**Departmental Requirements for M.S. in Mathematics:****Pure Mathematics**

The Master of Science degree in pure mathematics requires that the student demonstrate knowledge in certain core areas. There are two options. Both options require a student to earn a grade of A or B in 18 hours of core courses.

**Core courses**:

**Option I**:

- Advanced Calculus I and II (MATH 5043 and 5053)
- Modern Algebra I and II (MATH 5003 and 5013)
- General Topology (MATH 5303)
- Complex Variables (MATH 5273*)

**Option II**:

- Advanced Calculus I and II (MATH 5043 and 5053)
- Modern Algebra I and II (MATH 5003 and 5013)
- Six hours from the following list: Real Analysis I and II (MATH 5143 and 5153), Complex Analysis I and II (MATH 5283 and 5293), Geometric Topology (MATH 5313) and Algebraic Topology I (MATH 6323), Algebra I and II (MATH 5613 and 5623).

**Elective courses**: Students working towards the M.S. degree in pure mathematics should complete 12 hours of course work selected from the following list:

Geometry and Algorithms in Three-Dimensional Modeling (MATH 5423*), Combinatorics (MATH 5673*), Number Theory (MATH 5713*), Introduction to Cryptography (MATH 5753*), Groups and Representations (MATH 5803*), Advanced Linear Algebra (MATH 5023), Fourier Analysis and Wavelets (MATH 5213), Partial Differential Equations (MATH 5233), Ordinary Differential Equations (MATH 5243), General Topology (MATH 5303), Geometric Topology (MATH 5313), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553), Algebra I (MATH 5613), Algebra II (MATH 5623), Seminar and Practicum in the Teaching of College Mathematics (MATH 5903), Algebraic Topology I (MATH 6323).

Course numbers labeled * are cross-listed with an undergraduate section.

**Alternative course selections**:

· Courses taken as an undergraduate can be used to satisfy requirements for core and elective courses as long as they are consistent with the Graduate College requirements.

· Substitutions for any of the 12 hours of electives requires consent from the Graduate Committee. In no case may more than nine hours outside the mathematical sciences (mathematics, statistics, or computer science) be counted toward the M.S. degree.

**Courses taken in graduate school**: The courses taken in graduate school must total 33 hours. The courses taken on the M.S. degree program must include 21 hours of non-cross-listed courses in the mathematical sciences. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Report or thesis: Each student must complete either a report or a thesis. Students electing to write a report must complete three hours of MATH 5000. Those electing to write a thesis must complete six hours of MATH 5000; three of those hours may be counted toward the 12 hours of electives. Under both of these options, a written document and a public presentation based on this individually directed project is required.

Other requirements: The university catalog contains detailed procedures applicable to all Master's degrees.