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 Handbook

Pure mathematics

Students in a pure mathematics track must complete each of the following five areas.

  • The following courses:
    • 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.
  • Completion of written qualifying examinations in algebra and analysis as well as one area of the student's choosing.
  • Advanced course work, including at least two courses or seminars in the student's research area.
  • An acceptable dissertation and oral defense.
  • Teaching requirements:
    • 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.

  • The following courses:
    • 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
  • Completion of written qualifying examinations in analysis and numerical analysis as well as one area chosen from the following:
    • software systems & parallel processing
    • PDEs
    • numerical optimization & numerical PDEs
  • Advanced course work, including at least two courses or seminars in the student's research area.
  • An acceptable dissertation and oral defense.
  • Teaching requirements:
    • Math 590: Teaching Seminar
    • TATTO course
    • Teaching at least two one-semester courses