The Ph.D. in Mathematical Sciences is a Purdue University degree offered in the Department of Mathematical Sciences.

Students earning a Ph.D. in Mathematical Sciences have the option to specialize in pure mathematics, applied mathematics or mathematical statistics.

Our department is currently doing research in integrable systems, mathematical physics, dynamical systems, noncommutative geometry, operator algebras, differential geometry, partial differential equations, functional analysis, statistics and probability, applied mathematics, biomathematics, computational neurosciences, and scientific computing.

**Understanding the requirements**

Students are required to complete 42 credit hours of coursework in the following:

Four core MATH subject courses

- Introduction to Complex Variables I, MATH 53000
- Real Analysis & Measure Theory, MATH 54400
- Abstract Algebra, MATH 55300
- Linear Algebra, MATH 55400

Two MATH or STAT subject courses

- Numerical Analysis, MATH 51400
- Partial Differential Equations, MATH 52300
- Differential Geometry, MATH 56200
- Elementary Topology, MATH 57100
- Introduction to Algebraic Topology, MATH 57200
- Introduction to Probability, STAT 519003

Three courses (9 credit hours of coursework) at an advanced level in your field of specialty

Students in the applied mathematics specialty will select two courses from MATH/CSCI 51400, 51500, 61400, 61500, and one course that uses advanced mathematics, taken outside the mathematical sciences.

This program requires completion of at least 90 credit hours of combined course work and research. An M.S. degree from an accredited university may contribute up to 30 credit hours toward this requirement, subject to approval.