## Master of Science in Applied Mathematics

The **Department of Mathematics** offers a strong graduate program leading to the **Master of Science in Applied Mathematics**. Specific areas of study currently available include astrodynamics, statistics, probability, differential equations, applied analysis, computer vision, algebra, and coding theory. To respond to the needs of both students and employers, the Department has focused this graduate program into a system of four tracks, which are intended to help students develop their programs of study. These tracks are the K-14 Education track, the PhD preparation track, the Applied and Computational Mathematics track, and the Business and Management track. By channeling the Department’s efforts in these four areas, we feel that we can offer a graduate educational opportunity of exceptional quality. Customized programs of study are available for students whose interests in Applied Mathematics are not covered within the tracks.

To obtain the **Master of Science in Applied Mathematics**, students admitted into the program must complete at least 30 semester hours of approved graduate work, including Linear Algebra (Math 513) and Modern Analysis II (Math 532). All students must pass a comprehensive examination in Analysis. Students completing one of the four tracks of study will automatically fulfill the requirements for the MS Applied Math degree. A 3.00 grade point average in all course work applied towards the degree is required for regular acceptance into the program.

A student may complete up to 12 hours of appropriate graduate coursework in departments other than the Department of Mathematics. Such courses, unless they constitute part of an established track, MUST be PRE-approved by the advisor.

Students may select a thesis or non-thesis option. Students in the thesis option will replace up to 6 hours of courses work with a Master's thesis.

All students make an oral presentation regarding some aspect of advanced mathematics. For students pursuing the thesis option, the thesis defense will qualify as such a presentation.

Students who are enrolled "full–time" in the M.S. in Applied Mathematics program may qualify for one of the limited number of Graduate Teaching Fellowships available through the Department of Mathematics. Please contact the Department for additional information.

## Admissions Requirements:

Students must hold a Bachelor degree in mathematics (or a Bachelor degree in some other field, with extensive coursework in mathematics), including a course in real analysis comparable to the UCCS course MATH 431 (Modern Analysis I). A minimum undergraduate grade point average of 3.00 is required. For some programs of study, a course comparable to the UCCS course MATH 414 (Modern Algebra I) may also be required.

Under special circumstances students may be admitted to the program with a lower grade point average, or without a course in real analysis, as a Provisional Degree student. Scenarios under which this might occur include: the student's undergraduate work was completed a number of years ago; the student's undergraduate degree is not in mathematics; the student has not satisfactorily completed certain core mathematics courses (e.g. linear algebra, differential equations, advanced calculus, ...) The prerequisites which a student must then complete in order to change from Provisional to Regular status will be explicitly spelled out in the admission letter from the Department of Mathematics. Such prerequisites may include the completion of courses which will not count towards the **MS Applied Mathematics degree**.

## Miscellaneous Information

- Generally, up to 9 semester hours of graduate level mathematics courses completed prior to admission to the program may be applied towards the credit requirements of the MS Applied Mathematics degree.
- At least one mathematics course is usually offered at the 400/500 level during each Summer semester. "Full time" students normally complete the MS Applied Mathematics program in two calendar years. Prospective students holding full time jobs are also encouraged to enroll. Such students typically complete one course per semester, and normally complete the degree in four to five years.
- For a complete description of all courses taught by the mathematics department, as well as for a complete description of the requirements for the degree MS Applied Mathematics, students should obtain a copy of the UCCS Course Catalog, available at the UCCS Bookstore. See the Mathematics Department Course Offerings for a list of graduate mathematics courses to be offered in the future.

## The Ph.D Preparation track

The Ph.D Preparation track is designed for those individuals who are interested in obtaining a Masters Degree in Mathematics that will enable them to pursue a Ph.D degree in pure mathematics at a later time. It has been our experience that students interested in this track tend to emphasize pure mathematics rather than applied mathematics. To that end, the Ph.D Preparation track includes a solid exposure to pure mathematics with special emphasis in algebra, analysis and probability.

The Ph.D Preparation track consists of a core list of required courses together with an elective strategy.

## The Applied and Computational Mathematics track

The **Applied Mathematics and Scientific Computation Track** for the Masters Degree in Applied Mathematics is designed for those individuals pursuing careers in science and engineering with major mathematical or computational content. A mathematician working in an applied environment should have some knowledge of another discipline as well as modern computational skills. A typical problem requires construction of mathematical models from the concepts and data of the relevant branch of science, and reporting solutions and conclusions in the language of the discipline. To insure that graduates have some background in the major topics, a year sequence in Methods of Applied Mathematics and Scientific Computation is recommended. Courses from the core make up 18 of the required 30 hours for a Master's Degree.

## The Education Track within the Masters of Applied Mathematics Degree

The **Education track** is designed for those individuals who are interested in pursuing a career in teaching mathematics at the K through 14 level, but who desire the rigor and quality of a Master of Science degree in Applied Mathematics. Secondary schools and community colleges are increasingly interested in mathematics teachers who can demonstrate a competent use of technology within the classroom and who can integrate this technology with meaningful applications of mathematics. To that end, the Education track includes a core set of three courses that emphasize the use of applications and technology in the mathematics curriculum. A student successfully completing the Education track will have a solid background in the fundamental areas of mathematics (algebra, analysis), an excellent exposure to the applications of mathematics, particularly those that can be taught in the K-14 classroom, and robust training in the use of technology in the mathematics classroom.

## The elective strategies for the Education Track

After successfully passing the core list of courses above, the student must complete 12 additional graduate credit hours in mathematics. It is important to develop some depth in the areas of algebra, analysis, applied mathematics, geometry or probability. To that end, each student should specialize in two of the following areas by taking at least one course in each of the areas.

## The Business and Management track

The Business Track for the Master Degree in Applied Mathematics is designed for those individuals pursuing careers as actuaries, in financial services, or in other aspects of business and economics. Some of the core mathematical concepts in these areas include linear algebra, optimization, probability, statistics, and stochastic processes. Most applications require modern computational techniques.

Last updated January 26, 2016