The Department of Mathematics offers coursework and research leading to the PhD degree in mathematics. The department has a diversified graduate faculty with current areas of research in algebra, classical analysis, differential equations, geometry, harmonic analysis, logic and foundations, number theory, probability and stochastic processes, and topology.
For more information, visit the Department of Mathematics website.
Requirements
Admission Requirements
Applicants must have demonstrated mathematical maturity and accomplishment roughly at the level of a successful mathematics major at CU Boulder. Applicants must also demonstrate mathematical potential: success in courses in advanced calculus and abstract algebra help demonstrate this potential. General and mathematics GRE subject scores are required for PhD students.
Degree Requirements
Students must complete at least 30 credit hours of approved graduate coursework and 30 credit hours of thesis work.
Before being admitted to candidacy for the PhD degree in mathematics, a student must take two graduate courses each in algebra, real analysis and geometry/topology en route to passing two out of three preliminary exams in these fields. In addition, the student must take a course in complex analysis. The student must then pass a comprehensive exam.
Students should read the Doctoral Degree Requirements section carefully. The student is responsible for satisfying these requirements at the proper time.
Plan(s) of Study
Below is a sample course plan for first and second year students. In their third year onward, students typically complete dissertation research take elective coursework.
| Year One | Credit Hours | |
|---|---|---|
| MATH 6130 | Algebra 1 | 3 |
| MATH 6140 | Algebra 2 | 3 |
| MATH 6310 | Introduction to Real Analysis 1 | 3 |
| MATH 6320 | Introduction to Real Analysis 2 | 3 |
| MATH 5905 | Mathematics Teacher Training | 1 |
| ELECTIVE MATH CLASS (1) | Student Choice - check with faculty mentor or grad program director | 3 |
| Credit Hours | 16 | |
| Total Credit Hours | 16 | |
| Year Two | Credit Hours | |
|---|---|---|
| MATH 6210 | Introduction to Topology 1 | 3 |
| MATH 6230 | Introduction to Differential Geometry 1 | 3 |
| MATH 6350 | Functions of a Complex Variable 1 | 3 |
| MATH 5905 | Mathematics Teacher Training | 1 |
| ELECTIVE MATH CLASS (2) | 6 | |
| Credit Hours | 16 | |
| Total Credit Hours | 16 | |
Learning Outcomes
By the completion of the program, students will be able to:
- Have a mastery of fundamental knowledge in Mathematics (Algebra, Analysis, Geometry, Topology).
- Solve problems and communicate solutions in rigorous mathematical language.
- Explain mathematical concepts effectively.
- Conduct independent research.