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The online catalog includes the most recent changes to courses and degree
requirements that have been approved by the Faculty Senate, including changes
that are not yet effective.
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### Courses

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The online catalog includes the most recent changes to courses and degree
requirements that have been approved by the Faculty Senate, including changes
that are not yet effective.
Courses showing two entries of the same number
indicate that the course information is changing. The most recently approved
version is shown first, followed by the older version, in gray, with its
last-effective term preceding the course title. Courses shown in gray with only
one entry of the course number are being discontinued.
Course offerings by term can be accessed by clicking on the term links when viewing a specific campus catalog.
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#### Statistics (STAT)

205 [QUAN] Statistical Thinking 3 Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, or a minimum ALEKS math placement score of 45%. Scientific explanation; correlations and causality; presenting statistical evidence; graphical and numerical methods; chance and gambling; the bell-shaped distribution.

212 [QUAN] Introduction to Statistical Methods 4 (3-2) Course Prerequisite: MATH 101, 103, 105, or 251, each with a C or better, or credit for MATH 106, 108, 140, 171, 201, or a minimum ALEKS math placement score of 45%. Introduction to descriptive and inferential statistics: t-tests, chi-square tests, one-way ANOVA, simple linear regression and correlation.

360 Probability and Statistics 3 Course Prerequisite: MATH 140, 171, or 202, each with a C or better, or MATH 172 or 182. Probability models, sample spaces, random variables, distributions, moments, comparative experiments, tests, correlation and regression in engineering applications. Credit not granted for both STAT 360 and 370. Cooperative: Open to UI degree-seeking students.

370 Introductory Statistics for Engineers 3 Course Prerequisite: MATH 140, 171, or 202 with a C or better, or MATH 172 or 182. Probability axioms, probability models, random variables, expectation, confidence intervals, hypothesis testing, analysis of variance, control charts. Credit not granted for both STAT 360 and 370.

370 (Effective through Spring 2021) Introductory Statistics for Engineers 3 Course Prerequisite: MATH 172 or MATH 182. Probability axioms, probability models, random variables, expectation, confidence intervals, hypothesis testing, analysis of variance, control charts. Credit not granted for both STAT 360 and 370.

380 [M] Decision Making and Statistics 3 Course Prerequisite: STAT 360 or 370. Concepts and methods of decision science using simple mathematical, statistical and computer based tools to solve complex problems for sound decision making.

410 Topics in Probability and Statistics 3 May be repeated for credit; cumulative maximum 6 hours. Current topics in probability and statistics of mutual interest to faculty and students. Credit not granted for both STAT 410 and STAT 510. Recommended preparation: One 3-hour 300-level STAT course. Offered at 400 and 500 level.

412 Statistical Methods in Research I 3 Course Prerequisite: STAT 212, MATH 140, 171, 202, or graduate standing. Intermediate statistical methods, design and analysis of research studies: completely randomized and randomized block designs, multiple regression, categorical data analysis. Cooperative: Open to UI degree-seeking students.

419 Introduction to Multivariate Statistics 3 Course Prerequisite: MATH 220 or 225; one 300-400-level STAT. Introductory course covering multidimensional data, multivariate normal distribution, principal components, factor analysis, clustering, and discriminant analysis.

419 (Effective through Summer 2021) Introduction to Multivariate Statistics 3 Course Prerequisite: MATH 220; one 300-400-level STAT. Introductory course covering multidimensional data, multivariate normal distribution, principal components, factor analysis, clustering, and discriminant analysis.

422 Sampling Methods 3 Course Prerequisite: STAT 212, 360, or 370. Simple and stratified random sampling; systematic sampling; cluster sampling; double sampling, area sampling. Cooperative: Open to UI degree-seeking students.

423 Statistical Methods for Engineers and Scientists 3 Hypothesis testing; linear, multilinear, and nonlinear regression; analysis of variance for designed experiments; quality control; statistical computing. Credit not granted for both STAT 423 and STAT 523. Credit not normally granted for both STAT 423 and 430. Recommended preparation: One 3-credit 300-level STAT course. Offered at 400 and 500 level.

430 Statistical Methods in Engineering 3 Course Prerequisite: MATH 172 or 182; MATH 220. Random variables, sampling, hypothesis testing; linear, multilinear, and nonlinear regression; analysis of variance for designed experiments; statistical computing.

435 [M] Statistical Modeling for Data Analytics 3 (2-2) Course Prerequisite: STAT 360. Multiple linear regression with model selection, dealing with multicolinearity, assessing model assumptions, the LASSO, ridge regression, elastic nets, Loess smoothing, logistic regression, Poisson regression, and the application of the bootstrap to regression modeling.

436 Statistical Computing with SAS and R 3 (2-2) Course Prerequisite: One 300-400-level STAT. Introduction to the SAS and R statistical software packages; covers data entry, variable creation, debugging, graphics, and basic statistical methods.

437 High Dimensional Data Learning and Visualization 3 Course Prerequisite: STAT 435. Data visualization, metric-based clustering, probabilistic and metric-based classification, algebraic and probabilistic dimension reduction, scalable inferential methods, analysis of non-Euclidean data.

443 Applied Probability 3 Course Prerequisite: MATH 172 or MATH 182; MATH 220 or MATH 230. Axioms of probability theory; random variables; expectation; generating function; law of large numbers; central limit theorem; Markov chains.

446 Statistical Applications in Insurance 3 Course Prerequisite: STAT 443. Introduction to the application of mathematics and statistics to the insurance field with a focus on actuarial science.

447 Introduction to Time Series Analysis 3 Course Prerequisite: STAT 412 or concurrent enrollment, or STAT 423 or concurrent enrollment. Introduction to the analysis and application of time series including AR, MA, ARMA, and ARIMA models.

456 Introduction to Statistical Theory 3 Course Prerequisite: STAT 430 or 443. Sampling distributions; hypothesis testing and estimation; maximum likelihood; likelihood ratio tests; theory of least squares; nonparametrics. (Crosslisted course offered as STAT 456, MATH 456). Credit not granted for more than one of STAT/MATH 456 or STAT 556. Recommended preparation: One 3-credit 400-level STAT or probability course. Offered at 400 and 500 level.

508 Environmental Spatial Statistics 3 Theoretical introduction and practical training in spatial data analysis for graduate students in the environmental sciences. (Crosslisted course offered as SOIL SCI 508, STAT 508). Required preparation must include undergraduate statistics through applied multiple regression. Cooperative: Open to UI degree-seeking students.

510 Topics in Probability and Statistics 3 May be repeated for credit; cumulative maximum 6 hours. Current topics in probability and statistics of mutual interest to faculty and students. Credit not granted for both STAT 410 and STAT 510. Recommended preparation: One 3-hour 300-level STAT course. Offered at 400 and 500 level.

511 Statistical Methods for Graduate Researchers 4 (3-2) Fundamentals of experimental design and statistical methods for graduate students in the sciences. Covers t-test for one and two means, ANOVA through completely randomized designs with one and two factors, chi-square tests and regression analysis using R. Recommended preparation: One prior course in statistics. Cannot be used for credit in the Department of Mathematics and Statistics graduate programs. (Crosslisted course offered as STAT 511, AFS 511).

512 Analysis of Variance of Designed Experiments 3 (2-2) Principles of experimental design and analysis and interpretation of data. Required preparation: One 3-credit 400-level STAT course.

516 Time Series 3 ARIMA models; identification, estimation, diagnostics, and forecasting; seasonal adjustments, outlier detection, intervention analysis and transfer function modeling. (Crosslisted course offered as MGTOP 516, STAT 516). Recommended preparation: STAT 443. Cooperative: Open to UI degree-seeking students.

519 Applied Multivariate Analysis 3 Multivariate normal distribution, principal components, factor analysis, discriminant function, cluster analysis, Hotteling's T2 and MANOVA. (Crosslisted course offered as MGTOP 519, STAT 519). Recommended preparation: STAT 443.

520 Statistical Analysis of Qualitative Data 3 Binomial, Poisson, multinomial distribution; contingency tables, Fisher's tests, log-linear models; ordinal data; applications in biology, business, psychology, and sociology. Required preparation: Linear Algebra or Calculus I; one 3-credit 400-level STAT course. Cooperative: Open to UI degree-seeking students.

522 Biostatistics and Statistical Epidemiology 3 Rigorous approach to biostatistical and epidemiological methods including relative risk, odds ratio, cross-over designs, survival analysis and generalized linear models. Required preparation: Linear Algebra or Calculus I; one 3-credit 400-level STAT course. Cooperative: Open to UI degree-seeking students.

523 Statistical Methods for Engineers and Scientists 3 Hypothesis testing; linear, multilinear, and nonlinear regression; analysis of variance for designed experiments; quality control; statistical computing. Credit not granted for both STAT 423 and STAT 523. Credit not normally granted for both STAT 423 and 430. Recommended preparation: One 3-credit 300-level STAT course. Offered at 400 and 500 level.

530 Predictive Models: Foundations in Data Science 3 (2-2) Topics in regression and classification suing probabilistic and data-based methods to build statistical foundations for data science; lab component allows methods to be implemented using data-based software of student choice. Required preparation: One 3-credit 400-level STAT course.

530 (Effective through Summer 2021) Applied Linear Models 3 (2-2) The design and analysis of experiments by linear models. Required preparation: One 3-credit 400-level STAT course.

533 Theory of Linear Models 3 Theoretical basis of linear regression and analysis of variance models; a unified approach based upon the generalized inverse. Required preparation: Linear Algebra and one 3-hour 400-level statistics theory course. Cooperative: Open to UI degree-seeking students.

535 Regression Analysis 3 Conceptual development of regression; estimation, prediction, tests of hypotheses, variable selection, diagnostics, model validation, correlation, and nonlinear regression. Recommended preparation: One 3-credit 400-level STAT course. Cooperative: Open to UI degree-seeking students.

536 Statistical Computing 3 (2-3) Course Prerequisite: STAT 556. Generation of random variables, Monte Carlo simulation, bootstrap and jackknife methods, EM algorithm, Markov chain Monte Carlo methods. (Crosslisted course offered as STAT 536, MATH 536). Recommended preparation: One 3-credit 400-level probability or STAT course. Cooperative: Open to UI degree-seeking students.

544 Applied Stochastic Processes 3 Foundations of continuous time stochastic processes: Kolmogorov forward/backward equations, master equation; general introduction to stochastic calculus and stochastic differential equations; applications. Required preparation: One 3-credit 400-level probability course. Cooperative: Open to UI degree-seeking students.

548 Statistical Theory I 3 Probability spaces, combinatorics, multidimensional random variables, characteristic function, special distributions, limit theorems, stochastic processes, order statistics. (Crosslisted course offered as STAT 548, MATH 568). Recommended preparation: Calculus III and one 3-credit 400-level probability course. Cooperative: Open to UI degree-seeking students.

549 Statistical Theory II 3 Course Prerequisite: STAT 548 or MATH 568. Statistical inferences; estimation and testing hypotheses; regression analysis; sequential analysis and nonparametric methods. (Crosslisted course offered as STAT 549, MATH 569). Cooperative: Open to UI degree-seeking students.

556 Introduction to Statistical Theory 3 Sampling distributions; hypothesis testing and estimation; maximum likelihood; likelihood ratio tests; theory of least squares; nonparametrics. (Crosslisted course offered as STAT 456, MATH 456). Credit not granted for more than one of STAT/MATH 456 or STAT 556. Recommended preparation: One 3-credit 400-level STAT or probability course. Offered at 400 and 500 level.

565 Analyzing Microarray and Other Genomic Data 3 Statistical issues from pre-processing (transforming, normalizing) and analyzing genomic data (differential expression, pattern discovery and predictions). Required preparation: Linear Algebra. Cooperative: Open to UI degree-seeking students.

572 Quality Control 3 Simple quality assurance tools; process monitoring; Shewhart control charts; process characterization and capability; sampling inspection; factorial experiments. Recommended preparation: One 3-credit 400-level statistics or probability course.

573 Reliability 3 Probabilistic modeling and inference; product-limit estimator; probability plotting; maximum likelihood estimation with censored data; regression models for accelerated life testing. Recommended preparation: One 3-credit 400-level statistics or probability course.

574 Linear and Nonlinear Mixed Models 3 Course Prerequisite: STAT 530; STAT 556. The theoretical development and application of linear and nonlinear mixed models covering the theory of linear, generalized linear, and nonlinear mixed models.

575 The Theory of Multivariate Analysis 3 Course Prerequisite: STAT 556. The theoretical development and application of multivariate statistical methods; topics include multivariate distributions, MANOVA, principal components, factor analysis and classification. Required preparation: one course in linear algebra.

576 Bayesian Analysis 3 Course Prerequisite: STAT 556. Statistical principle for combing new evidence with prior beliefs, inference and simulation procedures for accommodating complex data and producing interpretable output. Recommended preparation: STAT 536.

577 Statistical Learning Theory 3 Course Prerequisite: STAT 536. Focus on learning and interpreting from data; both prediction and classification will be discussed for supervised and unsupervised learning.

590 Statistical Consulting Practicum V 1-2 May be repeated for credit; cumulative maximum 6 hours. Theory and practice of statistical consulting, participation in consulting session. Recommended preparation: STAT 530. S, F grading.

591 Seminar in Statistics 1 May be repeated for credit; cumulative maximum 10 hours. Course prerequisite: Graduate student in the Department of Mathematics and Statistics. Current research in statistics. S, F grading.

600 Special Projects or Independent Study V 1-18 May be repeated for credit. Independent study, special projects, and/or internships. Students must have graduate degree-seeking status and should check with their major advisor before enrolling in 600 credit, which cannot be used toward the core graded credits required for a graduate degree. S, F grading.

702 Master's Special Problems, Directed Study, and/or Examination V 1-18 May be repeated for credit. Independent research in special problems, directed study, and/or examination credit for students in a non-thesis master's degree program. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 702 credit. S, U grading.

800 Doctoral Research, Dissertation, and/or Examination V 1-18 May be repeated for credit. Course Prerequisite: Admitted to the Statistical Science PhD program. Independent research and advanced study for students working on their doctoral research, dissertation and/or final examination. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 800 credit. S, U grading.

- Mathematics and Statistics
### Courses

- Mathematics
- Statistics
### Schedules of Studies

- Mathematics – Actuarial Science Option
- Mathematics – Applied Option
- Mathematics - Secondary Teaching Option with Certification
- Secondary Mathematics Teaching Option Without Certification
- Mathematics - Statistics Option
- Mathematics – Theoretical Option
### Minors

- Statistics
- Mathematics
### Certificates

- Certificate in Quantitative Biology