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 555 – 755 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.