Mathematics (Ph.D.) Program Details
Degree Requirements
❱ Required coursework
❱ Qualifying or comprehensive examination
❱ Foreign language proficiency
❱ Graduate School writing proficiency requirement
❱ Graduate School Responsible Conduct of Research (RCR) requirement
❱ Dissertation
❱ Final oral examination/Dissertation defense
Research Specializations
❱ Algebra
❱ Analysis
❱ Applied mathematics
❱ Combinatorics, Probability, and Statistics
❱ Geometry
❱ Mathematics Education
❱ Number Theory
❱ Topology
Research Areas & Interests
Faculty Areas of Expertise
| First Name | Last Name | Research Area & Interests |
|---|---|---|
| Angelica | Babei | Algebraic Number Theory with a computational emphasis, particularly on orders in semisimple algebras |
| Paul | Bezandry | Stochastic differential and difference equations, focusing on almost periodic solutions and their stability, and probability theory |
| Alexander | Burstein | Enumerative Combinatorics, focusing on permutation patterns, permutation statistics, and the Riordan group |
| Senhuei | Chen | Parabolic systems arising in physical oceanography |
| Dennis | Davenport | Enumerative Combinatorics, the Riordan group, Ramsey Theory, Stone–Čech Compactification, and mathematics education, focusing on undergraduate research |
| Roberto | De Leo | Dynamical systems, geometry of foliations, fractal geometry, biomathematics, computational geometry, and topology |
| Stanley | Einstein-Matthews | Quantum field theory, geometry, pure mathematics, and functional analysis |
| Tepper | Gill | Relativistic quantum mechanics, classical electrodynamics, nonlinear dynamical systems, and probability theory |
| Katharine | Gurski | Fluid Dynamics, Numerical Analysis, Partial Differential Equations, Magnetohydrodynamics, and Mathematical Modeling |
| Joon | Ha | Mathematical Modeling of diabetes and neuroscience, Dynamical Systems, and clinical studies of diabetes |
| Neil | Hindman | Topology, Logic, Ramsey Theory, and Stone–Čech Compactification |
| Sam | Hopkins | Algebraic and enumerative combinatorics, exploring combinatorial reciprocity, plane partitions, and root system chip-firing |
| Sayomi | Kamimoto | Nonlinear dynamical systems, applied bifurcation theory, collective behaviors, and mathematical modeling |
| Yeona | Kang | Scientific computing and data analysis of dynamic brain PET imaging, as well as deep learning and machine learning with structural neural network modeling |
| Christopher | Kim | Computational Neuroscience, Machine Learning, and Applied Mathematics |
| Mohammad | Mahmood | Material Science and High-Pressure Synthesis |
| Amir | Maleki | Functional Analysis, Operator Theory, and Real Analysis |
| Henok | Mawi | Partial Differential Equations, Geometric Optics, and Optimal Mass Transport |
| Cheikh | Ndiaye | Geometric Analysis, Calculus of Variations, Partial Differential Equations, and Differential Geometry |
| Paul | Peart | Enumerative combinatorics and random walks |
| Francois | Ramaroson | Algebra and Number Theory, Analysis, Applied Mathematics, Logic and Foundations, Geometry, and Topology |
| Jie | Ren | Motivic Donaldson–Thomas Invariants, Moduli Spaces, Noncommutative Geometry, Mirror Symmetry, and quantum field theoretical foundations of quantum invariants |
| Louis | Shapiro | Combinatorics, notably the Riordan group and Riordan arrays, and algebra |
| Sankar | Sitaraman | Algebraic number theory, including cyclotomic fields and Diophantine equations |
| Bourama | Toni | Differential Analysis, including Archimedean and Non-Archimedean Dynamical Systems, bifurcation theory, and applications in mathematical biology and economics |
| Qi | Wang | Applied and computational mathematics, with interests in modeling complex systems, soft matter, and machine learning applications |
Research Fields
Algebra
Algebraic Geometry, Homological Algebra, Representation Theory, and Lie Theory
Analysis
Approximation Theory, Complex Analysis, Harmonic Analysis, Functional Analysis, Differential and Nonlinear Analysis, Inverse Problems, Operator Theory, Variational Calculus, Automorphic forms, L-functions, and Wavelets
Applied Mathematics
Ordinary Differential Equations, Dynamical Systems, Mathematical Biology, Mathematical Physics, Partial Differential Equations, Scattering and Input-State-Output Engineering Systems, Numerical Analysis, Mass Transport Problems, and Fluid Dynamics
Combinatorics, Probability, and Statistics
Algebraic Combinatorics, Enumerative Combinatorics, Generating Functions, Permutation Patterns, Finite Group Theory, Random Walks, Statistics, Stochastic Processes, Statistical Physics
Geometry
Differential Geometry, Complex Geometry, Hyperbolic Geometry, Symplectic Geometry, Riemannian Geometry, and Algebraic Topology
Mathematics Education
Mathematics Education
Number Theory
Number Theory
Topology
Topology
Program of Study*
CORE COURSES (21 CR)
MATH 210 Algebra I
MATH 211 Algebra II
MATH 222 Real Analysis I
MATH 223 Real Analysis II
MATH 229 Complex Analysis I
MATH 250 Topology I
MATH 280 Topics in History of Math
SELECTIVES (9 CR)
Students select one course from the following group:
MATH 220 Intro to Analysis I
MATH 221 Intro to Analysis II
MATH 208 Intro to Modern Algebra I
MATH 209 Intro to Modern Algebra II
MATH 185 Intro to Complex Analysis
MATH 186 Intro to Differential Geometry
MATH 189 Probability and Statistics
MATH 184 Intro to Number Theory
MATH 199 Intro to General Topology
Students select two courses from the following group:
MATH 214 Number Theory I
MATH 224 Applications of Analysis
MATH 230 Complex Analysis II
MATH 231 Functional Analysis I
MATH 252 Algebraic Topology I
MATH 253 Algebraic Topology II
MATH 259 Differential Geometry I
MATH 260 Differential Geometry II
MATH 237 Partial Differential Equations II
ELECTIVE COURSES (30 CR)
DISSERTATION (12 CR)
*Courses included in the sample program of study are subject to change. Students should consult with their programs regarding their required program of study.
Admission to Candidacy
Students are admitted to formal candidacy by the Graduate School when they have completed the required coursework, passed the qualifying or comprehensive examination, submitted an approved topic for research, and been recommended by the Department. Candidates must also have satisfied the Graduate School writing proficiency requirement and Responsible Conduct of Research (RCR) requirement.
Graduate Funding
Admitted students may be eligible to compete for Graduate School competitive awards, which provide tuition remission and a stipend during the academic year. Additionally, graduate research or teaching assistantships may be available at the department level. Research assistants and teaching assistants work no more than 20 hours a week under the program's direction, usually in support of faculty research (research assistants) or in support of assigned courses (teaching assistants). Please see the Funding website for more detailed information.