Topics and Syllabi for Comprehensive Exams

The topics for the Comprehensive Exams vary depending upon the degree program. They are listed below according to these programs along with the courses that serve as the best preparation for the exams. The following pages list the specifics within each topic for which students are responsible on the comprehensive exams. 

	Topic	Preparatory Courses
M.S. Pure Mathematics
	Advanced Calculus	Math 4143, 4153
	Modern Algebra	Math 4613, 5013
	General Topology	Math 5303
M.S. Applied Mathematics
	Advanced Calculus	Math 4143, 4153
	Complex Variables	Math 4283
	Numerical Analysis	Math 4513
	Advanced Linear Algebra	Math 5023
Ph.D.
	Real Analysis	Math 5143, 5153
	Complex Analysis	Math 5283, 5293
	Topology	Math 5313, 6323
	Algebra	Math 5613, 5623
	Statistics	Stat 4113, 4223
Ed.D.
	Real Analysis	Math 5143, 5153
	Complex Analysis	Math 5283, 5293
	General Topology	Math 5303
	Algebra	Math 5613, 5623
	Statistics, Computer Science	Sequence chosen by student
	or Numerical Analysis

For the Ph.D. with Specialization in Mathematics Education any four of the five exams may be chosen; all other Ph.D. students take the first four exams. For the Ed.D. Advanced Calculus (Math 4143, 4153) may be substituted for either Real Analysis or Complex Analysis. If this substitution is NOT made, then Modern Algebra (Math 4613, 5013) may be substituted for Algebra.

 Comprehensive Exam Topics