2025-2026 Academic Catalog

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Applied Mathematics, MS

Program Requirements

  1. Students must complete a minimum of 30 credit hours.
  2. Students must complete a minimum of 24 graduate (5000-level or higher) MATH credit hours.
  3. 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.
  4. Students must complete all coursework with CU Denver faculty.
  5. 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

  1. The remaining six hours must be either MATH courses numbered 5000 or above or approved courses outside the department numbered 4000 or above.
  2. 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.
  3. The following MATH courses will not count toward a graduate degree: MATH 5010 History of MathematicsMATH 5012 An Advanced Perspective on Number and OperationMATH 5015 Capstone Course for Secondary TeachersMATH 5017 Topics in Mathematics for TeachersMATH 5198 Mathematics for Bioscientists, and MATH 5830 Applied Statistics.
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
Real Analysis
Linear Algebra Core Requirement
Applied Linear Algebra
Complete a minimum of 24 additional graduate level credit hours of MATH coursework. 124
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 Hours30
1

The following MATH courses will not count toward a graduate degree: MATH 5010 History of MathematicsMATH 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.

Complete nine credit hours from the following courses: 19
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 Hours9
1

Additional courses may apply, given prior approval by the student's advisor and the Graduate Program Director.

Applied Probability and Uncertainty Quantification Concentration

Complete all of the following courses:12
Probability
Uncertainty Quantification
Probabilistic Modeling
Stochastic Processes
Numerical Analysis I
Partial Differential Equations
Real Analysis
Monte Carlo Methods
Total Hours12

Applied Statistics Concentration

Complete all of the following courses:12
Statistical Inference
Applied Regression Analysis
Workshop in Statistical Consulting
Probability
Probabilistic Modeling
Stochastic Processes
Complete one of the following courses: 13
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 Hours15
1

Additional courses may apply, given prior approval by the student's advisor and the Graduate Program Director.

Data Science Concentration

Complete all of the following:12
Applied Regression Analysis
Machine Learning Methods
Network Flows
Linear Programming
Nonlinear Programming
Numerical Analysis I
Partial Differential Equations
Uncertainty Quantification
Monte Carlo Methods
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 Hours15

Discrete Mathematics Concentration

Complete four of the following courses:12
Network Flows
Applied Graph Theory
Advanced Graph Theory
Applied Combinatorics
Combinatorial Structures
Topics in Discrete Math
Total Hours12

Mathematics of Engineering and Science Concentration

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 Hours15

Numerical Analysis Concentration

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 Hours15

Operations Research Concentration

Complete all of the following courses:6
Linear Programming
Probabilistic Modeling
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 Hours12

To learn more about the Student Learning Outcomes for this program, please visit our website.