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University of Colorado Denver College of Liberal Arts and Sciences

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Statistics Cert.
 

Statistics Certificate Programs

Department of Mathematical & Statistical Sciences


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There is a growing need for qualified statistical analysts of the ever-increasing amounts of data collected in business, industry, and government. The Certificates in Applied Statistics program is designed to give students a strong background in statistical methodology and data analysis in preparation for opportunities in the work force or for graduate studies.
 
Students will gain competence in such topics as descriptive statistics, estimation, confidence intervals, probability and inferential techniques, simple and multiple regression, analysis of variance, and more-advanced topics. Students can focus on a particular application area such as economics, psychology, sociology, geology or environmental science through the choice of an elective course and the data analysis project.
 
Programs are offered at the undergraduate and graduate level.
 
UNDERGRADUATE APPLIED STATISTICS CERTIFICATE
 
Admission Requirements: Completion of calculus 1, 2 and 3 as well as linear algebra, each at a B- or above. Students enrolled in the certificate program will be expected to utilize concepts from calculus and linear algebra without the use of technology, e.g., evaluation of limits, derivatives and integrals.
 
Course requirements: Four courses and a 1 hour independent study are required.
 
ONE COURSE IN PROBABILITY:
 
·         MATH 3800 - Probability and Statistics for Engineers. Basic probability theory, discrete and continuous random variables, point and interval estimation, test of hypotheses, one-way analysis of variance, and simple linear regression. Note: no co-credit with MATH 4810. Prereq: MATH 2411; coreq: MATH 2421. Semester Hours: 3 to 3
 
or
 
·         MATH 4810 – Probability.  Examines elementary theory of probability, including independence, conditional probability, and Bayes’ theorem; random variables, expectations and probability distributions; joint and conditional distributions; functions of random variables; limit theorems, including the central limit theorem. Note: No co-credit with MATH 3800. Prereq: MATH 3191; Coreq: MATH 2421. Cross-listed with MATH 5310. Semester Hours: 3 to 3
 
It is strongly advised that MATH4810 be taken rather than MATH3800.
 
ONE COURSE IN MATHEMATICAL STATISTICS:
 
·         MATH 4820 – Statistics. Point and confidence interval estimation, principles of maximum likelihood, sufficiency and completeness, tests of simple and composite hypothesis, linear models and multiple regression, analysis of variance. Prereq: MATH 3800 or MATH 4810 (preferred). Cross-listed with MATH 5320. Semester Hours: 3 to 3
 
ONE ADVANCED APPLICATIONS COURSE:
 
·         MATH 4387 - Regression Analysis, Modeling and Time Series. Topics include linear and multiple regression, basic experimental designs, one-way analysis of variance. Emphasis is on practical aspects and applications of linear models to the analysis of data in business engineering, behavioral, biological and physical sciences. Prereq: MATH 3191 and 3800/4820. Cross-listed with MATH 5387. Semester Hours: 3 to 3 When Offered: FALL
 
ONE ELECTIVE:
 
·         Any statistics course in the Department of Mathematical and Statistical Sciences at the 4000 level or higher (must be pre-approved by the Certificate Coordinator). MATH4830 cannot apply towards the certificate.
·         ECON 4030 - Data Analysis with SAS
·         ECON 4150 - Economic Forecasting
·         ECON 4811 - Introduction to Econometrics
·         GEOG 4770 - Applied Statistics for the Natural Sciences
·         GEOL 4770 - Applied Statistics for the Natural Sciences
·         Equivalent course pre-approved by the Certificate Coordinator
 
Project requirement: 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 4840, Independent Study, or in an equivalent course pre-approved by the Certificate Coordinator.
 
Additional requirements: Students must maintain a 3.0 GPA or above in these courses with no credit given for courses with grades below B-. Since a certificate is a University of Colorado Denver certification of a student's specialized knowledge in an advanced subject area, all courses in the certificate program must be taken in residency at University of Colorado Denver. Students much be enrolled in one course per year to maintain their status in the certificate program. Certificates must be completed within 3 years from matriculation.
 
 
GRADUATE APPLIED STATISTICS CERTIFICATE

Admission Requirements: Applicants must hold a baccalaureate degree (not necessarily in mathematics) from an accredited college or university (or demonstrate completion of work equivalent to the baccalaureate degree given at UC Denver) with at least a 3.0 grade point average (GPA). Students must also have 24 semester hours of mathematics, at least 18 of which are upper division courses with a grade of B- or better. These courses must include calculus 1, 2 and 3 as well as linear algebra and probability at the undergraduate level. Exceptions to admission criteria may be made on a case by case basis.
 
Course requirements: Four courses and a 1 hour independent study are required.
 
TWO FUNDAMENTAL COURSES IN STATISTICS:
 
·         MATH 5320 – Statistics. Point and confidence interval estimation, principles of maximum likelihood, sufficiency and completeness, tests of simple and composite hypothesis, linear models and multiple regression, analysis of variance. Prereq: MATH 3800. MATH 4810 highly recommended, but not required. Cross-listed with MATH 4820. Semester Hours: 3 to 3.   When Offered: SPRING
 
·         MATH 5387 - Regression Analysis, Modeling and Time Series. Topics include linear and multiple regression, basic experimental designs, one-way analysis of variance. Emphasis is on practical aspects and applications of linear models to the analysis of data in business engineering and behavioral, biological and physical sciences. Prereq: MATH 3191 and 3800/4820. Cross-listed with MATH 4387. Semester Hours: 3 to 3 When Offered: FALL
 
ONE ADVANCED APPLICATIONS COURSE:
 
Topics vary from year to year. Course must be pre-approved by certificate coordinator and cannot be MATH5830. Representative courses include:
 
·         MATH 5394 - Experimental Designs. Completely randomized block designs, factorial and fractional factorial experiments, balanced incomplete block designs, response surface methods. Prereq: MATH 4387/5387. Cross-listed with MATH 4394. Semester Hours: 3 to 3.
·         MATH 6388 - Advanced Statistical Methods for Research. The second in a two-semester course in applied statistics. Topics include multifactor analysis of variance and covariance, categorical data, general linear models, bootstrapping, and other computationally intensive statistical methods. Prereq: MATH 5387. Semester Hours: 3 to 3.
·         MATH 6393 - Introduction to Bayesian Statistics. Prior and posterior distributions, conjugate models, single and multiparameter models, hierarchical models, mixture models, numerical methods for evaluating posteriors, Monte Carlo methods, and Markov chain Monte Carlo. Prereq: MATH 3800 or both MATH 4810 and MATH 4820 (or equivalent). Some computer programming experience. Semester Hours: 3 to 3.
 
ONE ELECTIVE:
 
·         Any statistics course in the Department of Mathematical and Statistical Sciences at the 5000 level or higher (must be pre-approved by the Certificate Coordinator). MATH5830 cannot apply towards the certificate.
·         ECON 5150, ECON 5813, ECON 5823
·         ENVS 5600
·         GEOG 5770
·         GEOL 5770
·         SOC 5183
·         Equivalent course pre-approved by the Certificate Coordinator
 
Project requirement: 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.
 
Additional requirements: Students must maintain a 3.0 GPA or above in these courses with no credit given for courses with grades below B-. Since a certificate is a University of Colorado Denver certification of a student's specialized knowledge in an advanced subject area, all courses in the certificate program must be taken in residency at University of Colorado Denver. Students much be enrolled in one course per year to maintain their status in the certificate program. Certificates must be completed within 3 years from matriculation.