Applied Mathematics, MS
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Introduction
Our MS in Applied Mathematics program offers a degree in applied mathematics along with specialization opportunities in many areas, including
- Applied Probability and Uncertainty Quantification
- Applied Statistics
- Data Science
- Discrete Mathematics
- Mathematics of Engineering and Science
- Numerical Analysis
- Operations Research
The program provides training in applied mathematics and/or statistics and opportunities for introductory research in collaboration with internationally recognized scholars. Students have the option to tailor their coursework with maximum flexibility or specialize in one of several concentrations of the degree. Students in all areas have the opportunity to participate in real-world research through our innovative Math Clinic and Statistical Consulting workshop. Some highlights of our exciting research projects include evolutionary dynamics, climate modeling, wildfire simulations, machine learning, genetic inheritance and association, optimization in data analysis, and more.
The degree is designed to give students a contemporary education in many areas of data science. In all of its activities, the department embodies the outlook that mathematics, statistics, computing, and data science are powerful tools that can be used to solve problems of immediate and practical importance. Our program emphasizes the training of skills valued by many employers. These skills include problem solving, critical thinking, analysis, facility with data, the ability to process quantitative information, and perhaps most important of all, the ability to learn and master new skills and concepts quickly. Many of our MS graduates have continued towards employment in the Denver business and research sectors and Denver area community colleges.
See our degree requirements section for further information about our concentration areas.
These degree requirements are subject to periodic revision by the academic department, and the College of Liberal Arts and Sciences reserves the right to make exceptions and substitutions as judged necessary in individual cases. Therefore, the College strongly urges students to consult regularly with their Applied Mathematics faculty advisor to confirm the best plans of study before finalizing them.
Graduate Education Policies and Procedures apply to this program.
Program Requirements
- Students must complete a minimum of 30 credit hours.
- Students must complete a minimum of 24 graduate (5000-level or higher) MATH credit hours.
- Students must earn a minimum grade of B- (2.7) in all courses applied to the degree and must achieve a minimum cumulative GPA of 3.0. Students cannot complete program or ancillary course requirements as P+/P/F or S/U.
- Students must complete all coursework with CU Denver faculty.
- Students must complete either a thesis or project, each with a written component and an oral presentation before a committee consisting of three graduate faculty members.
Program Restrictions, Allowances and Recommendations
- The remaining six hours must be either MATH courses numbered 5000 or above or approved courses outside the department numbered 4000 or above.
- Up to nine semester hours of prior course work may be transferred in (subject to approval); these must be at the 5000 level or above with a B- or better grade. Courses already applied toward another degree (graduate or undergraduate) cannot be used toward the MS degree in applied mathematics.
- The following MATH courses will not count toward a graduate degree: MATH 5010 History of Mathematics, MATH 5012 An Advanced Perspective on Number and Operation, MATH 5015 Capstone Course for Secondary Teachers, MATH 5017 Topics in Mathematics for Teachers, MATH 5198 Mathematics for Bioscientists, and MATH 5830 Applied Statistics.
| Code | Title | Hours |
|---|---|---|
| The following program requirements must be satisfied by all students in the MS in Applied Mathematics Program. | ||
| Complete the following required courses: | 6 | |
| Analysis Core Requirement | ||
| Applied Analysis | ||
or MATH 6131 | Real Analysis | |
| Linear Algebra Core Requirement | ||
| Applied Linear Algebra | ||
| Complete a minimum of 24 additional graduate level credit hours of MATH coursework. 1 | 24 | |
A student must satisfy the course requirements for the MS degree in one of these areas. Substitutions or changes to the requirements may be made with the written approval of a student’s academic advisor and the Graduate Committee. | ||
A student may devote up to 6 hours (of the 30 required hours) to the writing of a thesis, or up to 3 hours to the completion of a project. Following completion of course work, all candidates must make an oral presentation of a thesis or a project before a committee consisting of three graduate faculty members. | ||
| Total Hours | 30 | |
- 1
The following MATH courses will not count toward a graduate degree: MATH 5010 History of Mathematics, MATH 5017 Topics in Mathematics for Teachers, and MATH 5830 Applied Statistics.
MS Degree without a Concentration Area
Note that MATH 6131 Real Analysis can be used to satisfy both the analysis core requirement and may also count as one of the three courses satisfying this requirement.
| Code | Title | Hours |
|---|---|---|
| Complete nine credit hours from the following courses: 1 | 9 | |
| Probability | ||
| Statistical Inference | ||
| Network Flows | ||
| Linear Programming | ||
| Numerical Analysis I | ||
Any MATH course at the 6000 level or higher (with the exception of MATH 6960 Research Methods in Mathematics and Statistics). | ||
| Total Hours | 9 | |
- 1
Additional courses may apply, given prior approval by the student's advisor and the Graduate Program Director.
Applied Probability and Uncertainty Quantification Concentration
| Code | Title | Hours |
|---|---|---|
| Complete all of the following courses: | 12 | |
| Probability | ||
| Uncertainty Quantification | ||
| Probabilistic Modeling | ||
or MATH 6380 | Stochastic Processes | |
| Numerical Analysis I | ||
or MATH 5733 | Partial Differential Equations | |
or MATH 6131 | Real Analysis | |
or MATH 7386 | Monte Carlo Methods | |
| Total Hours | 12 | |
Applied Statistics Concentration
| Code | Title | Hours |
|---|---|---|
| Complete all of the following courses: | 12 | |
| Statistical Inference | ||
| Applied Regression Analysis | ||
| Workshop in Statistical Consulting | ||
| Probability | ||
or MATH 5792 | Probabilistic Modeling | |
or MATH 6380 | Stochastic Processes | |
| Complete one of the following courses: 1 | 3 | |
| Intro to Statistical and Machine Learning | ||
| Machine Learning Methods | ||
| Uncertainty Quantification | ||
| Stochastic Processes | ||
| Spatial Data Analysis | ||
| Statistical and Machine Learning | ||
| Mathematical Probability | ||
| Monte Carlo Methods | ||
| Bayesian Statistics | ||
| Topics in Probability and Statistics | ||
| Total Hours | 15 | |
- 1
Additional courses may apply, given prior approval by the student's advisor and the Graduate Program Director.
Data Science Concentration
| Code | Title | Hours |
|---|---|---|
| Complete all of the following: | 12 | |
| Applied Regression Analysis | ||
| Machine Learning Methods | ||
| Network Flows | ||
or MATH 5593 | Linear Programming | |
or MATH 6595 | Nonlinear Programming | |
| Numerical Analysis I | ||
or MATH 5733 | Partial Differential Equations | |
or MATH 6101 | Uncertainty Quantification | |
or MATH 7386 | Monte Carlo Methods | |
or MATH 7665 | Numerical Linear Algebra | |
| Complete an additional course from the above lists or from the following list: | 3 | |
| Math Clinic | ||
| Real Analysis | ||
| Workshop in Statistical Consulting | ||
| Stochastic Processes | ||
| Spatial Data Analysis | ||
| Statistical and Machine Learning | ||
| Applied Graph Theory | ||
| Mathematical Probability | ||
| Stochastic Differential Equations | ||
| Bayesian Statistics | ||
| Integer Programming | ||
| Total Hours | 15 | |
Discrete Mathematics Concentration
| Code | Title | Hours |
|---|---|---|
| Complete four of the following courses: | 12 | |
| Network Flows | ||
| Applied Graph Theory | ||
| Advanced Graph Theory | ||
| Applied Combinatorics | ||
| Combinatorial Structures | ||
| Topics in Discrete Math | ||
| Total Hours | 12 | |
Mathematics of Engineering and Science Concentration
| Code | Title | Hours |
|---|---|---|
| Complete three of the following courses: | 9 | |
| Applied Regression Analysis | ||
| Numerical Analysis I | ||
| Partial Differential Equations | ||
| Math Clinic | ||
| Probabilistic Modeling | ||
| Complete two of the following courses: | 6 | |
| Numerical Analysis II | ||
| Uncertainty Quantification | ||
| Introduction to Finite Element Methods | ||
| Monte Carlo Methods | ||
| Numerical Linear Algebra | ||
| Total Hours | 15 | |
Numerical Analysis Concentration
| Code | Title | Hours |
|---|---|---|
| Complete all of the following courses: | 6 | |
| Numerical Analysis I | ||
| Partial Differential Equations | ||
| Complete three of the following courses: | 9 | |
| Linear Programming | ||
| Numerical Analysis II | ||
| Uncertainty Quantification | ||
| Nonlinear Programming | ||
| Introduction to Finite Element Methods | ||
| Monte Carlo Methods | ||
| Numerical Linear Algebra | ||
| Mathematical Foundations of Finite Element Methods | ||
| Total Hours | 15 | |
Operations Research Concentration
| Code | Title | Hours |
|---|---|---|
| Complete all of the following courses: | 6 | |
| Linear Programming | ||
| Probabilistic Modeling | ||
or MATH 6380 | Stochastic Processes | |
| Complete two of the following courses: | 6 | |
| Game Theory | ||
| Network Flows | ||
| Math Clinic (with approval) | ||
| Nonlinear Programming | ||
| Advanced Linear Programming | ||
| Integer Programming | ||
| Advanced Nonlinear Programming | ||
| Topics in Optimization | ||
| Total Hours | 12 | |
To learn more about the Student Learning Outcomes for this program, please visit our website.