The Statistics Certificate program requires four courses and an independent study (13 total credit hours). See the University of Colorado Denver course catalog for course browsing and descriptions.

Two Fundamental Courses in Statistics (6 credit hours)

MATH 5320 - Introduction to Mathematical Statistics
Sampling distributions, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing, simple linear regression. Prereq: Graduate standing in Applied Mathematics or Statistics or instructor permission. AMEN-MS/PHD/STAT-MS. Note: This course assumes that students have the equivalent of an undergraduate-level course in probability (e.g., MATH 3800 or 4810). Cross-listed with MATH 4820. Term offered: spring. Max hours: 3 Credits. Semester Hours: 3 to 3.

MATH 5387 - Applied Regression Analysis

Topics include simple and multiple linear regression, model diagnostics and remediation, and model selection. Emphasis is on practical aspects and applications of linear models to the analysis of data in business, engineering and behavioral, biological and physical sciences. No co-credit with MATH 4830/5830. Prereq: Grade of C- (1.7) or better in MATH 3191 and in MATH 3800 or 4820 or 3382. Note: Students who have a grade of B- or better in MATH 3191, an A in MATH 3800 or a B- or better in MATH 4820 pass this course at a much higher rate. Cross-listed with MATH 5387. Term offered: fall, spring, summer. Max hours: 3 Credits. Semester Hours: 3 to 3.

One Advanced Applications Course (3 credit hours)

Topics vary from year to year. Course must be pre-approved by Certificate Coordinator. MATH 5830 cannot apply towards the certificate. Representative courses include:

MATH 5394 - Experimental Designs

Designs covered will include: completely randomized, complete block, split plot, incomplete block, factorial and fractional factorial designs. Additionally, power and study design for non-experimental studies will be covered. Prereq: Graduate standing in Applied Mathematics or Statistics or instructor permission. AMEN-MS/PHD/STAT-MS. Note: This course assumes that students have the equivalent of an undergraduate-level course in regression analysis (e.g., MATH 4387). Cross-listed with MATH 4394. Term offered: spring of even years. Max hours: 3 Credits. Semester Hours: 3 to 3.

MATH 6388 - Statistical and Machine Learning

This course covers a variety of statistical and machine learning methods. Both supervised and unsupervised methods are covered with an emphasis on model training and error estimation. Topics include penalized regression, principal components, k-nearest neighbors, clustering, and neural networks. Additional higher-level topics such as random forests, support vector machines, and boosting are also covered as time permits. Students will gain exposure to high performance computing by working on a Linux cluster. Prereq: Graduate standing in Statistics or Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of graduate-level coursework in regression analysis (e.g. MATH 5387). Term offered: fall of odd years. Max hours: 3 Credits. Semester Hours: 3 to 3.

MATH 7393 - Bayesian Statistics

Prior and posterior distributions, conjugate models, single and multiparameter models, hierarchical models, numerical methods for evaluating posteriors, Monte Carlo methods, and Markov chain Monte Carlo. Prereq: Graduate standing in Applied Mathematics or Statistics or instructor permission. AMEN-MS/PHD/STAT-MS. Programming experience is strongly recommended. Term offered: spring of odd years. Max hours: 3 Credits. Semester Hours: 3 to 3.

One Elective Course (3 credit hours)

Choose any statistics course in the Department of Mathematical and Statistical Sciences at the 5000 level or higher. Course must be pre-approved by the Certificate Coordinator. MATH 5830 cannot apply towards the certificate. Representative courses include:

  • ECON 5150- Economic Forecasting
  • ECON 5813- Econometrics I
  • ECON 5823- Econometrics II
  • ENVS 5600- Applied Statistics for the Natural Sciences
  • Cross-listed with GEOG 5770, GEOL 5770​
  • SOCY 5183- Quantitative Data Analysis
  • Or an equivalent course pre-approved by the Certificate Coordinator

Project, Independent Study (1 credit hour)

An independent data analysis project with a report and presentation to demonstrate proficiency with data analysis techniques and a statistical computing software package. Enroll for one hour of MATH 5840, Independent Study, or in an equivalent course pre-approved by the Certificate Coordinator.​