Master of Science in Applied Mathematics

Overview

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.

Application forms are available HERE.

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

1. 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.
2. 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.
3. 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 Tracks

   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. These are described below. Please visit the Math Course Descriptions page for details about the courses.

The core course list for the Ph.D Preparatory Track (All 5 courses)

MATH 513 – Linear Algebra
MATH 515 – Modern Algebra II
MATH 532 – Modern Analysis II
MATH 533 – Real Analysis
MATH 545 – Complex Variables

The elective course list for the Ph.D Preparatory Track (Choose 5 courses)

MATH 517– Graduate Modern Algebra I
MATH 527 – Algebraic Coding Theory
MATH 543 – Ordinary Differential Equations
MATH 562 – Complex Variables II
MATH 585 – Stochastic Modeling

or any other 500-level mathematics course offered by University of Colorado at Colorado Springs, approved by the Mathematics Graduate Advisor.

   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. Please visit the Math Course Descriptions page for details about the courses.

Core course list for the Applied Science Track

MATH 513 - Linear Algebra
MATH 547 - Methods of Applied Mathematics
MATH 542 - Optimization
MATH 590 - Fourier Analysis
MATH 532 - Analysis
MATH 567 - Scientific Computation
MATH 585 - Stochastic Modeling
MATH 543 - Ordinary Differential Equations
MATH 565 - Numerical Analysis

Beyond the core, any graduate course offered by the Department of Mathematics or by other Science and Engineering departments is suitable for the degree, but students must develop a program of study with a Mathematics Graduate Advisor. The topics and corresponding courses from mathematics most likely to be encountered in applications are listed below.

Applied and Applicable Courses
MATH 545 - Complex Variables
MATH 552 - Perturbation Theory in Astrodynamics
MATH 535 - Applied Functional Analysis
MATH 548 - Mathematical Modeling
MATH 582 - Introduction to Mathematical Statistics
MATH 527 -Algebraic Coding Theory
MATH 525 - Introduction to Chaotic Dynamical Systems

   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 Education track consists of a core list of required courses together with an elective strategy. These are described below. Please visit the Math Course Descriptions page for details about the courses.

The core course list for the Education Track

MATH 510 – Technology in the Mathematics Classroom
MATH 513 – Linear Algebra
MATH 521 - Modern Geometry
MATH 532 – Modern Analysis II
MATH 582 – Introduction to Mathematical Statistics I

Recommended:
one from CURR 5301 - Mathematical Connections and Concepts or T ED 592 Secondary Math Methods

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.

Algebra
MATH 515 – Field theory,
MATH 517 – Groups, rings and modules,
MATH 527 – Coding theory

Analysis
MATH 533 – Real Analysis I
MATH 535 – Applied Functional Analysis
MATH 542 - Optimization
MATH 543 – Ordinary Differential Equations
MATH 545 – Complex Variables,
MATH 562 – Complex Variables II

Applied Mathematics and Computing
MATH 547 – Methods of Applied Mathematics
MATH 548 – Mathematical Modeling
MATH 552 – Perturbation Theory in Astrodynamics
MATH 565 – Numerical Analysis
MATH 584 – Computer vision

Geometry
MATH 521 – Higher Geometry,
MATH 523 – Fractal Geometry,
MATH 525 – Introduction to Chaotic Dynamical Systems,
MATH 526 – Elementary Differential Geometry

Probability and Statistics
MATH 585 – Stochastic modeling
MATH 583 – Linear Statistical Models
MATH 591 – Theory of Probability

 

   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. Please visit the Math Course Descriptions page for details about the courses.

Core Math courses for the Business Track

MATH 513 - Linear Algebra
MATH 532 - Analysis
MATH 581 - Mahematical Statistics I
MATH 582 - Mathematical Statistics II

Courses from the core make up 12 of the required 30 hours for a Masters Degree. Other topics and corresponding courses from Mathematics most likely to be encountered in business are listed below.

Specialty courses from Mathematics (Choose at least 2)

MATH 553 - Ordinary Differential Equations
MATH 565 - Numerical Analysis
MATH 448 - Mathematical Modeling
MATH 542 - Optimization

Both financial services and Actuarial options require courses from Economics and Finance. These options contain adequate preparation for the first two actuarial exams.

Additional required courses for Actuarial or Finance options

MATH 585 - Stochastic Modeling

Two of four economics and finance courses:
ECON 401 - Advanced Micro Economic Theory
ECON 402 - Advanced Macro Economic Theory
FIN 401 - Advanced Corporate Finance
FIN 402 - Cases and Concepts in Finance

Other Appropriate Courses From Business
Marketing
Operations Management
Information Systems
Risk Management

Departmental Course Catalog and Descriptions:

* The Catalog description of courses offered by the Mathematics Department
* The Semester offerings for courses by the Mathematics Department in the near future.
* The Expected Graduate offerings in the future.