and bold, new ideas. Our employees enjoy generous benefits, including a robust education assistance program, unparalleled retirement contributions, and a healthy work/life balance. APL’s campus is located in the Baltimore-Washington metro area. Learn more about our career opportunities at www.jhuapl.edu/careers.

APL is an Equal Opportunity/Affirmative Action employer. All qualified applicants will receive consideration for employment without regard to race, creed, color, religion, sex, gender identity or expression, sexual orientation, national origin, age, physical or mental disability, genetic information, veteran status, occupation, marital or familial status, political opinion, personal appearance, or any other characteristic protected by applicable law.

APL is committed to promoting an innovative environment that embraces diversity, encourages creativity, and supports inclusion of new ideas. In doing so, we are committed to providing reasonable accommodation to individuals of all abilities, including those with disabilities. If you require a reasonable accommodation to participate in any part of the hiring process, please contact [email protected]. Only by ensuring that everyone’s voice is heard are we empowered to be bold, do great things, and make the world a better place.

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VIDEO

  1. Writing That PhD Thesis

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  3. 3 Minute Thesis Competition 2022

  4. AMU PH.D ENTRANCE TEST PAPER APPLIED MATHEMATICS l Applied Mathematics Phd exam paper for 2023 2024

  5. Thesis Statements Mini Lecture

  6. David Parkes' untraditional path to Dean of Harvard SEAS

COMMENTS

  1. Recent PhD Theses

    PhD Theses 2016. Giuseppe Sellaroli. Non-compact groups, tensor operators and applications to quantum gravity. Robert H. Jonsson. Decoupling of Information Propagation from Energy Propagation. John Lang. Mathematical Modelling of Social Factors in Decision Making Processes at the Individual and Population Levels. John Yawney.

  2. Applied Mathematics Theses and Dissertations

    Theses/Dissertations from 2021. PDF. Mathematical Modelling & Simulation of Large and Small Scale Structures in Star Formation, Gianfranco Bino. PDF. Mathematical Modelling of Ecological Systems in Patchy Environments, Ao Li. PDF. Credit Risk Measurement and Application based on BP Neural Networks, Jingshi Luo. PDF.

  3. Ph.D. Program

    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 ...

  4. Ph.D. Dissertations

    Numerical Streamline Methods for Solving Steady Flow Problems (Methods, Compressible, Free Surface, Finite Difference.) Jie Sun. On Monotropic Piecewise Quadratic Programming (Network, Algorithm, Convex Programming, Decomposition Method.) Name Dissertation Title Advising Professor (s) 2022 Yuying Liu Ne.

  5. Mathematics PhD theses

    A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 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. 2023. Melanie Kobras - Low order models of storm track variability Ed Clark - Vectorial Variational Problems in L∞ and Applications ...

  6. Past PhD Dissertations

    Analytical and Numerical Investigation of Long-term Behavior of Microbial Flocculation Equations. Rebecca Mitchell. Designing a Finite-Time Mixer: Optimizing Stirring for Two-dimensional Maps. Wayne Mitchell. Low-communication, Parallel Multigrid Algorithms of Elliptic Partial Differential Equations.

  7. Graduate Theses

    Localized Pattern Formation in Continuum Models of Urban Crime. 2016. Konrad, Bernhard Paul. Ph.D. thesis. On the dynamics of HIV and malaria infection - insights from mathematical models. 2015. Karimfazli, Ida. Ph.D. thesis. Buoyancy-driven flow of viscoplastic fluids.

  8. Brown Digital Repository

    Applied Mathematics Theses and Dissertations. Full Record Association Between PM2.5 and Lung Cancer Incidence Rates (United States 1999-2013 Ecological Study with Generalized Linear Mixed Model) Description: Abstract Introduction: Cancer is a leading cause of death worldwide, accounting for 8.8 million deaths in 2015, and among which Lung ...

  9. Ph.D. in Applied Mathematics

    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.

  10. Dissertations

    2009. Andrey Rukhin. Asymptotic Analysis of Various Statistics for Random Graph Inference.Advisor: Carey Priebe. 2009 David Hutchison. Stopping times and confidence bounds for small-sample stochastic approximation algorithms.Advisor: James Spall and Alan Goldman. 2009. Hussein Aluie. Hydrodynamic and Magnetohydrodynamic Turbulence: Invariants, Cascades and Locality.

  11. Overview of the PhD Program

    For specific information on the Applied Mathematics PhD program, see the navigation links to the right. ... Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee ...

  12. Ph.D. Program

    The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation.

  13. Applied Mathematics Doctoral Program

    The Applied Mathematics PhD Program has a very strong track record in research and training. Placement of PhD students has been outstanding, with recent PhD students taking tenure-track/tenured faculty jobs at institutions such as Carnegie Mellon, Columbia, Drexel, Purdue, Tsinghua, UC Santa Cruz, Utah, Washington and alike, as well as private sector jobs in leading financial and high-tech ...

  14. PhD Step-by-Step Guide

    PhD Step-by-Step Guide. These are the general steps to obtain your PhD in Applied Mathematics at CU Boulder. 18 credit hours must be from APPM at 5000+ level. The 18 hours of APPM credits must include 5600 & 5610 (numerics I & II), 5440 & 5450 (analysis I & II), and one more approved \sequence" (see supplement for a list of approved sequences).

  15. Doctoral Program (PhD)

    For students interested in pursuing research in applied mathematics the 6 core courses are in analysis, numerical analysis and methods in applied mathematics. (B) ... PhD Thesis and Final Oral Examination. The final departmental steps in attaining the degree of Doctor of Philosophy are: 1. Completion of a thesis satisfactory to the major ...

  16. Applied Mathematics

    The PhD in applied mathematics with a certificate in IQ biology will strengthen this training with additional foundations in numerical and mathematical analysis, probability and statistics, mathematical biology and network analysis. ... and 30 credits of applied math dissertation credit.

  17. Mathematical Modeling Ph.D.

    The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Fall).

  18. PhD Applied Mathematics Research project proposal

    Abstract. PhD in Applied Mathematics - Research Proposal Scope of the research project: development of a game theory-based mathematical model for an autonomous machine decision-making system, with ...

  19. Applied Mathematics, PhD

    Students must complete 54 coursework hours and 24 dissertation research hours in order to qualify for the PhD in Applied Mathematics. The grade of each course has to be at least a B. The student's supervisory committee and the Joint Program Committee must approve the selection of all these courses.

  20. Recent Master's Theses

    Master's Theses 2022. Funmilayo Adeku. Sensitivity of the Thermal Structure and Circulation Patterns of a Simple Idealized Lake and Lake Erie to External Driving Forces. Darian McLaren. On the evaluation of quantum instruments with a consideration to measurements in trapped ion systems. Oluyemi Momoiyioluwa.

  21. Ph.D. Program

    In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics ... The QE chair and Dissertation Chair cannot be the same person ...

  22. Grad Student Handbook :: math.ucdavis.edu

    Applied Math PhD timeline: must advance to candidacy no later than by the end of the third year in the program. PhD students entering with an MA or MS or equivalent should advance to candidacy by the beginning of their 7th quarter. ... Dissertation/Thesis. MS Thesis in Applied Mathematics. A master's thesis on a topic selected under the advice ...

  23. Theses and Dissertations (Mathematics and Applied Mathematics)

    Analysis of the vibration of flexible structures. Research on vibrations of flexible structures is ongoing in engineering and applied mathematics fields. Flexible structures in practice can be considered as systems of interconnected rod-like components. This dissertation ...

  24. Graduate Program

    Soutir Bandyopadhyay AMS Director of Graduate Studies 303-373-3677 [email protected] Lisa Maddux AMS Department Manager Chauvenet Hall 141 303-273-3880 [email protected] [email protected]. New Student Orientation. All current students have access to the AMS Graduate Program CANVAS page.

  25. Planar structure for infinite index subfactors and strongly Markov

    Major in Applied Mathematics; Major in Mathematics; Major with a Teaching Concentration; Declaring the Major; Frequently Asked Questions; Honors Program; Minor; Advising; ... PhD Thesis (Author field refers to student + advisor) Topics . Past PhDs topic page, Phd-MathAnalysis topic page. Address.

  26. Khairul Bashar successfully defended his PhD dissertation

    Applied Math; About. Mission and Vision; Approach to Education; Meet the Dean ... Engage; Give; Jump to Footer. Khairul Bashar successfully defended his PhD dissertation . Congratulations! February 28, 2024. Home; Khairul Bashar successfully defended his PhD dissertation . ... University of Virginia School of Engineering and Applied Science ...

  27. 2024 PhD Graduate

    If you are graduating with a PhD in Engineering or Applied Mathematics and want to do research in control and estimation for autonomous systems, we'd love to have you join our team! ... applied mathematics, or a related technical field; Have at least two years of relevant academic work (formal dissertation/research) involving control theory ...