Mathematics PhD
The Department offers a Ph.D. in mathematics designed for those with an undergraduate degree in Mathematics. The Ph.D. is suitable for those wishing to pursue careers in academics or industry. Possible areas of research specialization include:
- Algebra and Number Theory: Division algebras and the Brauer group, Galois cohomology, real algebraic geometry, algebraic groups, algebraic number theory, computational methods
- Analysis/Geometry: complex analysis, conformal and quasiconformal mappings, global analysis on manifolds, microlocal analysis, geometric analysis, partial differential equations
- Combinatorics/Graph Theory: graph theory, random structures, ordered sets, projective planes, theory of computation
- Computational Mathematics: high performance computing, computational fluid dynamics, image processing, inverse problems, numerical analysis (linear algebra, PDEs, optimization), scientific computation
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Requirements
Students admitted to the program, in full standing, should have the equivalent of an undergraduate degree in mathematics.
Mathematics Graduate Program HandbookPure mathematics
Students in a pure mathematics track must complete each of the following five areas.
- Math 511 & 512: Analysis I & Analysis II
- Math 521 & 522: Algebra I & II
- Four additional courses chosen from at least three different areas among: Algebra/Number Theory, Analysis/Geometry, Computational math, Discrete math, Topology.
- Math 590: Teaching Seminar
- TATTO course
- Teaching at least two one-semester courses
Computational mathematics
Students in the computational mathematics tract must complete each of the following five areas.
- Math 511 & 512: Analysis I & Analysis II
- Math 515 & 516: Numerical Analysis I & II
- Two of the following courses:
- Math 550: Functional Analysis
- Math 561: Matrix Analysis
- CS 551: Software Systems
- CS 555: Parallel Processing
- One of the following sequences:
- CS 551 & 555: Software Systems & Parallel Processing
- Math 557 & 558: Partial Differential Equations I & II
- Math 771 & 772: Numerical Optimization & PDEs
- software systems & parallel processing
- PDEs
- numerical optimization & numerical PDEs
- Math 590: Teaching Seminar
- TATTO course
- Teaching at least two one-semester courses