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Statistics (STAT) Courses

Academic Unit: Statistics, School of

STAT 1001 - Introduction to the Ideas of Statistics [MATH]
(4 cr; Prereq-Mathematics requirement for admission to University; Student Option; offered Every Fall, Spring & Summer)
Graphical/numerical presentations of data. Judging the usefulness/reliability of results/inferences from surveys and other studies to interesting populations. Coping with randomness/variation in an uncertain world.
STAT 3011 - Introduction to Statistical Analysis [MATH]
(4 cr; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: ESPM 3012, STAT 5021 (ending 20-JAN-15), ANSC 3011 (starting 07-SEP-99, was ANSC 2211 until 19-JAN-10)
Standard statistical reasoning. Simple statistical methods. Social/physical sciences. Mathematical reasoning behind facts in daily news. Basic computing environment.
STAT 3021 - Introduction to Probability and Statistics
(3 cr; Prereq-Math 1272; Student Option; offered Every Fall, Spring & Summer)
Equivalent courses: STAT 3021H
This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements.
STAT 3021H - Introduction to Probability and Statistics Honors
(3 cr; Prereq-Math 1272; Student Option; offered Every Spring)
Equivalent courses: STAT 3021 (starting 17-JAN-23)
This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements.
STAT 3022 - Data Analysis
(4 cr; Prereq-3011 or 3021 or SOC 3811; Student Option; offered Every Fall & Spring)
Practical survey of applied statistical inference/computing covering widely used statistical tools. Multiple regression, variance analysis, experiment design, nonparametric methods, model checking/selection, variable transformation, categorical data analysis, logistic regression.
STAT 3032 - Regression and Correlated Data
(4 cr; Prereq-STAT 3011 or STAT 3021; Student Option; offered Every Fall & Spring)
This is a second course in statistics with a focus on linear regression and correlated data. The intent of this course is to prepare statistics, economics, and actuarial science students for statistical modeling needed in their discipline. The course covers the basic concepts of linear algebra and computing in R, simple linear regression, multiple linear regression, statistical inference, model diagnostics, transformations, model selection, model validation, and basics of time series and mixed models. Numerous datasets will be analyzed and interpreted using the open-source statistical software R.
STAT 3301 - Regression and Statistical Computing
(4 cr; Prereq-Stat 3021 and (CSci 1113 or CSci 1133), and co-requisite (CSci 2033 or Math 2142 or Math 2243 or Math 2373); A-F only; offered Every Fall & Spring)
This is a second course in statistics for students that have completed a calculus-based introductory course. Students will learn to analyze data with the multiple linear regression model. This will include inference, diagnostics, validation, transformations, and model selection. Students will also design and perform Monte Carlo simulation studies to improve their understanding of statistical concepts like coverage probability, Type I error probability, and power. This will allow students to understand the impacts of model misspecification and the quality of approximate inference.
STAT 3701 - Introduction to Statistical Computing
(4 cr; Prereq-(MATH 1272 or 1372 or 1572H), CSCI 1113, and STAT 3032; A-F only; offered Every Fall & Spring)
Elementary Monte Carlo, simulation studies, elementary optimization, programming in R, and graphics in R.
STAT 4051 - Statistical Machine Learning I
(4 cr; Prereq-(STAT 3701 or STAT 3301) and (STAT 4101 or STAT 5101 or MATH 5651); A-F or Audit; offered Every Fall & Spring)
This is the first semester of the applied statistics and statistical machine learning sequence for majors seeking a BA or BS in statistics or data science, coupled with the course STAT 4052. The course delves into the foundational statistics supporting contemporary machine learning techniques. The emphasis lies on identifying problem types, selecting appropriate analytical methods, accurate result interpretation, and hands-on exposure to real-world data analysis. The curriculum builds upon traditional multivariate statistical analysis and unsupervised learning, extending to modern machine learning topics. Topics include clustering, dimension reduction, matrix completion, factor analysis, covariance analysis, and graphical models. Additionally, advanced data structures such as text and graph data are covered. The course prioritizes the fundamental statistical principles integral to machine learning, demonstrated through the analysis and interpretation of numerous datasets.
STAT 4052 - Statistical Machine Learning II
(4 cr; A-F only; offered Every Fall & Spring)
This is the second semester of the core Applied Statistics sequence for majors seeking a BA or BS in statistics. Both Stat 4051 and Stat 4052 are required in the major. The course introduces a wide variety of applied statistical methods, methodology for identifying types of problems and selecting appropriate methods for data analysis, to correctly interpret results, and to provide hands-on experience with real-life data analysis. The course covers basic concepts of classification, both classical methods of linear classification rules as well as modern computer-intensive methods of classification trees, and the estimation of classification errors by splitting data into training and validation data sets; non-linear parametric regression; nonparametric regression including kernel estimates; categorical data analysis; logistic and Poisson regression; and adjustments for missing data. Numerous datasets will be analyzed and interpreted, using the open-source statistical software R and Rstudio.prerequisites: STAT 4051 and (STAT 4102 or STAT 5102)
STAT 4101 - Theory of Statistics I
(4 cr; Prereq-Math 1272 or Math 1372 or Math 1572H; Student Option; offered Every Fall & Spring)
Random variables/distributions. Generating functions. Standard distribution families. Data summaries. Sampling distributions. Likelihood/sufficiency.
STAT 4102 - Theory of Statistics II
(4 cr; Prereq-4101; Student Option; offered Every Fall & Spring)
Equivalent courses: STAT 5102 (ending 03-SEP-19)
Estimation. Significance tests. Distribution free methods. Power. Application to regression and to analysis of variance/count data.
STAT 4893W - Consultation and Communication for Statisticians [WI]
(3 cr; Prereq-Senior Statistics Major. STAT 4051 and STAT 4102 or STAT 5102; A-F only; offered Every Fall & Spring)
Equivalent courses: was STAT 4893 until 05-SEP-00
This course focuses on how to interact and collaborate as a statistician on a multidisciplinary team. Students will learn about all aspects of statistical consulting by performing an actual consultation. This includes: understanding the needs of the researcher, designing a study to investigate the client's needs, and communicating study results through graphs, writing, and oral presentations in a manner that a non-statistician can understand. Students will also discuss how to design research ethically (respecting the rights of the subjects in the research), how to analyze data without manipulating results, and how to properly cite and credit other people's work. Students will also be exposed to professional statisticians as a means of better understanding careers in statistics.
STAT 5021 - Statistical Analysis
(4 cr; Prereq-college algebra or instr consent; credit will not be granted if credit has been received for STAT 3011; Student Option; offered Every Fall & Spring)
Intensive introduction to statistical methods for graduate students needing statistics as a research technique.
STAT 5052 - Statistical and Machine Learning
(3 cr; A-F only; offered Periodic Fall & Spring; may be repeated for 4 credits)
The material covered will be the foundations of modern machine learning methods including regularization methods, discriminant analysis, neural nets, random forest, bagging, boosting, support vector machine, and clustering. Model comparison using cross-validation and bootstrap methods will be emphasized.
STAT 5101 - Theory of Statistics I
(4 cr; Prereq-(MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243); Student Option; offered Every Fall)
Equivalent courses: MATH 5651 (starting 20-JAN-15, ending 18-JAN-05), STAT 4101 (ending 20-JAN-15), MATH 4653 (ending 06-SEP-05)
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution.
STAT 5102 - Theory of Statistics II
(4 cr; Prereq-5101 or Math 5651; Student Option; offered Every Fall & Spring)
Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory.
STAT 5201 - Sampling Methodology in Finite Populations
(3 cr; Prereq-3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent; Student Option; offered Every Spring)
Simple random, systematic, stratified, unequal probability sampling. Ratio, model based estimation. Single stage, multistage, adaptive cluster sampling. Spatial sampling.
STAT 5302 - Applied Regression Analysis
(4 cr; Prereq-3032 or 3022 or 4102 or 5021 or 5102 or instr consent Please note this course generally does not count in the Statistical Practice BA or Statistical Science BS degrees. Please consult with a department advisor with questions.; Student Option; offered Every Fall, Spring & Summer)
Simple, multiple, and polynomial regression. Estimation, testing, prediction. Use of graphics in regression. Stepwise and other numerical methods. Weighted least squares, nonlinear models, response surfaces. Experimental research/applications.
STAT 5303 - Designing Experiments
(4 cr; Prereq-3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent; Student Option; offered Every Fall, Spring & Summer)
Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design.
STAT 5401 - Applied Multivariate Methods
(3 cr; Student Option; offered Periodic Fall)
Bivariate and multivariate distributions. Multivariate normal distributions. Analysis of multivariate linear models. Repeated measures, growth curve, and profile analysis. Canonical correlation analysis. Principal components and factor analysis. Discrimination, classification, and clustering. pre-req: STAT 3032 or 3301 or 3022 or 4102 or 5021 or 5102 or instr consent Although not a formal prerequisite of this course, students are encouraged to have familiarity with linear algebra prior to enrolling. Please consult with a department advisor with questions.
STAT 5421 - Analysis of Categorical Data
(3 cr; Prereq-STAT 3022 or 3032 or 3301 or 5302 or 4051 or 8051 or 5102 or 4102; Student Option; offered Every Fall & Spring)
Varieties of categorical data, cross-classifications, contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables/loglinear models. Maximum-likelihood estimation. Tests for goodness of fit. Logistic regression. Generalized linear/multinomial-response models.
STAT 5511 - Time Series Analysis
(3 cr; Prereq-STAT 4102 or STAT 5102; Student Option; offered Every Fall)
Characteristics of time series. Stationarity. Second-order descriptions, time-domain representation, ARIMA/GARCH models. Frequency domain representation. Univariate/multivariate time series analysis. Periodograms, non parametric spectral estimation. State-space models.
STAT 5601 - Nonparametric Methods
(3 cr; Prereq-Stat classes 3032 or 3022 or 4102 or 5021 or 5102 or instr consent; Student Option; offered Every Fall & Spring)
Order statistics. Classical rank-based procedures (e.g., Wilcoxon, Kruskal-Wallis). Goodness of fit. Topics may include smoothing, bootstrap, and generalized linear models.
STAT 5701 - Statistical Computing
(3 cr; Prereq-(Stat 5102 or Stat 8102) and (Stat 5302 or STAT 8051) or consent; A-F or Audit; offered Every Fall)
Statistical programming, function writing, graphics using high-level statistical computing languages. Data management, parallel computing, version control, simulation studies, power calculations. Using optimization to fit statistical models. Monte Carlo methods, reproducible research.
STAT 5731 - Bayesian Astrostatistics
(4 cr; Prereq-MATH 2263 and MATH 2243, or equivalent; or instructor consent Suggested: statistical course at the level of AST 4031, AST 5031, STAT 3021, or STAT 5021; A-F only; offered Every Fall)
Equivalent courses: AST 5731
This course will introduce Bayesian methods for interpreting and analyzing large data sets from astrophysical experiments. These methods will be demonstrated using astrophysics real-world data sets and a focus on modern statistical software, such as R and python.
STAT 5931 - Topics in Statistics (Topics course)
(3 cr; Student Option; offered Periodic Fall)
Topics vary according to student needs and available staff.
STAT 5993 - Tutorial
(1 cr [max 6]; Prereq-instr consent; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 12 times)
Directed study in areas not covered by regular offerings.
STAT 8051 - Advanced Regression Techniques: linear, nonlinear and nonparametric methods
(4 cr; Prereq-Statistics grad or instr consent; A-F or Audit; offered Every Fall)
Linear/generalized linear models, modern regression methods including nonparametric regression, generalized additive models, splines/basis function methods, regularization, bootstrap/other resampling-based inference.
STAT 8052 - Applied Statistical Methods 2: Design of Experiments and Mixed -Effects Modeling
(4 cr; Prereq-8051 or instr consent; A-F or Audit; offered Every Spring)
Design experiments/analyze data with fixed effects, random/mixed effects models. ANOVA for factorial designs. Contrasts, multiple comparisons, power/sample size, confounding, fractional factorials. Computer-generated designs. Response surfaces. Multi-level models. Generalized estimating equations (GEE) for longitudinal data with non-normal errors.
STAT 8053 - Applied Statistical Methods 3: Multivariate Analysis and Advanced Regression
(3 cr; Prereq-PhD student in stat or DGS permission and 8052; A-F or Audit; offered Every Fall)
Standard multivariate analysis. Multivariate linear model, classification, clustering, principal components, factor analysis, canonical correlation. Topics in advanced regression.
STAT 8054 - Statistical Methods 4: Advanced Statistical Computing
(3 cr; Prereq-STAT 8053 or instr consent; A-F or Audit; offered Every Spring)
Optimization, numerical integration, Markov chain Monte Carlo, related topics.
STAT 8055 - Applied Project (independent study)
(2 cr; Prereq-[8054, 8801] or instr consent; S-N only; offered Every Fall)
Collaborative applied statistical practice with a member of University community, including consulting, problem solving, presentation/documentation of results.
STAT 8056 - Statistical Learning and Data Mining
(3 cr; Student Option No Audit; offered Periodic Spring)
Equivalent courses: PUBH 8475
STAT8056 covers a range of emerging topics in machine learning and data science, including high-dimensional analysis, recommender systems, undirected and directed graphical models, feed-forward networks, and unstructured data analysis. This course will introduce various statistical and computational techniques for prediction and inference. These techniques are directly applicable to many fields, such as business, engineering, and bioinformatics. This course requires the basic knowledge of machine learning and data mining (e.g., STAT8053).
STAT 8101 - Theory of Statistics 1
(3 cr; Prereq-Statistics grad major or instr consent; Student Option; offered Every Fall)
Review of linear algebra. Introduction to probability theory. Random variables, their transformations/expectations. Standard distributions, including multivariate Normal distribution. Probability inequalities. Convergence concepts, including laws of large numbers, Central Limit Theorem. delta method. Sampling distributions.
STAT 8102 - Theory of Statistics 2
(3 cr; Prereq-8101, Statistics graduate major or instr consent; Student Option; offered Every Spring)
Statistical inference. Sufficiency. Likelihood-based methods. Point estimation. Confidence intervals. Neyman Pearson hypothesis testing theory. Introduction to theory of linear models.
STAT 8105 - Generative Artificial Intelligence: Principles and Practices
(3 cr; A-F only; offered Periodic Fall & Spring)
This course is thoughtfully curated to provide comprehensive coverage of Generative AI, merging foundational principles with cutting-edge applications. What sets this curriculum apart is its infusion with the instructor?s extensive research experience, which brings a unique depth and authenticity to the learning material. The course will delve into a variety of topics, ensuring that students grasp both the theoretical principles, algorithmic underpinnings, and practical implementations. While lectures will emphasize key areas, diligent engagement with assigned readings is expected for a holistic understanding.
STAT 8111 - Mathematical Statistics I
(3 cr; Prereq-[5102 or 8102 or instr consent], [[Math 5615, Math 5616] or real analysis], matrix algebra; Student Option; offered Every Fall)
Probability theory, basic inequalities, characteristic functions, and exchangeability. Multivariate normal distribution. Exponential family. Decision theory, admissibility, and Bayes rules.
STAT 8112 - Mathematical Statistics II
(3 cr; Prereq-8111; Student Option; offered Every Spring)
Statistical inference, estimation, and hypothesis testing. Convergence and relationship between convergence modes. Asymptotics of maximum likelihood estimators, distribution functions, quantiles. Delta method.
STAT 8141 - Probability Assessment
(3 cr; Prereq-5102; Student Option; offered Periodic Spring)
Probability as a language of uncertainty for quantifying and communicating expert opinion and for use as Bayesian prior distributions. Methods for elicitation and construction of subjective probabilities. De Finetti coherence, predictive elicitation, fitting subjective-probability models, computer-aided elicitation, and use of experts.
STAT 8171 - Sequential Analysis
(3 cr; Prereq-8112; Student Option; offered Periodic Fall)
Walds's sequential probability ratio test and modifications. Sequential decision theory. Martingales. Sequential estimation, design, and hypothesis testing. Recent developments.
STAT 8311 - Linear Models
(3 cr; Prereq-Linear algebra, 5102 or 8102 or instr consent; Student Option; offered Every Fall; may be repeated for 4 credits)
General linear model theory from a coordinate-free geometric approach. Distribution theory, ANOVA tables, testing, confidence statements, mixed models, covariance structures, variance components estimation.
STAT 8312 - Linear and Nonlinear Regression
(3 cr; Prereq-8311; Student Option; offered Periodic Fall)
Nonlinear regression: asymptotic theory, Bates-Watts curvatures, super leverage, parameter plots, projected residuals, transform-both-sides methodology, Wald versus likelihood inference. Topics in linear and generalized linear models as they relate to nonlinearity issues, including diagnostics, semi-parametric models, and model assessment.
STAT 8321 - Regression Graphics
(3 cr; Prereq-8311; Student Option; offered Periodic Fall)
Foundations: dimension-reduction subspaces, Li-Duan Lemma, structural dimension. Inferring about central dimension-reduction subspaces by using 3D plots, graphical regression, inverse regression graphics, net-effect plots, principal Hessian directions, sliced inverse regression and predictor transformations. Graphics for model assessment.
STAT 8333 - FTE: Master's
(1 cr; Prereq-Master's student, adviser and DGS consent; No Grade Associated; offered Every Fall, Spring & Summer; 6 academic progress units; 6 financial aid progress units)
(No description)
STAT 8401 - Topics in Multivariate Methods (Topics course)
(3 cr; Prereq-8311; Student Option; offered Every Fall)
Bivariate and multivariate distributions. Multivariate normal distributions. Hotellings's T-squared, MANOVA, MANCOVA, and regression with multivariate dependent variable. Repeated measures, growth curve, and profile analysis. Canonical correlation analysis. Principle components and factor analysis. Discrimination, classification, clustering.
STAT 8411 - Multivariate Analysis
(3 cr; Prereq-8152; Student Option; offered Periodic Fall & Spring)
Multivariate normal distribution. Inference on the mean, covariance, and correlation and regression coefficients; related sampling distributions such as Hotelling's T-squared and Wishart distributions. Multivariate analysis of variance. Principal components and canonical correlation. Discriminant analysis.
STAT 8421 - Theory of Categorical Data Analysis
(3 cr; Prereq-8062 or instr consent; Student Option; offered Periodic Fall)
Categorical data, multidimensional cross-classified arrays, mixed categorical and continuous data. Loglinear, logit, and multinomial response models. Ordinal responses. Current research topics.
STAT 8444 - FTE: Doctoral
(1 cr; Prereq-Doctoral student, adviser and DGS consent; No Grade Associated; offered Every Fall, Spring & Summer; 6 academic progress units; 6 financial aid progress units)
(No description)
STAT 8501 - Introduction to Stochastic Processes with Applications
(3 cr; Prereq-5101 or 8101; Student Option; offered Periodic Fall)
Markov chains in discrete and continuous time, renewal processes, Poisson process, Brownian motion, and other stochastic models encountered in applications.
STAT 8511 - Time Series Analysis
(3 cr; Prereq-5102 or 8111 or instr consent; Student Option; offered Periodic Fall)
Characteristics of time series. Stationarity. Second-order descriptions. Time-domain representation, ARIMA/GARCH models. Frequency domain representation, univariate/multivariate analysis. Periodograms, non-parametric spectral estimation, state space models.
STAT 8581 - Big Data in Astrophysics
(4 cr; A-F only; offered Every Spring)
Equivalent courses: AST 8581, CSCI 8581, PHYS 8581
This course will introduce key concepts and techniques used to work with large datasets, in the context of the field of astrophysics. Prerequisites: MATH 2263 and MATH 2243, or equivalent; or instructor consent. Suggested: familiarity with astrophysics topics such as star formation and evolution, galaxies and clusters, composition and expansion of the universe, gravitational wave sources and waveforms, and high-energy astrophysics.
STAT 8666 - Doct Pre-Thesis Cr
(1 cr [max 6]; Prereq-Doctoral student who has not passed prelim oral; no required consent for 1st/2nd registrations, up to 12 combined cr; dept consent for 3rd/4th registrations, up to 24 combined cr; doctoral student admitted before summer 2007 may register up to four times, up to 60 combined cr; No Grade Associated; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 2 times)
TBD
STAT 8701 - Computational Statistical Methods
(3 cr; Prereq-8311, programming exper; Student Option; offered Every Spring)
Random variate generation, variance reduction techniques. Robust location estimation and regression, smoothing additive models, regression trees. Programming projects; basic programming ability and familiarity with standard high-level language (preferably FORTRAN or C) are essential.
STAT 8721 - Programming Paradigms and Dynamic Graphics in Statistics
(3 cr; Prereq-8062, 8102; Student Option; offered Periodic Fall)
Alternative programming paradigms to traditional procedural programming, including object-oriented programming and functional programming. Applications to development of dynamic statistical graphs and representation and use of functional data, such as mean function in nonlinear regression log likelihoods and prior densities in Bayesian analysis.
STAT 8777 - Thesis Credits: Master's
(1 cr [max 18]; Prereq-Max 18 cr per semester or summer; 10 cr total required [Plan A only]; No Grade Associated; offered Every Fall & Spring; may be repeated for 50 credits; may be repeated 4 times)
(No description)
STAT 8801 - Statistical Consulting
(3 cr; Prereq-STAT 8051 and STAT Grad Student or Instructor Consent; S-N or Audit; offered Every Spring)
Principles of effective consulting/problem-solving, meeting skills, reporting. Aspects of professional practice/behavior, ethics, continuing education.
STAT 8811 - Statistical Consulting Practicum
(3 cr; Prereq-Statistics grad student or instr consent; S-N or Audit; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 4 times)
Providing (under faculty supervision) statistical support to clients, primarily University researchers. Exercises in problem solving, ethics, listening/communication skills.
STAT 8821 - Curricular Practical Training
(1 cr; Prereq-Statistics grad student, dept consent; S-N only; offered Every Fall, Spring & Summer; may be repeated for 3 credits; may be repeated 3 times)
Industrial work assignment using advanced statistical techniques. Grade based on final report and presentation covering work assignment.
STAT 8888 - Thesis Credit: Doctoral
(1 cr [max 24]; Prereq-Max 18 cr per semester or summer; 24 cr required; No Grade Associated; offered Every Fall & Spring; may be repeated for 100 credits; may be repeated 10 times)
(No description)
STAT 8900 - Student Seminar
(1 cr; Prereq-Statistics graduate student; S-N or Audit; offered Every Fall & Spring; may be repeated for 2 credits; may be repeated 2 times)
Preparation or presentation of seminar on statistical topics.
STAT 8913 - Literature Seminar
(1 cr; Prereq-Statistics grad major or instr consent; S-N only; offered Every Fall & Spring; may be repeated for 4 credits; may be repeated 4 times)
Students will read, present, discuss, and critique current literature/research.
STAT 8931 - Advanced Topics in Statistics (Topics course)
(3 cr; Student Option; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 4 times)
Topics vary according to student needs/available staff.
STAT 8932 - Advanced Topics in Statistics (Topics course)
(3 cr; Student Option; offered Periodic Fall & Spring; may be repeated for 12 credits; may be repeated 4 times)
Topics vary according to student needs/available staff.
STAT 8933 - Advanced Topics in Statistics (Topics course)
(3 cr; Student Option; offered Every Fall & Spring; may be repeated for 12 credits; may be repeated 4 times)
Topics vary according to student needs and available staff.
STAT 8992 - Directed Readings and Research
(1 cr [max 6]; Prereq-instr consent; Student Option; offered Every Fall, Spring & Summer; may be repeated for 12 credits; may be repeated 3 times)
Directed study in areas not covered by regular offerings.

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