### 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

## 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

Topology

## 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

## 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.