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.
Qualifying Examination
A doctoral student in the mathematics track must take written examinations on abstract algebra and real analysis, as well as an oral examination in his or her chosen area of specialization. Subjects include complex analysis, control and calculus of variations, differential equations, dynamical systems, functional analysis, geometry, probability, and topology.
Required Courses
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 | ||
18 credit hours of approved course work | 18 | |
Total Units | 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 course work.