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Texas A&M University
Qualifying and Breadth Requirements

The Department of Mathematics offers 5 distinct qualifying exams in the following subjects: Each qualifying exam has a duration of 4 hours, and is offered twice a year (January and August). The syllabi and schedules can be found in the Qualifying Exam section of the Graduate Program web page.

  • The Qualifying Exams are designed to assess students' competence in basic mathematical skills and knowledge in the corresponding areas, at the level of the core courses displayed in the table below.
  • The Breadth Requirement is designed to ensure that students acquire a broad education and a solid background in mathematics, thus requiring that they demonstrate basic knowledge in the various areas displayed in the table below.
Core Courses:

Set I

Set II


Set IV


Math 653/Math 654

Real Analysis

Math 607/Math 608

Diff. Geometry

Math 622/Math623

Applied Analysis

Math 641/Math 642

Discrete Math/Number Theory

Math 613/Math 630/Math 627

Complex Analysis

Math 617/Math 618


Math 636/Math 637

Numerical Analysis

Math 609/Math 610

* Qualifying Exam Requirement:

  • Students must pass at least 1 qualifying exam by the end of 3rd semester of enrollment (not counting Summers) and 2 qualifying exams by the end of the second year of enrollment.
  • These two qualifying exams must come from different sets in the above table.

* Breadth Requirement:

  • Students must take at least 4 regular courses (no seminars) at a level greater or equal to the core courses and obtain a B or higher in each course.
  • In each of the 4 sets of subjects displayed in the table above, the student must either take a corresponding course or pass a qualifying exam. (See the list below for courses that can be used to fulfill the breadth requirements.)
  • A student is expected to have fulfilled these requirements by the end of the fourth year of enrollment.

* Courses for Breadth Requirement:

The following courses can be used to fulfill the breadth requirements in the respective areas. Additional courses may be used with the approval of the Graduate Committee. Typically, seminar and special topic classes cannot be used towards the breadth equirement.




Math 653, Math 654

Discrete Math/Number Theory

Math 613, Math 630, Math 626, Math 627

Real Analysis
Math 607, Math 608, Math 655, Math 656
Complex Analysis
Math 617, Math 618, Math 650
Differential Geometry
Math 622, Math 623
Math 636, Math 637, Math 643, Math 644
Applied Analysis
Math 611, Math 612, Math 641, Math 642, Math 658, Math 670
Numerical Analysis
Math 609, Math 610, Math 661