Michael Dunphy | |
Peter Stechlinski | |
Colin Phipps | |
Andree Susanto | |
Derek Steinmoeller | |
Venkata Manem | |
Alex Shum | |
PhD Theses 2013
József Vass | |
Andrijana Burazin | |
Nancy Soontiens | |
Amenda Chow | |
Rasha Al Jamal | |
Wentao Liu | |
Minghua Lin | |
Killian Miller | |
PhD Theses 2012
Rahul Rahul | |
Ruibin Qin | |
Dominique Brunet | |
Yasunori Aoki | |
Easwar Magesan | |
Christopher Ferrie | |
Dhanaraja Kasinathan | |
Wai Man NG | |
Matthew Johnston | |
PhD Theses 2011
Raluca Jessop | |
Yufang Hao | |
Mohamad Alwan | |
Yanwei Wang | |
Christopher Subich | |
Timothy Rees | |
Volodymyr Gerasik | |
PhD Theses 2010
Jun Liu | |
Kathleen Wilkie | |
Sean Speziale | |
Nataliya Portman | |
PhD Theses 2009
Rudy Gunawan | |
Gibin George Powathil | |
Matthew Calder | |
PhD Theses 2008
Gregory Mayer | |
Cedric Beny | |
Lijun Wang | |
Kahrizsangi Ebrahimi | |
Robert Martin | |
PhD Theses 2007
Shannon Kennedy | |
Alexander Korobov | |
Qing Wang | |
Duncan Mowbray | |
Donald Campbell | |
Applied and Computational Mathematics Master's Thesis - 625.803
This is the first in a two-course sequence (EN.625.803 and EN.625.804) designed for students in the master’s program who wish to work with a faculty advisor to conduct significant, original independent research in the field of applied and computational mathematics. (Each course is one semester.) A sequence may be used to fulfill two courses within the 700-level course requirements for the master’s degree; only one sequence may count toward the degree. For sequence 625.803 and 625.804, the student is to produce a bound hard-copy thesis for submission to the JHU library and an electronic version of the thesis based on standards posted at https://www.library.jhu.edu/library-services/electronic-theses-dissertations/. (The student is also encouraged to write a technical paper for publication based on the thesis.) The intent of the research is to expand the body of knowledge in the broad area of applied mathematics, with the research leading to professional-quality documentation. A full description of the guidelines (which includes the list of approved ACM research faculty) and the approval form can be found at https://ep.jhu.edu/current-students/student-forms/.
Course Prerequisite(s)
Completion of at least six courses towards the Master of Science, including EN.625.601 Real Analysis and/or EN.625.609 Matrix Theory, EN.625.603 Statistical Methods and Data Analysis, and at least one of the following three two-semester sequences: EN.625.717–EN.625.718 Advanced Differential Equations: Partial Differential Equations and Nonlinear Differential Equations and Dynamical Systems, EN.625.721– EN.625.722 Probability and Stochastic Processes I and II, or EN.625.725– EN.625.726 Theory of Statistics I and II. It is recommended that the sequence represent the final two courses of the degree.
Course Offerings
There are no sections currently offered, however you can view a sample syllabus from a prior section of this course.
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Digital Commons @ USF > College of Arts and Sciences > Mathematics and Statistics > Theses and Dissertations
Mathematics and Statistics Theses and Dissertations
Theses/dissertations from 2023 2023.
Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani
Applied Analysis for Learning Architectures , Himanshu Singh
Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze
Theses/Dissertations from 2022 2022
New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana
Advances and Applications of Optimal Polynomial Approximants , Raymond Centner
Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty
On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly
Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He
Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias
Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi
A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman
Theses/Dissertations from 2021 2021
Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri
Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi
Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou
Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando
Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu
Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang
Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang
Theses/Dissertations from 2020 2020
Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi
Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun
Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu
On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman
Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek
Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen
Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan
Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop
On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink
Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang
Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala
Theses/Dissertations from 2019 2019
Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian
Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar
Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil
Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter
Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz
Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi
Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi
Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos
The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva
Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak
Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich
An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado
Power Graphs of Quasigroups , DayVon L. Walker
Theses/Dissertations from 2018 2018
Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed
Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai
A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah
Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa
Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields
Generalizations of Quandles and their cohomologies , Matthew J. Green
Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu
Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou
Human Activity Recognition Based on Transfer Learning , Jinyong Pang
Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham
Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel
Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova
Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang
Theses/Dissertations from 2017 2017
Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack
Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon
On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill
Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill
Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly
Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera
Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao
Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati
Dynamics of Multicultural Social Networks , Kristina B. Hilton
Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi
Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally
Patterns in Words Related to DNA Rearrangements , Lukas Nabergall
Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na
Schreier Graphs of Thompson's Group T , Allen Pennington
Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya
Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo
Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi
Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou
Theses/Dissertations from 2016 2016
A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea
Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery
Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman
On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr
Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim
Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano
Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure
Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru
Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park
Leonard Systems and their Friends , Jonathan Spiewak
Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun
Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu
Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu
Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang
On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd
Theses/Dissertations from 2015 2015
Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen
Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko
Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana
Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf
Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner
Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao
Theses/Dissertations from 2014 2014
Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo
Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability , Jonathan Burns
On the Classification of Groups Generated by Automata with 4 States over a 2-Letter Alphabet , Louis Caponi
Statistical Analysis, Modeling, and Algorithms for Pharmaceutical and Cancer Systems , Bong-Jin Choi
Topological Data Analysis of Properties of Four-Regular Rigid Vertex Graphs , Grant Mcneil Conine
Trend Analysis and Modeling of Health and Environmental Data: Joinpoint and Functional Approach , Ram C. Kafle
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Applied Mathematics Research
In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.
Applied Mathematics Fields
- Combinatorics
- Computational Biology
- Physical Applied Mathematics
- Computational Science & Numerical Analysis
- Theoretical Computer Science
- Mathematics of Data
Applied Math Committee
Quick links
Research Areas
It is possible to apply mathematics to almost any field of human endeavor. Here are some of the fields we’re working on now.
Scientific Computing and Numerical Analysis
Researchers : Loyce Adams , Bernard Deconinck , Randy LeVeque , Ioana Dumitriu , Anne Greenbaum , James Riley
Many practical problems in science and engineering cannot be solved completely by analytical means. Research in the area of numerical analysis and scientific computation is concerned with the development and analysis of numerical algorithms, the implementation of these algorithms on modern computer architectures, and the use of numerical methods in conjunction with mathematical modeling to solve large-scale practical problems. Major research areas in this department include computational fluid dynamics (CFD), interface and front tracking methods, iterative methods in numerical linear algebra, and algorithms for parallel computers.Current research topics in CFD include:
- high resolution methods for solving nonlinear conservation laws with shock wave solutions
- numerical methods for atmospheric flows, particularly cloud formation
- Cartesian grid methods for solving multidimensional problems in complicated geometries on uniform grids
- spectral methods for fluid stability problems
- front tracking methods for fluid flow problems with free surfaces or immersed interfaces in the context of porous media flow (ground water or oil reservoir simulation) and in physiological flows with elastic membranes.
- nonequilibrium flows in combustion and astrophysical simulation
- immersed interface methods for solidification or melting problems and seismic wave equations with discontinuous coefficients that arise in modeling the geological structure of the earth.
Another research focus is the development of methods for large-scale scientific computations that are suited to implementation on parallel computer architectures. Current interests include:
- preconditioners for the iterative solution of large linear or nonlinear systems
- methods for the symmetric and nonsymmetric eigenvalue problems
- methods for general interface problems in complicated domains.
The actual implementation and testing of methods on parallel architectures is possible through collaboration with the Department of Computer Science, the Boeing Company, and the Pacific Northwest Labs.
Nonlinear Waves and Coherent Structures
Researchers : Bernard Deconinck , Nathan Kutz , Randy LeVeque
Most problems in applied mathematics are inherently nonlinear. The effects due to nonlinearities may become important under the right circumstances. The area of nonlinear waves and coherent structures considers how nonlinear effects influence problems involving wave propagation. Sometimes these effects are desirable and lead to new applications (mode-locked lasers, optical solitons and nonlinear optics). Other times one has no choice but to consider their impact (water waves). The area of nonlinear waves encompasses a large collection of phenomena, such as the formation and propagation of shocks and solitary waves. The area received renewed interest starting in the 1960s with the development of soliton theory, which examines completely integrable systems and classes of their special solutions.
Mathematical Biology
Researchers : Mark Kot , Hong Qian , Eric Shea-Brown , Elizabeth Halloran , Suresh Moolgavkar , Eli Shlizerman , Ivana Bozic
Mathematical biology is an increasingly large and well-established branch of applied mathematics. This growth reflects both the increasing importance of the biological and biomedical sciences and an appreciation for the mathematical subtleties and challenges that arise in the modelling of complex biological systems. Our interest, as a group, lies in understanding the spatial and temporal patterns that arise in dynamic biological systems. Our mathematical activities range from reaction-diffusion equations, to nonlinear and chaotic dynamics, to optimization. We employ a variety of tools and models to study problems that arise in development, epidemiology, ecology, neuroscience, resource management, and biomechanics; and we maintain active collaborations with a large number and variety of biologists and biomedical departments both in the University and elsewhere. For more information, please see the Mathematical Biology page .
Atmospheric Sciences and Climate Modeling
Researchers : Chris Bretherton , Ka-Kit Tung , Dale Durran
Mathematical models play a crucial role in our understanding of the fluid dynamics of the atmosphere and oceans. Our interests include mathematical methods for studying the hydrodynamical instability of shear flows, transition from laminar flow to turbulence, applications of fractals to turbulence, two-dimensional and quasi-geostrophic turbulence theory and computation, and large-scale nonlinear wave mechanics.We also develop and apply realistic coupled radiative- chemical-dynamical models for studying stratospheric chemistry, and coupled radiative-microphysical-dynamical models for studying the interaction of atmospheric turbulence and cloud systems These two topics are salient for understanding how man is changing the earth’s climate.Our work involves a strong interaction of computer modelling and classical applied analysis. This research group actively collaborates with scientists in the Atmospheric Science, Oceanography, and Geophysics department, and trains students in the emerging interdisciplinary area of earth system modeling, in addition to providing a traditional education in classical fluid dynamics.
Mathematical Methods
Researchers : Bernard Deconinck , Robert O'Malley , Jim Burke , Archis Ghate , John Sylvester , Gunther Uhlmann
The department maintains active research in fundamental methods of applied mathematics. These methods can be broadly applied to a vast number of problems in the engineering, physical and biological sciences. The particular strengths of the department of applied mathematics are in asymptotic and perturbation methods, applied analysis, optimization and control, and inverse problems.
Mathematical Finance
Researchers : Tim Leung , Matt Lorig , Doug Martin
The department’s growing financial math group is active in the areas of derivative pricing & hedging, algorithmic trading, portfolio optimization, insurance, risk measures, credit risk, and systemic risk. Research includes collaboration with students as well as partners from both academia and industry.
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Department of Mathematics
Senior theses.
An undergraduate thesis is a singly-authored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research.
To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project. The advisor will almost surely be a faculty member of the pure math department, though on occasion we have accepted theses written by people with applied math advisors. In these rare cases, the theses have been essentially pure math theses.
| | | |
2010 | Alex Kruckman | The Ax-Kochen Theorem: An Application of Model Theory to Algebra | Dan Abramovich/Michael Rosen |
2010 | Thomas Lawler | On the Local Structure of Triangulation Graphs | Richard Schwartz |
2011 | Andrew Furnas | Mathematical Modeling of Woven Fabric | Govind Menon |
2011 | Eric Sporkin | Modifying the BLS Signature Scheme Using Isogenies | Reinier Broker |
2011 | Tyler K. Woodruff | Discrepancy Upper Bounds for Certain Families of Rotated Squares | Jill Pipher |
2012 | Nadejda Drenska | Representation of Periodic Data with Fourier Methods and Wavelets | Jill Pipher |
2012 | Zev Chonoles | Hermite's Theorem for Function Fields | Michael Rosen |
2013 | Kevin Casto | | Richard Schwartz/Govind Menon |
2013 | In-Jee Jeong | | Richward Schwartz |
2013 | Benjamin LeVeque | | Jeffrey Hoffstein |
2013 | Lucas Mason-Brown | | Michael Rosen |
2013 | Yilong Yang | | Richard Schwartz |
2014 | Nicholas Lourie | | Richard Schwartz |
2014 | Michael Thaler | Extending Conway's Tiling Groups to a Triangular Lattice with Three Deformations | Richard Schwartz |
2015 | Justin Semonsen | Factorization of Birational Maps | Dan Abramovich |
2015 | Kamron Vachiraprasith | On the Average Order of Arithmetic Functions Over Monic Square-Free Polynomials in Finite Fields | Michael Rosen |
2015 | Francis White | | Sergei Treil |
2015 | Zijian Yao | Arakelov Theory on Arithmetic Surfaces | Stephen Lichtenbaum |
2016 | Claire Frechette | | Melody Chan |
2018 | Collin Cademartori | | Govind Menon |
2018 | Michael Mueller | | Thomas Goodwillie |
2018 | Lewis Silletto | | Richard Schwartz |
2020 | Jongyung Lee | | Dan Abramovich |
2020 | Owen Lynch | | Yuri Sulyma |
2021 | Alexander Bauman | | Bena Tshishiku |
2021 | Matei P. Coiculescu | | Richard Schwartz |
2021 | Henry Talbott | | Richard Schwartz |
2021 | Nathan Zelesko | | Melody Chan |
2022 | Griffin Edwards | | Yuri Sulyma |
2022 | Dichuan David Gao | | Justin Holmer |
2022 | Jasper Liu | | Jeffrey Hoffstein |
2024 | Alex Feiner | | Joseph Silveman |
2024 | Tyler Lane | | Brendan Hassett |
2024 | Smita Rajan | | Brendan Hassett |
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Home > A&S > Math > Math Undergraduate Theses
Mathematics Undergraduate Theses
Theses from 2019 2019.
The Name Tag Problem , Christian Carley
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis? , Chloe Munroe
Theses from 2018 2018
A Convolutional Neural Network Model for Species Classification of Camera Trap Images , Annie Casey
Pythagorean Theorem Area Proofs , Rachel Morley
Euclidian Geometry: Proposed Lesson Plans to Teach Throughout a One Semester Course , Joseph Willert
Theses from 2017 2017
An Exploration of the Chromatic Polynomial , Amanda Aydelotte
Complementary Coffee Cups , Brandon Sams
Theses from 2016 2016
Nonlinear Integral Equations and Their Solutions , Caleb Richards
Principles and Analysis of Approximation Techniques , Evan Smith
Theses from 2014 2014
An Introductory Look at Deterministic Chaos , Kenneth Coiteux
A Brief Encounter with Linear Codes , Brent El-Bakri
Axioms of Set Theory and Equivalents of Axiom of Choice , Farighon Abdul Rahim
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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. .
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| University of Southern California |
| Jun 23, 2024 | | Application deadline: December 15 Completion of the program requires a maximum effort by the student for a minimum of four years of full-time work. Screening Procedure The screening procedure consists of written examinations covering core applied mathematics content. Students must pass three written exams for the following core subjects: - Applied Probability
- Real Analysis
- Partial Differential Equations
The department offers the examinations twice a year, prior to the beginning of the Fall and Spring semesters. At least one of the screening examinations must be successfully completed by the end of the second semester in the program. All of the examinations must be successfully completed by the end of the fourth semester. The qualifying examination should follow two or three semesters after the successful completion of the screening procedure. Qualifying Exam Committee No later than at the end of the first semester after passing the screening procedure, the student must form a qualifying exam committee. The committee must consist of an adviser (committee chair) and four other faculty members, including at least one from another department. Qualifying Examination The qualifying examination consists of written and oral components. The written portion of the qualifying examination consists of a PhD dissertation proposal. This document (10 pages minimum) should include: introduction, statement of the problem, literature survey, methodology, summary of preliminary results, proposed research, references, appendix (including one or two fundamental references). This should be submitted to the department at least one week before the qualifying examination. The oral portion of the qualifying examination consists of a presentation of the PhD dissertation proposal and examination by the committee. The student must demonstrate research potential. The student must register for Math 794a in the semester immediately following successful completion of the qualifying examination. Course RequirementsThe student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit. Courses outside of the Mathematics Department must be approved by the Graduate Committee. These must include - MATH 794a Doctoral Dissertation Units: 2
- MATH 794b Doctoral Dissertation Units: 2
And six courses from the following:- MATH 502b Numerical Analysis Units: 3
- MATH 505b Applied Probability Units: 3
- MATH 507b Theory of Probability Units: 3
- MATH 509 Stochastic Differential Equations Units: 3
- MATH 520 Complex Analysis Units: 3
- MATH 525b Real Analysis Units: 3
- MATH 530b Stochastic Calculus and Mathematical Finance Units: 3
- MATH 532 Combinatorial Analysis Units: 3
- MATH 541b Introduction to Mathematical Statistics Units: 3
- MATH 542 Analysis of Variance and Design Units: 3
- MATH 545 Introduction to Time Series Units: 3
- MATH 547 Mathematical Foundations of Statistical Learning Theory Units: 3
- MATH 550 Statistical Consulting and Data Analysis Units: 3
- MATH 555b Partial Differential Equations Units: 3
- MATH 565a Ordinary Differential Equations Units: 3
- MATH 574 Applied Matrix Analysis Units: 3
- MATH 580 Introduction to Functional Analysis Units: 3
- MATH 585 Mathematical Theory of Optimal Control Units: 3
If a student receives a grade of B- or lower in any of the required courses, the requirement can be waived upon passing the screening exam for the course at the master’s level or higher. Additional RequirementsTransfer of Credit No transfer of credit will be considered until the screening examination is passed. A maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the PhD. A grade below B will not be accepted and at most one grade of B will be accepted. Dissertation Committee and Defense Following successful completion of the screening procedure and approval of a dissertation topic by the chair of the student’s qualifying exam committee, the student proceeds with research towards the dissertation. The student must form a dissertation committee consisting of at least three members, including the thesis advisor (committee chair) and a member outside the mathematics department. The PhD thesis, based on a substantial amount of original research conducted by the student, must be defended and approved by the dissertation committee. Megamenu GlobalMegamenu featured, megamenu social, math/stats thesis and colloquium topics. Updated: April 2024 Math/Stats Thesis and Colloquium Topics 2024- 2025The degree with honors in Mathematics or Statistics is awarded to the student who has demonstrated outstanding intellectual achievement in a program of study which extends beyond the requirements of the major. The principal considerations for recommending a student for the degree with honors will be: Mastery of core material and skills, breadth and, particularly, depth of knowledge beyond the core material, ability to pursue independent study of mathematics or statistics, originality in methods of investigation, and, where appropriate, creativity in research. An honors program normally consists of two semesters (MATH/STAT 493 and 494) and a winter study (WSP 031) of independent research, culminating in a thesis and a presentation. Under certain circumstances, the honors work can consist of coordinated study involving a one semester (MATH/STAT 493 or 494) and a winter study (WSP 030) of independent research, culminating in a “minithesis” and a presentation. At least one semester should be in addition to the major requirements, and thesis courses do not count as 400-level senior seminars. An honors program in actuarial studies requires significant achievement on four appropriate examinations of the Society of Actuaries. Highest honors will be reserved for the rare student who has displayed exceptional ability, achievement or originality. Such a student usually will have written a thesis, or pursued actuarial honors and written a mini-thesis. An outstanding student who writes a mini-thesis, or pursues actuarial honors and writes a paper, might also be considered. In all cases, the award of honors and highest honors is the decision of the Department. Here is a list of possible colloquium topics that different faculty are willing and eager to advise. You can talk to several faculty about any colloquium topic, the sooner the better, at least a month or two before your talk. For various reasons faculty may or may not be willing or able to advise your colloquium, which is another reason to start early. RESEARCH INTERESTS OF MATHEMATICS AND STATISTICS FACULTY Here is a list of faculty interests and possible thesis topics. You may use this list to select a thesis topic or you can use the list below to get a general idea of the mathematical interests of our faculty. Colin Adams (On Leave 2024 – 2025) Research interests: Topology and tiling theory. I work in low-dimensional topology. Specifically, I work in the two fields of knot theory and hyperbolic 3-manifold theory and develop the connections between the two. Knot theory is the study of knotted circles in 3-space, and it has applications to chemistry, biology and physics. I am also interested in tiling theory and have been working with students in this area as well. Hyperbolic 3-manifold theory utilizes hyperbolic geometry to understand 3-manifolds, which can be thought of as possible models of the spatial universe. Possible thesis topics: - Investigate various aspects of virtual knots, a generalization of knots.
- Consider hyperbolicity of virtual knots, building on previous SMALL work. For which virtual knots can you prove hyperbolicity?
- Investigate why certain virtual knots have the same hyperbolic volume.
- Consider the minimal Turaev volume of virtual knots, building on previous SMALL work.
- Investigate which knots have totally geodesic Seifert surfaces. In particular, figure out how to interpret this question for virtual knots.
- Investigate n-crossing number of knots. An n-crossing is a crossing with n strands of the knot passing through it. Every knot can be drawn in a picture with only n-crossings in it. The least number of n-crossings is called the n-crossing number. Determine the n-crossing number for various n and various families of knots.
- An übercrossing projection of a knot is a projection with just one n-crossing. The übercrossing number of a knot is the least n for which there is such an übercrossing projection. Determine the übercrossing number for various knots, and see how it relates to other traditional knot invariants.
- A petal projection of a knot is a projection with just one n-crossing such that none of the loops coming out of the crossing are nested. In other words, the projection looks like a daisy. The petal number of a knot is the least n for such a projection. Determine petal number for various knots, and see how it relates to other traditional knot invariants.
- In a recent paper, we extended petal number to virtual knots. Show that the virtual petal number of a classical knot is equal to the classical petal number of the knot (This is a GOOD question!)
- Similarly, show that the virtual n-crossing number of a classical knot is equal to the classical n-crossing number. (This is known for n = 2.)
- Find tilings of the branched sphere by regular polygons. This would extend work of previous research students. There are lots of interesting open problems about something as simple as tilings of the sphere.
- Other related topics.
Possible colloquium topics : Particularly interested in topology, knot theory, graph theory, tiling theory and geometry but will consider other topics. Christina Athanasouli Research Interests: Differential equations, dynamical systems (both smooth and non-smooth), mathematical modeling with applications in biological and mechanical systems My research focuses on analyzing mathematical models that describe various phenomena in Mathematical Neuroscience and Engineering. In particular, I work on understanding 1) the underlying mechanisms of human sleep (e.g. how sleep patterns change with development or due to perturbations), and 2) potential design or physical factors that may influence the dynamics in vibro-impact mechanical systems for the purpose of harvesting energy. Mathematically, I use various techniques from dynamical systems and incorporate both numerical and analytical tools in my work. Possible colloquium topics: Topics in applied mathematics, such as: - Mathematical modeling of sleep-wake regulation
- Mathematical modeling vibro-impact systems
- Bifurcations/dynamics of mathematical models in Mathematical Neuroscience and Engineering
- Bifurcations in piecewise-smooth dynamical systems
Julie Blackwood Research Interests: Mathematical modeling, theoretical ecology, population biology, differential equations, dynamical systems. My research uses mathematical models to uncover the complex mechanisms generating ecological dynamics, and when applicable emphasis is placed on evaluating intervention programs. My research is in various ecological areas including ( I ) invasive species management by using mathematical and economic models to evaluate the costs and benefits of control strategies, and ( II ) disease ecology by evaluating competing mathematical models of the transmission dynamics for both human and wildlife diseases. - Mathematical modeling of invasive species
- Mathematical modeling of vector-borne or directly transmitted diseases
- Developing mathematical models to manage vector-borne diseases through vector control
- Other relevant topics of interest in mathematical biology
Each topic (1-3) can focus on a case study of a particular invasive species or disease, and/or can investigate the effects of ecological properties (spatial structure, resource availability, contact structure, etc.) of the system. Possible colloquium topics: Any topics in applied mathematics, such as: Research Interest : Statistical methodology and applications. One of my research topics is variable selection for high-dimensional data. I am interested in traditional and modern approaches for selecting variables from a large candidate set in different settings and studying the corresponding theoretical properties. The settings include linear model, partial linear model, survival analysis, dynamic networks, etc. Another part of my research studies the mediation model, which examines the underlying mechanism of how variables relate to each other. My research also involves applying existing methods and developing new procedures to model the correlated observations and capture the time-varying effect. I am also interested in applications of data mining and statistical learning methods, e.g., their applications in analyzing the rhetorical styles in English text data. - Variable selection uses modern techniques such as penalization and screening methods for several different parametric and semi-parametric models.
- Extension of the classic mediation models to settings with correlated, longitudinal, or high-dimensional mediators. We could also explore ways to reduce the dimensionality and simplify the structure of mediators to have a stable model that is also easier to interpret.
- We shall analyze the English text dataset processed by the Docuscope environment with tools for corpus-based rhetorical analysis. The data have a hierarchical structure and contain rich information about the rhetorical styles used. We could apply statistical models and statistical learning algorithms to reduce dimensions and gain a more insightful understanding of the text.
Possible colloquium topics: I am open to any problems in statistical methodology and applications, not limited to my research interests and the possible thesis topics above. Richard De Veaux Research interests: Statistics. My research interests are in both statistical methodology and in statistical applications. For the first, I look at different methods and try to understand why some methods work well in particular settings, or more creatively, to try to come up with new methods. For the second, I work in collaboration with an investigator (e.g. scientist, doctor, marketing analyst) on a particular statistical application. I have been especially interested in problems dealing with large data sets and the associated modeling tools that work for these problems. - Human Performance and Aging.I have been working on models for assessing the effect of age on performance in running and swimming events. There is still much work to do. So far I’ve looked at masters’ freestyle swimming and running data and a handicapped race in California, but there are world records for each age group and other events in running and swimming that I’ve not incorporated. There are also many other types of events.
- Variable Selection. How do we choose variables when we have dozens, hundreds or even thousands of potential predictors? Various model selection strategies exist, but there is still a lot of work to be done to find out which ones work under what assumptions and conditions.
- Problems at the interface.In this era of Big Data, not all methods of classical statistics can be applied in practice. What methods scale up well, and what advances in computer science give insights into the statistical methods that are best suited to large data sets?
- Applying statistical methods to problems in science or social science.In collaboration with a scientist or social scientist, find a problem for which statistical analysis plays a key role.
Possible colloquium topics: - Almost any topic in statistics that extends things you’ve learned in courses — specifically topics in Experimental design, regression techniques or machine learning
- Model selection problems
Thomas Garrity (On Leave 2024 – 2025) Research interest: Number Theory and Dynamics. My area of research is officially called “multi-dimensional continued fraction algorithms,” an area that touches many different branches of mathematics (which is one reason it is both interesting and rich). In recent years, students writing theses with me have used serious tools from geometry, dynamics, ergodic theory, functional analysis, linear algebra, differentiability conditions, and combinatorics. (No single person has used all of these tools.) It is an area to see how mathematics is truly interrelated, forming one coherent whole. While my original interest in this area stemmed from trying to find interesting methods for expressing real numbers as sequences of integers (the Hermite problem), over the years this has led to me interacting with many different mathematicians, and to me learning a whole lot of math. My theses students have had much the same experiences, including the emotional rush of discovery and the occasional despair of frustration. The whole experience of writing a thesis should be intense, and ultimately rewarding. Also, since this area of math has so many facets and has so many entrance points, I have had thesis students from wildly different mathematical backgrounds do wonderful work; hence all welcome. - Generalizations of continued fractions.
- Using algebraic geometry to study real submanifolds of complex spaces.
Possible colloquium topics: Any interesting topic in mathematics. Leo Goldmakher Research interests: Number theory and arithmetic combinatorics. I’m interested in quantifying structure and randomness within naturally occurring sets or sequences, such as the prime numbers, or the sequence of coefficients of a continued fraction, or a subset of a vector space. Doing so typically involves using ideas from analysis, probability, algebra, and combinatorics. Possible thesis topics: Anything in number theory or arithmetic combinatorics. Possible colloquium topics: I’m happy to advise a colloquium in any area of math. Susan Loepp Research interests: Commutative Algebra. I study algebraic structures called commutative rings. Specifically, I have been investigating the relationship between local rings and their completion. One defines the completion of a ring by first defining a metric on the ring and then completing the ring with respect to that metric. I am interested in what kinds of algebraic properties a ring and its completion share. This relationship has proven to be intricate and quite surprising. I am also interested in the theory of tight closure, and Homological Algebra. Topics in Commutative Algebra including: - Using completions to construct Noetherian rings with unusual prime ideal structures.
- What prime ideals of C[[ x 1 ,…, x n ]] can be maximal in the generic formal fiber of a ring? More generally, characterize what sets of prime ideals of a complete local ring can occur in the generic formal fiber.
- Characterize what sets of prime ideals of a complete local ring can occur in formal fibers of ideals with height n where n ≥1.
- Characterize which complete local rings are the completion of an excellent unique factorization domain.
- Explore the relationship between the formal fibers of R and S where S is a flat extension of R .
- Determine which complete local rings are the completion of a catenary integral domain.
- Determine which complete local rings are the completion of a catenary unique factorization domain.
Possible colloquium topics: Any topics in mathematics and especially commutative algebra/ring theory. Steven Miller For more information and references, see http://www.williams.edu/Mathematics/sjmiller/public_html/index.htm Research interests : Analytic number theory, random matrix theory, probability and statistics, graph theory. My main research interest is in the distribution of zeros of L-functions. The most studied of these is the Riemann zeta function, Sum_{n=1 to oo} 1/n^s. The importance of this function becomes apparent when we notice that it can also be written as Prod_{p prime} 1 / (1 – 1/p^s); this function relates properties of the primes to those of the integers (and we know where the integers are!). It turns out that the properties of zeros of L-functions are extremely useful in attacking questions in number theory. Interestingly, a terrific model for these zeros is given by random matrix theory: choose a large matrix at random and study its eigenvalues. This model also does a terrific job describing behavior ranging from heavy nuclei like Uranium to bus routes in Mexico! I’m studying several problems in random matrix theory, which also have applications to graph theory (building efficient networks). I am also working on several problems in probability and statistics, especially (but not limited to) sabermetrics (applying mathematical statistics to baseball) and Benford’s law of digit bias (which is often connected to fascinating questions about equidistribution). Many data sets have a preponderance of first digits equal to 1 (look at the first million Fibonacci numbers, and you’ll see a leading digit of 1 about 30% of the time). In addition to being of theoretical interest, applications range from the IRS (which uses it to detect tax fraud) to computer science (building more efficient computers). I’m exploring the subject with several colleagues in fields ranging from accounting to engineering to the social sciences. Possible thesis topics: - Theoretical models for zeros of elliptic curve L-functions (in the number field and function field cases).
- Studying lower order term behavior in zeros of L-functions.
- Studying the distribution of eigenvalues of sets of random matrices.
- Exploring Benford’s law of digit bias (both its theory and applications, such as image, voter and tax fraud).
- Propagation of viruses in networks (a graph theory / dynamical systems problem). Sabermetrics.
- Additive number theory (questions on sum and difference sets).
Possible colloquium topics: Plus anything you find interesting. I’m also interested in applications, and have worked on subjects ranging from accounting to computer science to geology to marketing…. Ralph Morrison Research interests: I work in algebraic geometry, tropical geometry, graph theory (especially chip-firing games on graphs), and discrete geometry, as well as computer implementations that study these topics. Algebraic geometry is the study of solution sets to polynomial equations. Such a solution set is called a variety. Tropical geometry is a “skeletonized” version of algebraic geometry. We can take a classical variety and “tropicalize” it, giving us a tropical variety, which is a piecewise-linear subset of Euclidean space. Tropical geometry combines combinatorics, discrete geometry, and graph theory with classical algebraic geometry, and allows for developing theory and computations that tell us about the classical varieties. One flavor of this area of math is to study chip-firing games on graphs, which are motivated by (and applied to) questions about algebraic curves. Possible thesis topics : Anything related to tropical geometry, algebraic geometry, chip-firing games (or other graph theory topics), and discrete geometry. Here are a few specific topics/questions: - Study the geometry of tropical plane curves, perhaps motivated by results from algebraic geometry. For instance: given 5 (algebraic) conics, there are 3264 conics that are tangent to all 5 of them. What if we look at tropical conics–is there still a fixed number of tropical conics tangent to all of them? If so, what is that number? How does this tropical count relate to the algebraic count?
- What can tropical plane curves “look like”? There are a few ways to make this question precise. One common way is to look at the “skeleton” of a tropical curve, a graph that lives inside of the curve and contains most of the interesting data. Which graphs can appear, and what can the lengths of its edges be? I’ve done lots of work with students on these sorts of questions, but there are many open questions!
- What can tropical surfaces in three-dimensional space look like? What is the version of a skeleton here? (For instance, a tropical surface of degree 4 contains a distinguished polyhedron with at most 63 facets. Which polyhedra are possible?)
- Study the geometry of tropical curves obtained by intersecting two tropical surfaces. For instance, if we intersect a tropical plane with a tropical surface of degree 4, we obtain a tropical curve whose skeleton has three loops. How can those loops be arranged? Or we could intersect degree 2 and degree 3 tropical surfaces, to get a tropical curve with 4 loops; which skeletons are possible there?
- One way to study tropical geometry is to replace the usual rules of arithmetic (plus and times) with new rules (min and plus). How do topics like linear algebra work in these fields? (It turns out they’re related to optimization, scheduling, and job assignment problems.)
- Chip-firing games on graphs model questions from algebraic geometry. One of the most important comes in the “gonality” of a graph, which is the smallest number of chips on a graph that could eliminate (via a series of “chip-firing moves”) an added debt of -1 anywhere on the graph. There are lots of open questions for studying the gonality of graphs; this include general questions, like “What are good lower bounds on gonality?” and specific ones, like “What’s the gonality of the n-dimensional hypercube graph?”
- We can also study versions of gonality where we place -r chips instead of just -1; this gives us the r^th gonality of a graph. Together, the first, second, third, etc. gonalities form the “gonality sequence” of a graph. What sequences of integers can be the gonality sequence of some graph? Is there a graph whose gonality sequence starts 3, 5, 8?
- There are many computational and algorithmic questions to ask about chip-firing games. It’s known that computing the gonality of a general graph is NP-hard; what if we restrict to planar graphs? Or graphs that are 3-regular? And can we implement relatively efficient ways of computing these numbers, at least for small graphs?
- What if we changed our rules for chip-firing games, for instance by working with chips modulo N? How can we “win” a chip-firing game in that context, since there’s no more notion of debt?
- Study a “graph throttling” version of gonality. For instance, instead of minimizing the number of chips we place on the graph, maybe we can also try to decrease the number of chip-firing moves we need to eliminate debt.
- Chip-firing games lead to interesting questions on other topics in graph theory. For instance, there’s a conjectured upper bound of (|E|-|V|+4)/2 on the gonality of a graph; and any graph is known to have gonality at least its tree-width. Can we prove the (weaker) result that (|E|-|V|+4)/2 is an upper bound on tree-width? (Such a result would be of interest to graph theorists, even the idea behind it comes from algebraic geometry!)
- Topics coming from discrete geometry. For example: suppose you want to make “string art”, where you have one shape inside of another with string weaving between the inside and the outside shapes. For which pairs of shapes is this possible?
Possible Colloquium topics: I’m happy to advise a talk in any area of math, but would be especially excited about talks related to algebra, geometry, graph theory, or discrete mathematics. Shaoyang Ning (On Leave 2024 – 2025) Research Interest : Statistical methodologies and applications. My research focuses on the study and design of statistical methods for integrative data analysis, in particular, to address the challenges of increasing complexity and connectivity arising from “Big Data”. I’m interested in innovating statistical methods that efficiently integrate multi-source, multi-resolution information to solve real-life problems. Instances include tracking localized influenza with Google search data and predicting cancer-targeting drugs with high-throughput genetic profiling data. Other interests include Bayesian methods, copula modeling, and nonparametric methods. - Digital (disease) tracking: Using Internet search data to track and predict influenza activities at different resolutions (nation, region, state, city); Integrating other sources of digital data (e.g. Twitter, Facebook) and/or extending to track other epidemics and social/economic events, such as dengue, presidential approval rates, employment rates, and etc.
- Predicting cancer drugs with multi-source profiling data: Developing new methods to aggregate genetic profiling data of different sources (e.g., mutations, expression levels, CRISPR knockouts, drug experiments) in cancer cell lines to identify potential cancer-targeting drugs, their modes of actions and genetic targets.
- Social media text mining: Developing new methods to analyze and extract information from social media data (e.g. Reddit, Twitter). What are the challenges in analyzing the large-volume but short-length social media data? Can classic methods still apply? How should we innovate to address these difficulties?
- Copula modeling: How do we model and estimate associations between different variables when they are beyond multivariate Normal? What if the data are heavily dependent in the tails of their distributions (commonly observed in stock prices)? What if dependence between data are non-symmetric and complex? When the size of data is limited but the dimension is large, can we still recover their correlation structures? Copula model enables to “link” the marginals of a multivariate random variable to its joint distribution with great flexibility and can just be the key to the questions above.
- Other cross-disciplinary, data-driven projects: Applying/developing statistical methodology to answer an interesting scientific question in collaboration with a scientist or social scientist.
Possible colloquium topics: Any topics in statistical methodology and application, including but not limited to: topics in applied statistics, Bayesian methods, computational biology, statistical learning, “Big Data” mining, and other cross-disciplinary projects. Anna Neufeld Research interests: My research is motivated by the gap between classical statistical tools and practical data analysis. Classic statistical tools are designed for testing a single hypothesis about a single, pre-specified model. However, modern data analysis is an adaptive process that involves exploring the data, fitting several models, evaluating these models, and then testing a potentially large number of hypotheses about one or more selected models. With this in mind, I am interested in topics such as (1) methods for model validation and selection, (2) methods for testing data-driven hypotheses (post-selection inference), and (3) methods for testing a large number of hypotheses. I am also interested in any applied project where I can help a scientist rigorously answer an important question using data. - Cross-validation for unsupervised learning. Cross-validation is one of the most widely-used tools for model validation, but, in its typical form, it cannot be used for unsupervised learning problems. Numerous ad-hoc proposals exist for validating unsupervised learning models, but there is a need to compare and contrast these proposals and work towards a unified approach.
- Identifying the number of cell types in single-cell genomics datasets. This is an application of the topic above, since the cell types are typically estimated via unsupervised learning.
- There is growing interest in “post-prediction inference”, which is the task of doing valid statistical inference when some inputs to your statistical model are the outputs of other statistical models (i.e. predictions). Frameworks have recently been proposed for post-prediction inference in the setting where you have access to a gold-standard dataset where the true inputs, rather than the predicted inputs, have been observed. A thesis could explore the possibility of post-prediction inference in the absence of this gold-standard dataset.
- Any other topic of student interest related to selective inference, multiple testing, or post-prediction inference.
- Any collaborative project in which we work with a scientist to identify an interesting question in need of non-standard statistics.
- I am open to advising colloquia in almost any area of statistical methodology or applications, including but not limited to: multiple testing, post-selection inference, post-prediction inference, model selection, model validation, statistical machine learning, unsupervised learning, or genomics.
Allison Pacelli Research interests: Math Education, Math & Politics, and Algebraic Number Theory. Math Education. Math education is the study of the practice of teaching and learning mathematics, at all levels. For example, do high school calculus students learn best from lecture or inquiry-based learning? What mathematical content knowledge is critical for elementary school math teachers? Is a flipped classroom more effective than a traditional learning format? Many fascinating questions remain, at all levels of education. We can talk further to narrow down project ideas. Math & Politics. The mathematics of voting and the mathematics of fair division are two fascinating topics in the field of mathematics and politics. Research questions look at types of voting systems, and the properties that we would want a voting system to satisfy, as well as the idea of fairness when splitting up a single object, like cake, or a collection of objects, such as after a divorce or a death. Algebraic Number Theory. The Fundamental Theorem of Arithmetic states that the ring of integers is a unique factorization domain, that is, every integer can be uniquely factored into a product of primes. In other rings, there are analogues of prime numbers, but factorization into primes is not necessarily unique! In order to determine whether factorization into primes is unique in the ring of integers of a number field or function field, it is useful to study the associated class group – the group of equivalence classes of ideals. The class group is trivial if and only if the ring is a unique factorization domain. Although the study of class groups dates back to Gauss and played a key role in the history of Fermat’s Last Theorem, many basic questions remain open. Possible thesis topics: - Topics in math education, including projects at the elementary school level all the way through college level.
- Topics in voting and fair division.
- Investigating the divisibility of class numbers or the structure of the class group of quadratic fields and higher degree extensions.
- Exploring polynomial analogues of theorems from number theory concerning sums of powers, primes, divisibility, and arithmetic functions.
Possible colloquium topics: Anything in number theory, algebra, or math & politics. Anna Plantinga Research interests: I am interested in both applied and methodological statistics. My research primarily involves problems related to statistical analysis within genetics, genomics, and in particular the human microbiome (the set of bacteria that live in and on a person). Current areas of interest include longitudinal data, distance-based analysis methods such as kernel machine regression, high-dimensional data, and structured data. - Impacts of microbiome volatility. Sometimes the variability of a microbial community is more indicative of an unhealthy community than the actual bacteria present. We have developed an approach to quantifying microbiome variability (“volatility”). This project will use extensive simulations to explore the impact of between-group differences in volatility on a variety of standard tests for association between the microbiome and a health outcome.
- Accounting for excess zeros (sparse feature matrices). Often in a data matrix with many zeros, some of the zeros are “true” or “structural” zeros, whereas others are simply there because we have fewer observations for some subjects. How we account for these zeros affects analysis results. Which methods to account for excess zeros perform best for different analyses?
- Longitudinal methods for compositional data. When we have longitudinal data, we assume the same variables are measured at every time point. For high-dimensional compositions, this may not be the case. We would generally assume that the missing component was absent at any time points for which it was not measured. This project will explore alternatives to making that assumption.
- Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology (or variations on existing methods) to answer an interesting scientific question.
Any topics in statistical application, education, or methodology, including but not restricted to: - Topics in applied statistics.
- Methods for microbiome data analysis.
- Statistical genetics.
- Electronic health records.
- Variable selection and statistical learning.
- Longitudinal methods.
Cesar Silva Research interests : Ergodic theory and measurable dynamics; in particular mixing properties and rank one examples, and infinite measure-preserving and nonsingular transformations and group actions. Measurable dynamics of transformations defined on the p-adic field. Measurable sensitivity. Fractals. Fractal Geometry. Possible thesis topics: Ergodic Theory. Ergodic theory studies the probabilistic behavior of abstract dynamical systems. Dynamical systems are systems that change with time, such as the motion of the planets or of a pendulum. Abstract dynamical systems represent the state of a dynamical system by a point in a mathematical space (phase space). In many cases this space is assumed to be the unit interval [0,1) with Lebesgue measure. One usually assumes that time is measured at discrete intervals and so the law of motion of the system is represented by a single map (or transformation) of the phase space [0,1). In this case one studies various dynamical behaviors of these maps, such as ergodicity, weak mixing, and mixing. I am also interested in studying the measurable dynamics of systems defined on the p-adics numbers. The prerequisite is a first course in real analysis. Topological Dynamics. Dynamics on compact or locally compact spaces. Topics in mathematics and in particular: - Any topic in measure theory. See for example any of the first few chapters in “Measure and Category” by J. Oxtoby. Possible topics include the Banach-Tarski paradox, the Banach-Mazur game, Liouville numbers and s-Hausdorff measure zero.
- Topics in applied linear algebra and functional analysis.
- Fractal sets, fractal generation, image compression, and fractal dimension.
- Dynamics on the p-adic numbers.
- Banach-Tarski paradox, space filling curves.
Mihai Stoiciu Research interests: Mathematical Physics and Functional Analysis. I am interested in the study of the spectral properties of various operators arising from mathematical physics – especially the Schrodinger operator. In particular, I am investigating the distribution of the eigenvalues for special classes of self-adjoint and unitary random matrices. Topics in mathematical physics, functional analysis and probability including: - Investigate the spectrum of the Schrodinger operator. Possible research topics: Find good estimates for the number of bound states; Analyze the asymptotic growth of the number of bound states of the discrete Schrodinger operator at large coupling constants.
- Study particular classes of orthogonal polynomials on the unit circle.
- Investigate numerically the statistical distribution of the eigenvalues for various classes of random CMV matrices.
- Study the general theory of point processes and its applications to problems in mathematical physics.
Possible colloquium topics: Any topics in mathematics, mathematical physics, functional analysis, or probability, such as: - The Schrodinger operator.
- Orthogonal polynomials on the unit circle.
- Statistical distribution of the eigenvalues of random matrices.
- The general theory of point processes and its applications to problems in mathematical physics.
Elizabeth Upton Research Interests: My research interests center around network science, with a focus on regression methods for network-indexed data. Networks are used to capture the relationships between elements within a system. Examples include social networks, transportation networks, and biological networks. I also enjoy tackling problems with pragmatic applications and am therefore interested in applied interdisciplinary research. - Regression models for network data: how can we incorporate network structure (and dependence) in our regression framework when modeling a vertex-indexed response?
- Identify effects shaping network structure. For example, in social networks, the phrase “birds of a feather flock together” is often used to describe homophily. That is, those who have similar interests are more likely to become friends. How can we capture or test this effect, and others, in a regression framework when modeling edge-indexed responses?
- Extending models for multilayer networks. Current methodologies combine edges from multiple networks in some sort of weighted averaging scheme. Could a penalized multivariate approach yield a more informative model?
- Developing algorithms to make inference on large networks more efficient.
- Any topic in linear or generalized linear modeling (including mixed-effects regression models, zero-inflated regressions, etc.).
- Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology to answer an interesting scientific question.
- Any applied statistics research project/paper
- Topics in linear or generalized linear modeling
- Network visualizations and statistics
Get the Reddit appr/mathematics is a subreddit dedicated to focused questions and discussion concerning mathematics. Ideas for an undergraduate thesis in Mathematics?Hello all! I’m an undergraduate math major. This semester I am starting a thesis for the College of Honors in the field of mathematics at my school. I have struggled the whole semester in trying to find a topic to write on and how to find sources on the topic. One of my professors suggested finding a topic I like and writing about its applications. I know as an undergrad I don’t need to contribute any “original work/ideas” to the field of mathematics. But does anyone, particularly someone who has does math research or written a thesis in mathematics have any ideas that might be interesting (and frankly, easier to write about)? I honestly am at a loss here trying to find a topic and beginning writing in the first place. Any tips or resources would be appreciated. I do enjoy calculus, financial mathematics, and abstract algebra. So far I’ve taken: Calculus 1&2, Linear and Abstract Algebra, Probability, Statistical Methods (I have NOT completed Real Analysis, Differential Equations, Calculus 3 or Number Theory yet) just so everyone has an idea. Thank you for your help! - Write my thesis
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181 Mathematics Research Topics From PhD ExpertsIf you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit. And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services. Our Newest Research Topics in MathWe know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought. So, without further ado, here are the 181 brand new topics for your next math research paper: Cool Math Topics to ResearchAre you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now: - Roll two dice and calculate a probability
- Discuss ancient Greek mathematics
- Is math really important in school?
- Discuss the binomial theorem
- The math behind encryption
- Game theory and its real-life applications
- Analyze the Bernoulli scheme
- What are holomorphic functions and how do they work?
- Describe big numbers
- Solving the Tower of Hanoi problem
Undergraduate Math Research TopicsIf you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics: - Methods to count discrete objects
- The origins of Greek symbols in mathematics
- Methods to solve simultaneous equations
- Real-world applications of the theorem of Pythagoras
- Discuss the limits of diffusion
- Use math to analyze the abortion data in the UK over the last 100 years
- Discuss the Knot theory
- Analyze predictive models (take meteorology as an example)
- In-depth analysis of the Monte Carlo methods for inverse problems
- Squares vs. rectangles (compare and contrast)
Number Theory Topics to ResearchInterested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics: - Discuss the greatest common divisor
- Explain the extended Euclidean algorithm
- What are RSA numbers?
- Discuss Bézout’s lemma
- In-depth analysis of the square-free polynomial
- Discuss the Stern-Brocot tree
- Analyze Fermat’s little theorem
- What is a discrete logarithm?
- Gauss’s lemma in number theory
- Analyze the Pentagonal number theorem
Math Research Topics for High SchoolHigh school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here: - Discuss Brun’s constant
- An in-depth look at the Brahmagupta–Fibonacci identity
- What is derivative algebra?
- Describe the Symmetric Boolean function
- Discuss orders of approximation in limits
- Solving Regiomontanus’ angle maximization problem
- What is a Quadratic integral?
- Define and describe complementary angles
- Analyze the incircle and excircles of a triangle
- Analyze the Bolyai–Gerwien theorem in geometry
- Math in our everyday life
Complex Math TopicsIf you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics: - Mathematics and its appliance in Artificial Intelligence
- Try to solve an unsolved problem in math
- Discuss Kolmogorov’s zero-one law
- What is a discrete random variable?
- Analyze the Hewitt–Savage zero-one law
- What is a transferable belief model?
- Discuss 3 major mathematical theorems
- Describe and analyze the Dempster-Shafer theory
- An in-depth analysis of a continuous stochastic process
- Identify and analyze Gauss-Markov processes
Easy Math Research Paper TopicsPerhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics: - Define the hyperbola
- Do we need to use a calculator during math class?
- The binomial theorem and its real-world applications
- What is a parabola in geometry?
- How do you calculate the slope of a curve?
- Define the Jacobian matrix
- Solving matrix problems effectively
- Why do we need differential equations?
- Should math be mandatory in all schools?
- What is a Hessian matrix?
Logic Topics to ResearchWe have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now: - Discuss the reductio ad absurdum approach
- Discuss Boolean algebra
- What is consistency proof?
- Analyze Trakhtenbrot’s theorem (the finite model theory)
- Discuss the Gödel completeness theorem
- An in-depth analysis of Morley’s categoricity theorem
- How does the Back-and-forth method work?
- Discuss the Ehrenfeucht–Fraïssé game technique
- Discuss Aleph numbers (Aleph-null and Aleph-one)
- Solving the Suslin problem
Algebra Topics for a Research PaperWould you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper: - Discuss the differential equation
- Analyze the Jacobson density theorem
- The 4 properties of a binary operation in algebra
- Analyze the unary operator in depth
- Analyze the Abel–Ruffini theorem
- Epimorphisms vs. monomorphisms: compare and contrast
- Discuss the Morita duality in algebraic structures
- Idempotent vs. nilpotent in Ring theory
- Discuss the Artin-Wedderburn theorem
- What is a commutative ring in algebra?
- Analyze and describe the Noetherian ring
Math Education Research TopicsThere is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics: - What are the goals a mathematics professor should have?
- What is math anxiety in the classroom?
- Teaching math in UK schools: the difficulties
- Computer programming or math in high school?
- Is math education in Europe at a high enough level?
- Common Core Standards and their effects on math education
- Culture and math education in Africa
- What is dyscalculia and how does it manifest itself?
- When was algebra first thought in schools?
- Math education in the United States versus the United Kingdom
Computability Theory Topics to ResearchWriting about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research: - What is a multiplication table?
- Analyze the Scholz conjecture
- Explain exponentiating by squaring
- Analyze the Myhill-Nerode theorem
- What is a tree automaton?
- Compare and contrast the Pushdown automaton and the Büchi automaton
- Discuss the Markov algorithm
- What is a Turing machine?
- Analyze the post correspondence problem
- Discuss the linear speedup theorem
- Discuss the Boolean satisfiability problem
Interesting Math Research TopicsWe know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics: - What is two-element Boolean algebra?
- The life of Gauss
- The life of Isaac Newton
- What is an orthodiagonal quadrilateral?
- Tessellation in Euclidean plane geometry
- Describe a hyperboloid in 3D geometry
- What is a sphericon?
- Discuss the peculiarities of Borel’s paradox
- Analyze the De Finetti theorem in statistics
- What are Martingales?
- The basics of stochastic calculus
Applied Math Research TopicsInterested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you: - Discuss Newton’s laws of motion
- Analyze the perpendicular axes rule
- How is a Galilean transformation done?
- The conservation of energy and its applications
- Discuss Liouville’s theorem in Hamiltonian mechanics
- Analyze the quantum field theory
- Discuss the main components of the Lorentz symmetry
- An in-depth look at the uncertainty principle
Geometry Topics for a Research PaperGeometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today: - Most useful trigonometry functions in math
- The life of Archimedes and his achievements
- Trigonometry in computer graphics
- Using Vincenty’s formulae in geodesy
- Define and describe the Heronian tetrahedron
- The math behind the parabolic microphone
- Discuss the Japanese theorem for concyclic polygons
- Analyze Euler’s theorem in geometry
Math Research Topics for Middle SchoolYes, even middle school children can write about mathematics. We have some original math research topics for middle school right here: - Finding critical points in a graph
- The basics of calculus
- What makes a graph ultrahomogeneous?
- How do you calculate the area of different shapes?
- What contributions did Euclid have to the field of mathematics?
- What is Diophantine geometry?
- What makes a graph regular?
- Analyze a full binary tree
Math Research Topics for College StudentsAs you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here: - What are extremal problems and how do you solve them?
- Discuss an unsolvable math problem
- How can supercomputers solve complex mathematical problems?
- An in-depth analysis of fractals
- Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
- Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
- An in-depth look at Einstein’s field equation
- The math behind computer vision and object recognition
Calculus Topics for a Research PaperLet’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away: - When do we need to apply the L’Hôpital rule?
- Discuss the Leibniz integral rule
- Calculus in ancient Egypt
- Discuss and analyze linear approximations
- The applications of calculus in real life
- The many uses of Stokes’ theorem
- Discuss the Borel regular measure
- An in-depth analysis of Lebesgue’s monotone convergence theorem
Simple Math Research Paper Topics for High SchoolThis is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school: - The life and work of the famous Pierre de Fermat
- What are limits and why are they useful in calculus?
- Explain the concept of congruency
- The life and work of the famous Jakob Bernoulli
- Analyze the rhombicosidodecahedron and its applications
- Calculus and the Egyptian pyramids
- The life and work of the famous Jean d’Alembert
- Discuss the hyperplane arrangement in combinatorial computational geometry
- The smallest enclosing sphere method in combinatorics
Business Math TopicsIf you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here: - Is paying a loan with another loan a good approach?
- Discuss the major causes of a stock market crash
- Best debt amortization methods in the US
- How do bank loans work in the UK?
- Calculating interest rates the easy way
- Discuss the pros and cons of annuities
- Basic business math skills everyone should possess
- Business math in United States schools
- Analyze the discount factor
Probability and Statistics Topics for ResearchProbability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research: - What is the autoregressive conditional duration?
- Applying the ANOVA method to ranks
- Discuss the practical applications of the Bates distribution
- Explain the principle of maximum entropy
- Discuss Skorokhod’s representation theorem in random variables
- What is the Factorial moment in the Theory of Probability?
- Compare and contrast Cochran’s C test and his Q test
- Analyze the De Moivre-Laplace theorem
- What is a negative probability?
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Master's Theses 2019. Cameron Meaney. Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs. Jennie Newman. Model for the RE-TC thalamic circuit with application to childhood absence epilepsy. Jesse Legaspi.
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.
Senior Thesis. A thesis is a more ambitious undertaking than a project. Most thesis writers within Applied Mathematics spend two semesters on their thesis work, beginning in the fall of senior year. Students typically enroll in Applied Mathematics 91r or 99r (or Economics 985, if appropriate) during each semester of their senior year.
In this dissertation we explore the theory and applications of Gröbner bases, and the algorithms that allow us to compute them. ... vibration of elastic bodies and structures consisting of elastic bodies is an active research field in engineering and applied mathematics. Typically, a mathematical model is a complex system of partial ...
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.
Department of Applied Mathematics University of Washington Lewis Hall 201 Box 353925 Seattle, WA 98195-3925
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.
the topic is in pure or applied mathematics (if in doubt about suitability, check with the Director of . Undergraduate Studies). In general, focused theses on a circumscribed topic do well, whereas theses that ... sophistication of the topic. In particular, the thesis topic need not be 'cutting edge' mathematics, it only needs to be cutting ...
Applied Mathematics Theses and Dissertations. Available to Brown-affiliated users only. Full Record Advances in the Discontinuous Galerkin Method: Hybrid Schemes and Applications to the Reactive Infiltration Instability in an Upwelling Compacting Mantle ... In this dissertation we propose, analyze and computationally implement finite element ...
625.803. Primary Program. Applied and Computational Mathematics. This is the first in a two-course sequence (EN.625.803 and EN.625.804) designed for students in the master's program who wish to work with a faculty advisor to conduct significant, original independent research in the field of applied and computational mathematics.
Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data, Taysseer Sharaf. PDF. Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3, Richard Alan Warner. PDF. Ensemble Learning Method on Machine Maintenance Data, Xiaochuang Zhao
Applied Mathematics Thesis Topics - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document discusses challenges students often face when writing an applied mathematics thesis and provides suggestions for seeking assistance. It notes that writing a thesis in applied mathematics requires precision and expertise across various complex steps.
Applied Mathematics Research. In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. Applied Mathematics Fields The mathematics of surface tension. Combinatorics; Computational Biology
Major research areas in this department include computational fluid dynamics (CFD), interface and front tracking methods, iterative methods in numerical linear algebra, and algorithms for parallel computers.Current research topics in CFD include: front tracking methods for fluid flow problems with free surfaces or immersed interfaces in the ...
Senior Theses. An undergraduate thesis is a singly-authored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research. To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project.
Topics of interest range from Cryptology to Statistics, from Differential Equations to Mathematics Pedagogy. The Senior Thesis in Mathematical Sciences course allows students to engage in independent mathematical work in an active and modern subject area of the mathematical sciences, guided by an official research faculty member in the ...
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 ...
The screening procedure consists of written examinations covering core applied mathematics content. Students must pass three written exams for the following core subjects: ... Following successful completion of the screening procedure and approval of a dissertation topic by the chair of the student's qualifying exam committee, the student ...
Thesis Topics in Applied Mathematics - Free download as PDF File (.pdf), Text File (.txt) or read online for free.
Updated: April 2024 Math/Stats Thesis and Colloquium Topics 2024- 2025 The degree with honors in Mathematics or Statistics is awarded to the student who has demonstrated outstanding intellectual achievement in a program of study which extends beyond the requirements of the major. The principal considerations for recommending a student for the degree with honors will be: Mastery of core ...
I have not found a thesis adviser yet, so I don't have anyone to talk to about this problem. "Deaths of despair" was a concept introduced in 2015. Perhaps you can incorporate that into your studies. Perhaps combine various data sets to propose new actuarial table based on poverty/dispair. following.
Applied Math Thesis Topics for Undergr . Applied Math I'll be taking a thesis course for the Fall Semester but I have no idea where to start with developing a topic for my thesis. I need to present a rough outline of my thesis for registration in a few weeks. Does anyone have suggestions of how to come up with a thesis topic?
The topic I chose for my undergraduate thesis was Category Theory, which I applied to see all the concepts I learnt in uni from this "clean" point of view while also linking them. ... You have a lot of applied math classes. I'm an engineer so I might be biased, but you can easily write about signal processing knowing calc 1 and 2. You might ...
If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics: Methods to count discrete objects. The origins of Greek symbols in mathematics. Methods to solve simultaneous equations. Real-world applications of the theorem of Pythagoras.
AMAT MS (Thesis) IGAM-THES AMAT-THES Preliminary Exam PEXM PEXM Core Courses IGAM-MAJR1 AMATMS-CORE Teaching and Learning in the Sciences IGAM-MAJR2 AMATMS-TEACH Applied Mathematics Seminar IGAM-MAJR3 AMATMS-SEM Taching Assistantship TAM TAM Special Topics Courses IGAM-THES2 AMATMS-TOPICS Thesis THES THES AMAT MS (Cap Stone) IGAM-NTHS AMAT-NTHS