XII--Course Descriptions
Department of Mathematics and Statistics
Suggested initial course sequences:
89-204 Statistics I S,F,W(3-2) [0.50] |
A course stressing the practical methods of Statistics. Topics include: Descriptive Statistics; univariate models such as binomial, Poisson, geometric, uniform and normal; Central Limit theorem; expected value; the t, F and chi-square models; point and interval estimation; hypothesis testing methods up to two-sample data; simple regression and correlation; ANOVA for CRD and RCBD. Assignments will deal with real data from the natural sciences. |
Prerequisites: OAC calculus or equivalent. |
Exclusions: 89-100, 89-206, 89-208, 89-210, 89-212. |
Course Profile |
89-205 Statistics II S,F,W(3-2) [0.50] |
The methods of 89-204 are extended to the multi-sample cases. Methods include: simple and multiple regression analysis including ANOVA and lack-of-fit; experimental design including analysis for CRD, RCBD, LSD, SPD and factorial experiments with interaction; ANCOVA; Bioassay. Assignments employing data from the natural sciences will be processed in the microcomputer laboratory. |
Prerequisites: 89-204 or 89-210 or equivalent. |
Exclusions: 89-209. |
Course Profile |
89-206 Statistics for Business Decisions W(3-2) [0.50] |
A course designed for students interested in the application of statistics in a business setting. Topics covered will include the role of statistics in business decisions, organization of data, frequency distributions, probability, normal and sampling distributions, hypothesis tests, linear regression and an introduction to time series, quality control and operations research. (Also offered through distance education format.) |
Prerequisites: 1 OAC (or equivalent) mathematics or [0.50] credit in mathematics. |
Exclusions: 89-100, 89-204, 89-208, 89-210, 89-212. |
Course Profile |
89-208 Introductory Applied Statistics I F(3-2) [0.50] |
Frequency distributions, graphing and tabulation of data. Measures of central tendency, variability and association. Elementary probability. Hypothesis testing and confidence intervals. Basic concepts of experimental design; treatment designs. Analysis of variance for simple and complex experiments. (Recommended only for students in the B.A.Sc. program.) |
Prerequisites: 1 OAC (or equivalent) mathematics or [0.50] credit in mathematics. |
Exclusions: 89-100, 89-204, 89-206, 89-210, 89-212. |
Course Profile |
89-209 Introductory Applied Statistics II W(3-2) [0.50] |
Design of sample surveys. Analysis of qualitative data. Simple linear regression and correlation. Multiple regression and analysis of covariance. Some non-parametric methods. Survey of special topics such as factor analysis and cluster analysis. |
Prerequisites: 89-208. |
Exclusions: 89-205. |
Course Profile |
89-210 Introductory Probability and Statistics F(3-2) [0.50] |
Basic probability; Discrete random variables, examples (e.g. Bernoulli, binomial, geometric), expected values, variances; Markov chains and their properties; Continuous random variables (e.g Gaussian); Methods of elementary data summarizations, analysis and statistical inference (estimation, testing, regression, correlation, and related distributions). Laboratory work will include basic experimentation with sampling and with statistical computer packages. |
Prerequisites: 63-101 or 63-121 or 66-121. |
Corequisites: (63-215 or 63-216), (63-208 or 63-220). |
Exclusions: 89-204, 89-206, 89-208, 89-212. |
Course Profile |
89-212 Probability and Statistics for Engineers W(3-1) [0.50] |
Sample spaces. Probability, conditional probability, independence. Bayes' theorem. Probability distributions. Probability densities. Algebra of expected values. Descriptive statistics. Inferences concerning means, variances, and proportions. Curve fitting, the method of least squares, correlation. Introduction to quality control and reliability. Recommended especially for students in the B.Sc.(Eng.) program. |
Prerequisites: 1 of 63-101, 63-121, 63-208, 66-121. |
Exclusions: 89-100, 89-204, 89-206, 89-208, 89-210. |
Course Profile |
89-310 Introductory Mathematical Statistics I F(3-0) [0.50] |
Probability spaces; discrete and continuous random variables; multivariate distributions; expectations; moments, Chebyshev's inequality, product moments; sums of random variables, generating functions; Gamma, Beta, t and F distributions; central limit theorem; sampling distributions. |
Prerequisites: (63-121 or 66-121), (89-204 or 89-210). |
Course Profile |
89-311 Introductory Mathematical Statistics II W(3-0) [0.50] |
Elementary statistical decision theory. Estimation, consistency, sufficiency; Cramer-Rao inequality; maximum likelihood estimator and its properties; best linear unbiased estimator; least squares; linear regression, experimental design models; 1-way and 2-way classifications, latin squares; robustness of t and F tests; non-parametric methods. Numerical examples will illustrate the theory. |
Prerequisites: 89-310. |
Course Profile |
89-321 Experimental Design W(3-0) [0.50] |
Randomization theory of designs; general theory of factorial experiments; fractional replication; theory of incomplete block designs; analysis of groups of experiments; treatments applied in sequence with emphasis directed to the mathematical aspects. |
Prerequisites: 89-310, 89-324. |
Formerly: 89-422 |
Course Profile |
89-324 Applied Regression Analysis F(3-2) [0.50] |
Theory and applications of regression techniques; linear, non-linear and multiple regression and correlation; analysis of residuals; other statistical techniques including: response surfaces and covariance analysis, prediction and time-series analysis. The computer lab involves interactive data analysis and investigation of the methodology using SAS/S-PLUS statistical software. |
Prerequisites: (63-121 or 66-121), 63-215 (may be taken concurrently or with instructor permission), (89-205 or 89-210). |
Course Profile |
89-332 Sampling Theory with Applications W(3-0 [0.50] |
Non-probability and probability sampling. Simple random sampling, stratified sampling, cluster sampling, systematic sampling, double sampling, two-phase sampling, multi-stage cluster sampling. Estimation procedures and applications of above techniques. |
Prerequisites: (63-121 or 66-121), (89-205 or 89-324 or 89-310). |
Course Profile |
89-351 Environmental Risk Assessment W(3-0) [0.50] |
Contemporary statistical methods for assessing risk, including dose-response models, survival analysis, relative risk analysis, bioassay, estimating methods for zero risk, trend analysis, association risks. Case studies illustrate the methods. |
Prerequisites: (1 of 63-100, 63-108, 63-120 or 66-111), 89-205 or 89-210 or equivalent. |
Course Profile |
89-405 Topics in Applied Statistics I W(3-0) [0.50] |
Topics such as statistical computing procedures, quality control, bioassay, and introductory stochastic processes. Intended for statistics students and interested students in other disciplines with appropriate previous courses in statistics. Information on particular offerings will be available at the beginning of each academic year. (Offered in odd-numbered years.) |
Prerequisites: 89-311, 89-324. |
Course Profile |
89-406 Topics in Applied Statistics II W(3-0) [0.50] |
Same as for 89-405. (Offered in even-numbered years.) |
Prerequisites: 89-311, 89-324. |
Course Profile |
89-408 Data Analysis F(3-2) [0.50] |
2-way contingency tables, measures of association, Poisson and multinominal sampling, models for ordinal response, generalized linear models, quasi-likelihood, generalized estimating equations, application to longitudinal data. |
Prerequisites: 89-311, 89-324. |
Course Profile |
89-434 Statistical Inference W(3-0) [0.50] |
This course on methods of statistical inference reviews and extends the theory of estimation introducted in 89-311: interval estimation tests for simple and composite hypotheses, likelihood ratio tests. Recent likelihood concepts as well as classical large sample theory, asymptotics and approximations and their applications are covered. this material is directly relevant to current research and applications in areas as diverse as survival analysis, nonparametric regression and environmetrics. Specialized topis such as EM algorithm, martingales, etc. may be introduced as needed for current departmental research. |
Prerequisites: 89-311, 89-324. |
Course Profile |
89-435 Applied Multivariate Statistical Methods F(3-0) [0.50] |
Samplings from the multivariate normal distribution, Wishart and Hotelling's Tē distribution statistical inference on the mean vector, canonical correlations, multivariate analysis of variance and covariance, multivariate regression, principal components analysis, factor analysis. Topics will be illustrated using examples from various disciplines. |
Prerequisites: 89-311, 89-324. |
Course Profile |
89-436 Applied Time Series Analysis W(3-2) [0.50] |
Trend, serial dependence and stationarity, simple descriptive methods; stationary, autoregressive and moving average processes; nonstationary time series; model identification, estimation, and forecasting; Bivariate Time Series. |
Prerequisites: 89-324. |
Course Profile |
89-451 Advanced Risk Analysis F(3-0) [0.50] |
Measures of risk, 2x2 tables, combining 2x2 tables, trend tests, combination and time dependent bioassays, joint action toxicity models, teratology and estimation of survival functions. Extensive use will be made of SAS and S-plus. Course is based on real data in risk analysis. |
Prerequisites: 89-311, 89-324, 89-351. |
Course Profile |
1998-99 Undergraduate Calendar |