# University of Vermont

## 2012-2013 Catalogue

### Mathematics (Master of Science)

#### Overview

The Department of Mathematics offers programs towards the Master of Science, Master of Science in Teaching, and the Doctor of Philosophy in Mathematical Sciences. There are two areas of concentration: pure mathematics and applied mathematics. The programs emphasize the interaction between these two areas and the common role of scientific computation. Students can take courses common to both areas, enabling them to gain an appreciation of the mathematical techniques and the connections between theory and applications.

The department offers an Accelerated Masterâ€™s Program (AMP) leading to a B.S. and M.S. degree in five years. Interested students should contact the department by the end of their sophomore year.

Departmental research interests include classical analysis, harmonic analysis, Fourier analysis, approximation theory, algebra, number theory, graph theory, combinatorics, fluid mechanics, biomathematics, differential equations, numerical analysis, and modeling.

#### General Requirements

#### Specific Requirements

##### Requirements for Admission to Graduate Studies for the Degree of Master of Science

Because of the breadth of pure and applied mathematics, it is recognized that applicants for admission will have diverse backgrounds. Admission requirements are therefore flexible. Applicants should have demonstrated strength in either pure or applied mathematics, a bachelor's degree with a major in mathematics or a closely related discipline, and satisfactory scores on both the general and subject (mathematics) sections of the Graduate Record Examination.

##### Minimum Degree Requirements for the Degree of Master of Science

Each student must complete one of the following options:

* Option A (Thesis):* Twenty-four semester hours of acceptable graduate credits in advanced mathematics courses; six semester hours of thesis research culminating in a master's thesis, or

* Option B (Non-Thesis):* Thirty semester hours of acceptable graduate credits in advanced mathematics courses; no thesis required.

Under either option students must take, or acquire the knowledge of the content in, the courses MATH 331 and MATH 333, and must satisfactorily complete at least four 300-level mathematics courses and the seminar MATH 382. In both options students must select a major concentration from among the areas: Analysis, Algebra, Applied Mathematics, or Discrete Mathematics. The concentration shall consist of at least nine approved credits in advanced mathematics courses in the respective area, three of which must be at the 300-level; students in option B. may count the six credits of thesis credit towards these nine credits. In both options students must also select a minor concentration consisting of at least three approved credits of advanced mathematics complementary to the major area. With approval of the student's advisor up to six credits of courses outside mathematics may be used to fulfill the major, minor, or degree requirements.

#### Affiliations

- Colleges and Schools: College of Engineering and Mathematical Sciences. Graduate College.
- Departments and Programs: Mathematics and Statistics Department.