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.

Set I	Set II	Set III	Set IV
Algebra 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	Topology Math 636/Math 637	Numerical Analysis Math 609/Math 610

* Qualifying Exam Requirement:

• Students must pass at least 2 qualifying exams.
• These two qualifying exams must come from different sets in the above table.

* Breadth Requirement:

• Students must take at least 4 regular courses 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 typical student is expected to have fulfilled these requirements by the end of the second 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.

Subject	Courses
Algebra	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
Topology	Math 636, Math 637, Math 643, Math 644
Applied Analysis	Math 641, Math 642, Math 658, Math 670
Numerical Analysis	Math 609, Math 610, Math 661