A student in the traditional mathematics program must demonstrate knowledge of the basic concepts and techniques of algebra, analysis (real and complex), and topology. This includes taking all courses in the three basic areas and successfully completing qualifying examinations in algebra and analysis. Mathematics PhD students must take 36 credit hours of approved courses with a grade average of B or better. For students entering with a Master’s degree in a mathematical subject compatible with our program, as determined by the graduate committee, this requirement is reduced to 18 credit hours of approved courses.
Qualifying Examination
Each student will be required to take two written qualifying exams in real analysis and abstract algebra. Syllabi for the exams are available to students. Exams will be offered twice a year, usually in January and May. Students may attempt each exam up to two times. Under normal circumstances, students are expected to have passed both exams by the end of their fifth semester.
Area Examination
A doctoral student in the mathematics program must pass an oral area examination in his or her chosen area of specialization. The subjects for the area exam will be determined by the student and their advising committee. Past topics have included complex analysis, control and calculus of variations, differential equations, dynamical systems, functional analysis, geometry, probability, and topology.
Course Requirements:
| Abstract Algebra: | 6 | |
| Abstract Algebra I | ||
| Abstract Algebra II | ||
| Analysis: | 9 | |
| Introduction to Real Analysis I | ||
| Introduction to Real Analysis II | ||
| Complex Analysis I | ||
| Geometry and Topology (one of the following): | 3 | |
| Introduction to Topology | ||
| Algebraic Topology | ||
| Differential Geometry | ||
| Differential Manifolds | ||
| Approved Coursework | 18 | |
| Total Credit Hours | 36 | |
A student with a Master’s degree in a mathematical subject compatible with our program, as determined by the graduate committee, must take 18 credit hours of approved courses. The graduate committee will determine which of the specific course requirements stated above have been satisfied by the master’s coursework.