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 


Algebraic Geometry, Homological Algebra, Representation Theory, and Lie Theory


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


Differential Geometry, Complex Geometry, Hyperbolic Geometry, Symplectic Geometry, Riemannian Geometry, and Algebraic Topology

Mathematics Education

Mathematics Education

Number Theory

Number Theory



Program of Study* 


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


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



*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.