Master of Science (M.S.) Applied Mathematics

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The Department of Mathematics offers a strong graduate program leading to the Master of Science (M.S.) in Applied Mathematics. Specific areas of study currently available include probability and statistics, differential equations, applied analysis, algebra, and coding theory.

  • Students will understand core graduate mathematics material and students must demonstrate substantial comprehension of Linear Algebra and Analysis, the common core subjects required of all students in the program.
  • Competence in written and oral communication is essential for most mathematical careers. Such communication skills are also important in many other aspects of life, therefore students will be able to deliver written and oral presentations demonstrating comprehension of complex mathematical content and the ability to communicate that complex mathematical content to a broad audience (general department faculty and graduate students).
  • The program prepares students for a variety of mathematical careers. The current program has four identified tracks: Ph.D. Preparation, Applied, Education, or Business. Students should be prepared for employment requiring mathematical skill and sophistication at the Master’s level.
  • Students shall develop a more sophisticated view of mathematics than is achieved in the undergraduate program. The opportunity for sophisticated learning comes both in and outside the classroom. Student exposure to mathematical research and advanced applications is an important aspect of this goal.
  • Students successfully completing the Ph.D. Preparation track should be able to enter quality doctoral programs with a reasonable probability of success.
  • Students should have the opportunity to hear research talks in seminars and colloquia, and participate in research projects (this might come through on campus employment, independent study, or thesis work). Students are strongly encouraged to attend our biweekly colloquium.

The admission criteria include but are NOT limited to the following requirements. Any decision regarding admission is made by the Graduate Committee on an individual basis, after taking into consideration the application material and supporting documents.

  • Must hold a bachelor's degree in mathematics (or in some other field, with extensive course work in mathematics), including a course in analysis comparable to the UCCS course MATH 3410.
  • Must have an overall GPA of at least 3.0, as well as a GPA of at least 3.0 in mathematics courses.
  • Must submit GRE General Test scores, from the most recent test, taken within the last 2 years. A percentile of 80 or higher is recommended on the Quantitative Reasoning portion. (For Spring 2021 or later admission.)
  • International applicants must demonstrate English language proficiency and submit additional documentation, as specified on the Applications page.

Under special circumstances students may be admitted with a lower GPA or without a course in analysis, as provisional degree students.

See also the admission requirements of the Graduate School

Please visit the Applications page to apply.

  • A 3.0 grade point average in coursework applied towards the degree.
  • All degree courses must be part of an approved plan of study, developed by the student and approved by the advisor (Graduate Chair) within the first semester after being admitted to the program. This plan may be revised at any time with the approval of the advisor. The plan will require students to demonstrate some cohesiveness in the courses chosen, or to demonstrate a clear subject area of concentration.
  • Courses will have graduate rank only if members of the graduate school faculty teach them and are at the 5000 level or above.
  • Modern Analysis I (MATH 4310) plus at least 27 semester hours of approved graduate work, including Linear Algebra (MATH 5130) and Modern Analysis II (MATH 5320). All students must pass the comprehensive examination in Modern Analysis. All students must complete Linear Algebra (MATH 5130) and the Analysis sequence (MATH 4310 and MATH 5320) in their first year of admission, and attempt the Comprehensive exam in Analysis offered in the Summer.
    : The MATH 4310 requirement may be waived on a case-by-case basis only for UCCS students who completed MATH 4310 with a grade of B or higher within one year before admission to the program, and for students in the Accelerated Master's Program. If a waiver is approved by the Graduate Chairthen MATH 4310 shall be replaced by 3 semester hours of approved graduate work.
  • Students completing one of the four tracks of study will automatically fulfill the requirements for the M.S. in Applied Mathematics degree.
  • All students must successfully complete one of the following: MATH 5480, MATH 5650, MATH 5670, or MATH 3670/5900 to fulfill the computational competency requirement. Please note that knowledge of a computer language such as MATLAB is necessary to complete this requirement. This requirement may be waived at the discretion of the Graduate Chair upon providing evidence of previous computing experience.
  • A student may complete up to 9 hours of appropriate graduate course work in departments other than the Department of Mathematics, as part of the “tracks” program. Such courses MUST be pre-approved by the advisor.
  • Students may select a thesis or non thesis option. Students in the thesis option will replace 6 hours of graduate level courses 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.

The department Graduate Committee must approve exceptions to these requirements.

  • 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 M.S. in Applied Mathematics degree.
  • Occasionally a graduate course is offered during the Summer semester. Full-time students normally complete the M.S. in Applied Mathematics program in two calendar years. Prospective students holding full-time jobs are also encouraged to enroll. However, they should have the flexibility to complete 1-2 courses per semester, and normally complete the degree in 3-4 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 M.S. in Applied Mathematics, see the UCCS Course Catalog.

Students can tailor their own curriculum within the M.S. program, by choosing one of the following four tracks: Ph.D. Preparation, Applied, Education, or Business. However, it is not mandatory to adhere to any particular track.

Each track requires the following three courses.

  • MATH 4310 - Modern Analysis I
  • MATH 5130 - Linear Algebra
  • MATH 5320 - Modern Analysis II

Plus one of the following courses.

  • MATH 5480 - Mathematical Modeling
  • MATH 5650 - Numerical Analysis
  • MATH 5670 - Scientific Computation
  • MATH 5900 - Graduate Seminar

Specific information for each track can be found below.

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 requires the courses listed in the M.S. Tracks tab above, the following three courses.

  • MATH 5150 - Modern Algebra II
  • MATH 5330 - Real Analysis
  • MATH 5450/5610 - Complex Variables

Plus three elective courses from the following list.

  • MATH 5170 - Rings and Modules I
  • MATH 5210 - Differential Geometry
  • MATH 5270 - Algebraic Coding Theory
  • MATH 5430 - Ordinary Differential Equations
  • MATH 5620 - Complex Analysis II
  • MATH 5850 - Stochastic Modeling

or any other 5000-level MATH course approved by the Mathematics Graduate Chair.

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. 

This track requires the courses listed in the M.S. Tracks tab above, the following four courses.

  • MATH 5470 - Methods of Applied Mathematics
  • MATH 5670 - Scientific Computation
  • MATH 5430 - Ordinary Differential Equations
  • MATH 5650 - Numerical Analysis

Plus two elective courses from the following list.

  • MATH 5250 - Introduction to Chaotic Dynamical Systems
  • MATH 5350 - Applied Functional Analysis
  • MATH 5420 - Optimization
  • MATH 5450/5610 - Complex Variables
  • MATH 5820 - Mathematical Statistics II
  • MATH 5850 - Stochastic Modeling

or any other 5000-level mathematics, science, or engineering course approved by the Mathematics Graduate Chair.

The Education Track is designed for those individuals who are interested in pursuing a career in teaching mathematics at the K- 14 level, but who desire the rigor and quality of a Master of Science (M.S.) 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 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.

This track requires the courses listed in the M.S. Tracks tab above, the following two courses.

  • MATH 5810 - Mathematical Statistics I
  • MATH 5820 - Mathematical Statistics II

Plus complete 9-12 hours in at least two of the following areas.

  • Algebra
  • Analysis
  • Applied Mathematics & Computing
  • Geometry
  • Probability & Statistics

Taking one of the following courses is recommended but not required.

  • CURR 5301 - Mathematical Connections and Concepts
  • TED 5920 - Secondary Math Methods

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. 

This track requires the courses listed in the M.S. Tracks tab above, the following two courses.

  • MATH 5810 - Mathematical Statistics I
  • MATH 5820 - Mathematical Statistics II

Plus two courses from the following list.

  • MATH 5420 - Optimization
  • MATH 5480 - Mathematical Modeling
  • MATH 5650 - Numerical Analysis
  • MATH 5850 - Stochastic Modeling

Plus two courses from the following list.

  • ECON 4010 - Advanced Microeconomic Theory
  • ECON 4020 - Advanced Macroeconomic Theory
  • FNCE 4000 - Advanced Corporate Finance
  • FNCE 4100 - Cases and Concepts in Finance