Applied Mathematics, PhD
Graduate School Policies and Procedures apply to this program.
Please click here to see Mathematical and Statistical Sciences department information.
Introduction
The Department of Mathematical and Statistical Sciences offers a PhD in Applied Mathematics. The degree is designed to give candidates a contemporary, comprehensive education in applied mathematics and to provide research opportunities in the special fields of computational mathematics, discrete mathematics, mathematics of science and engineering, operations research, optimization, probability, and statistics.
These program 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 program advisor and CLAS advisor to confirm the best plans of study before finalizing them.
Program Requirements
- Students must complete a minimum of 72 approved credit hours.
- Students must complete all credits at the graduate 6000-level and above.
- Students must earn a minimum grade of B (3.0) or better in all core courses, a B- (2.7) in all other courses taken at CU Denver and must achieve a minimum cumulative program GPA of 3.0. All graded attempts in required and elective courses are calculated in the program GPA. Students cannot complete program or ancillary course requirements as pass/fail.
- Students must complete 42 credit hours with CU Denver faculty.
Program Restrictions, Allowances and Recommendations
- There are six phases of the PhD program. A candidate must fulfill course requirements, pass the preliminary examinations, establish a PhD committee, meet the academic residency requirement, pass the comprehensive examination and write and defend a dissertation.
- The following MATH courses will NOT count toward a graduate degree: MATH 5000-5009, 5010, 5012-5015, 5017, 5198, 5250 and 5830.
- Students must complete 42 semester hours of non-thesis course work at the graduate level (up to 30 hours of this course work may be transferred in, including courses taken as part of a master's degree). In addition, 30 hours of dissertation credit must be taken. Three readings courses (1 semester hour each) are required as part of the formal course work. Students must also satisfy a breadth requirement by completing a total of six graduate math courses from among several areas of mathematics, with no more than three of these courses from any one area.
- The preliminary examinations are designed to determine that students who intend to pursue the PhD program are qualified to do so. These four-hour written examinations are in the areas of applied analysis and applied linear algebra. Students must pass these exams by the start of their fourth semester.
- Six semesters of full-time scholarly work are required, as specified in the rules of the Graduate School. All students are strongly advised to spend at least one year doing full-time course work or research with no outside employment.
- The comprehensive examination is taken after completion of the preliminary exams, completion of at least three semesters of residency, and upon completion of essentially all non-thesis coursework. The exam is designed to determine mastery of graduate-level mathematics and the ability to embark on dissertation research. It consists of a six-hour written examination and an oral follow-up examination. Students must pass the comprehensive exam by the beginning of the 4th year. Within six months after passing the comprehensive examination, the candidate must present a dissertation proposal to their dissertation committee.
- Each student must write and defend a dissertation containing original contributions and evidence of significant scholarship. The dissertation defense is public and must be given before an examining committee approved by the Graduate School.
For more detailed information about the Applied Mathematics PhD, see department website.
Required Courses
| Code | Title | Hours |
|---|---|---|
| Take the following | 3 | |
| MATH 5779 | Math Clinic | 3 |
| Code | Title | Hours |
|---|---|---|
| Take a minimum of three readings courses. | 3 | |
| MATH 7921 | Readings in Mathematics | 1 |
| MATH 7922 | Rdgs:Math Fndts-Cmptr Sc | 1 |
| MATH 7923 | Readings: Discrete Mathematics | 1 |
| MATH 7924 | Rdgs:Comp Mathematics | 1 |
| MATH 7925 | Readings: Optimization | 1 |
| MATH 7926 | Rdgs:Applied Prob/Stats | 1 |
| MATH 7927 | Rdgs:Comp/Math Biology | 1 |
Breadth Requirement
| Code | Title | Hours |
|---|---|---|
| Students must also satisfy a breadth requirement by completing a total of six graduate math courses from among several areas of mathematics, with no more than three of these courses from any one area. | 18 | |
Computational Mathematics
| Code | Title | Hours |
|---|---|---|
| MATH 5660 | Numerical Analysis I | 3 |
| MATH 5661 | Numerical Analysis II | 3 |
| MATH 5791 | Continuous Modeling | 3 |
| MATH 6735 | Continuum Mechanics | 3 |
Discrete Mathematics
| Code | Title | Hours |
|---|---|---|
| MATH 5110 | Theory of Numbers | 3 |
| MATH 5793 | Discrete Math Modeling | 3 |
| MATH 6023 | Topics in Discrete Math | 3 |
Operations Research (including Probability)
| Code | Title | Hours |
|---|---|---|
| MATH 5310 | Probability | 3 |
| MATH 5390 | Game Theory | 3 |
| MATH 5490 | Network Flows | 3 |
| MATH 5593 | Linear Programming | 3 |
| MATH 5792 | Probabilistic Modeling | 3 |
| MATH 5794 | Optimization Modeling | 3 |
| MATH 6380 | Stochastic Processes | 3 |
| MATH 7593 | Advanced Linear Programming | 3 |
| MATH 7594 | Integer Programming | 3 |
| MATH 7595 | Advanced Nonlinear Programming | 3 |
Statistics
| Code | Title | Hours |
|---|---|---|
| MATH 5320 | Statistical Inference | 3 |
| MATH 5387 | Applied Regression Analysis | 3 |
| MATH 5394 | Experimental Designs | 3 |
| MATH 6330 | Workshop in Statistical Consulting | 3 |
| MATH 6384 | Spatial Data Analysis | 3 |
| MATH 6388 | Statistical and Machine Learning | 3 |
| MATH 7381 | Mathematical Statistics I | 3 |
| MATH 7382 | Mathematical Statistics II | 3 |
| MATH 7393 | Bayesian Statistics | 3 |
| MATH 7397 | Nonparametric Statistics | 3 |
General
| Code | Title | Hours |
|---|---|---|
| MATH 5135 | Functions of a Complex Variable | 3 |
| MATH 5733 | Partial Differential Equations | 3 |
| MATH 6131 | Real Analysis | 3 |
| MATH 7132 | Functional Analysis | 3 |
Additional Electives
| Code | Title | Hours |
|---|---|---|
| Complete an addtional 18 credit hours of graduate level coursework, in consultation with the program director. | 18 | |
| MATH 5027 | Topics in Applied Mathematics | 3 |
| MATH 5070 | Applied Analysis | 3 |
| MATH 5110 | Theory of Numbers | 3 |
| MATH 5135 | Functions of a Complex Variable | 3 |
| MATH 5310 | Probability | 3 |
| MATH 5320 | Statistical Inference | 3 |
| MATH 5337 | Intro to Statistical and Machine Learning | 3 |
| MATH 5350 | Mathematical Theory of Interest | 3 |
| MATH 5351 | Actuarial Models | 3 |
| MATH 5387 | Applied Regression Analysis | 3 |
| MATH 5388 | Machine Learning Methods | 3 |
| MATH 5390 | Game Theory | 3 |
| MATH 5394 | Experimental Designs | 3 |
| MATH 5410 | Modern Cryptology | 3 |
| MATH 5432 | Computational Graph Theory | 3 |
| MATH 5446 | Theory of Automata | 3 |
| MATH 5490 | Network Flows | 3 |
| MATH 5576 | Mathematical Foundations of Artificial Intelligence I | 3 |
| MATH 5593 | Linear Programming | 3 |
| MATH 5610 | Computational Biology | 3 |
| MATH 5660 | Numerical Analysis I | 3 |
| MATH 5661 | Numerical Analysis II | 3 |
| MATH 5674 | Parallel Computing and Architectures | 3 |
| MATH 5718 | Applied Linear Algebra | 3 |
| MATH 5733 | Partial Differential Equations | 3 |
| MATH 5791 | Continuous Modeling | 3 |
| MATH 5792 | Probabilistic Modeling | 3 |
| MATH 5793 | Discrete Math Modeling | 3 |
| MATH 5794 | Optimization Modeling | 3 |
| MATH 5840 | Independent Study | 1-3 |
| MATH 5880 | Directed Research | 1-6 |
| MATH 5939 | Internship | 1-6 |
| MATH 5950 | Master's Thesis | 1-8 |
| MATH 5960 | Master's Project | 1-8 |
| MATH 6023 | Topics in Discrete Math | 3 |
| MATH 6101 | Uncertainty Quantification | 3 |
| MATH 6131 | Real Analysis | 3 |
| MATH 6330 | Workshop in Statistical Consulting | 3 |
| MATH 6360 | Exploratory Data Analysis | 3 |
| MATH 6376 | Statistical Computing | 3 |
| MATH 6380 | Stochastic Processes | 3 |
| MATH 6384 | Spatial Data Analysis | 3 |
| MATH 6388 | Statistical and Machine Learning | 3 |
| MATH 6395 | Multivariate Methods | 3 |
| MATH 6398 | Calculus of Variations and Optimal Control | 3 |
| MATH 6404 | Applied Graph Theory | 3 |
| MATH 6595 | Nonlinear Programming | 3 |
| MATH 6653 | Introduction to Finite Element Methods | 3 |
| MATH 6735 | Continuum Mechanics | 3 |
| MATH 6840 | Independent Study | 1-3 |
| MATH 6960 | Research Methods in Mathematics and Statistics | 3 |
| MATH 7101 | Topology | 3 |
| MATH 7132 | Functional Analysis | 3 |
| MATH 7376 | Statistical Computing | 3 |
| MATH 7381 | Mathematical Statistics I | 3 |
| MATH 7382 | Mathematical Statistics II | 3 |
| MATH 7384 | Mathematical Probability | 3 |
| MATH 7385 | Stochastic Differential Equations | 3 |
| MATH 7386 | Monte Carlo Methods | 3 |
| MATH 7393 | Bayesian Statistics | 3 |
| MATH 7397 | Nonparametric Statistics | 3 |
| MATH 7405 | Advanced Graph Theory | 3 |
| MATH 7409 | Applied Combinatorics | 3 |
| MATH 7410 | Combinatorial Structures | 3 |
| MATH 7413 | Modern Algebra I | 3 |
| MATH 7414 | Modern Algebra II | 3 |
| MATH 7419 | Mathematical Coding Theory | 3 |
| MATH 7421 | Projective Geometry | 3 |
| MATH 7593 | Advanced Linear Programming | 3 |
| MATH 7594 | Integer Programming | 3 |
| MATH 7595 | Advanced Nonlinear Programming | 3 |
| MATH 7663 | Finite Difference Methods for Partial Differential Equations | 3 |
| MATH 7665 | Numerical Linear Algebra | 3 |
| MATH 7667 | Introduction to Approximation Theory | 3 |
| MATH 7821 | Topics in Projective Geometry | 3 |
| MATH 7822 | Topics in Linear Algebra | 3 |
| MATH 7823 | Topics in Discrete Math | 3 |
| MATH 7824 | Topics in Computational Mathematics | 3 |
| MATH 7825 | Topics in Optimization | 3 |
| MATH 7826 | Topics in Probability and Statistics | 3 |
| MATH 7827 | Topics in Applied Mathematics | 3 |
| MATH 7840 | Independent Study | 1-3 |
| MATH 7921 | Readings in Mathematics | 1 |
| MATH 7922 | Rdgs:Math Fndts-Cmptr Sc | 1 |
| MATH 7923 | Readings: Discrete Mathematics | 1 |
| MATH 7924 | Rdgs:Comp Mathematics | 1 |
| MATH 7925 | Readings: Optimization | 1 |
| MATH 7926 | Rdgs:Applied Prob/Stats | 1 |
| MATH 7927 | Rdgs:Comp/Math Biology | 1 |
| MATH 8660 | Mathematical Foundations of Finite Element Methods | 3 |
| MATH 8664 | Iterative Methods in Numerical Linear Algebra | 3 |
Dissertation
| Code | Title | Hours |
|---|---|---|
| Take the following | 30 | |
| MATH 8990 | Doctoral Dissertation | 1-10 |
To learn more about the Student Learning Outcomes for this program, please visit our website.