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flow pass a cylinder with Reynolds number 200. The simulation was done using the augmented immersed interface method.
GRADUATE BROCHURE

PhD Qualifying Examination and Required Courses


Qualifying Examination

One-year sequences for the Written Qualifying Examination. Select three sequences. This page describes the standard tracks. The Interdisciplinary Tracks are described here. Full details on scheduling and retake policies are found here.

MA 521 - 721 Abstract Algebra
MA 520 - 720 Linear Algebra and Lie Algebra
MA 522 - 722 Computer Algebra II
MA 523 - 723 Applied Matrix Theory
MA 551 - 753 Topology
MA 580 - 780 Numerical Analysis
MA 515 - 715 Analysis
MA 531 - 731 System & Control
MA 532 - 732 Ordinary Differential Equations
MA 534 - 734 Partial Differential Equations
MA 573 - 574
Modeling
MA 524 - 724 Combinatorics
MA 546 - 747 Applied Probability and Stochastic Processes
MA 518 555 Differential Geometry


Required Courses

Students who have not had the equivalent of MA 405 (Introduction to Linear Algebra and Matrices), MA 407 (Introduction to Modern Algebra), and MA 425 - 426 (Mathematical Analysis I and II) must make up these courses. Students who have not had the equivalent of MA 426 may take it for graduate credit by registering for MA 591M.

The following courses must be passed with a grade of A or B.

  • All students: MA 515 Real Analysis and MA 521 Modern Algebra.
  • Mathematics students: three from Group 1 and one from Group 2.
  • Applied Mathematics students: two from Group 1 and two from Group 2.
Group 1
MA 513 Complex Variables
MA 551 Topology
MA 518 Differential Geometry
MA 520 Linear Algebra
MA 715 Functional Analysis

Group 2
MA 580 Numerical Analysis
MA 532 Ordinary Differential Equations
MA 534 Partial Differential Equations
MA 546 Probability
MA 785, 584, or 587 Numerical Differential Equations

 

Concentration in Computational Mathematics (CMA)

CMA students must fulfill all the requirements for the PhD in Applied Mathematics. One of the three subjects for the qualifying examination must be Numerical Analysis such as MA 580 - 780. In addition to MA 580 and 780, CMA students must take three courses from the list of approved CMA courses.

Concentration in Interdisciplinary Mathematics (MAI)

The MAI concentration is available to Ph.D. students in either Mathematics or Applied Mathematics. It is not available to Masters students.

MAI students fulfill all the requirements for the Ph.D in MA or AMA except that they have the option of substituting a qualifier in another field for one of the three required math PhD qualifying examinations. This substitution requires prior approval of the Director of Graduate Programs (DGP) or Graduate Program Administrator (GPA). The substituted exam does not have to be on the same date as the two math qualifying examinations. The taking of the two math qualifying examinations and the substituted exam will be considered as one set of examinations and the usual departmental retest policies will hold.

In addition to the MA or AMA PhD requirements the IMA student would be required to demonstrate evidence of interdisciplinary work. This would be done as follows:

Required of all MAI students

  • Member of committee from other discipline.
  • At least 2 courses in the other discipline, at least one of which is not cross-listed with mathematics.
  • A formal research proposal to be presented at the preliminary oral exam. The proposal could be as much as several fully developed chapters of the final thesis or as little as a few pages. The proposal would clearly explain the interdisciplinary research plan. A copy would be filed with the Math Dept Graduate Program Office.

MAI Students are required to do at least two of:
  • Attend and present at a conference in the other discipline.
  • Publish in the literature of the other discipline.
  • Have a Summer internship.
  • Take a Preliminary examination in the other discipline.

 

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