# 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

## 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.