Statistics (B.Sc.)
Faculty List
M. Evans, B.Sc. (Western Ontario), M.Sc., Ph.D.,
Professor
Samarakoon, M. Sc (Alberta), Ph. D (Toronto),
Assistant Professor
A. Hashim, B.Sc. (Colombo), Ph.D. (Missouri),
Senior Lecturer
K. Butler, Ph.D. (Simon Fraser University),
Lecturer
Discipline Representative: TBA
Probability and statistics have developed over a period of several hundred years as attempts to quantify uncertainty. With its origins in modeling games of chance, probability theory has become a sophisticated mathematical discipline with applications in such fields as demography, genetics and physics.
Statistics is concerned with the proper collection and analysis of data, both to reduce uncertainty and to provide for its assessment via probability. Applications range from pre-election polling to the design and analysis of experiments to determine the relative efficacies of different vaccines.
STAB22H and STAB27H serve as a non-technical introduction to statistics. These courses are designed for students from disciplines where statistical methods are applied. STAB52H is a mathematical treatment of probability. STAB57H is an introduction to the methods and theory of statistical inference. The C-level courses build on the introductory material to provide a deeper understanding of statistical methodology and of its practical implementation.
Guidelines for 1st year course selection
Students who intend to complete the Major Program in Statistics should include [CSCA48H or PSCB57H ], MATA23H , MATA30H & [MATA36H or MATA37H ] in their 1st year course selection.
Co-operative programs & Concurrent Teacher Education
The Specialist Program in Quantitative Analysis and the Major Program in Statistics are eligible for inclusion in the Co-operative Program in Physical Sciences and in the Concurrent Teacher Education Program (CTEP). Please refer to the Physical Sciences, the Co-operative Programs and the Concurrent Teacher Education sections of this Calendar for further information.
Science Engagement Courses
For service-learning courses and team research opportunities see the Science Engagement section of this Calendar.
SPECIALIST PROGRAM IN QUANTITATIVE ANALYSIS
Supervisor of Studies: M. Evans Email: evans@utsc.utoronto.ca
The Program in Quantitative Analysis is an interdisciplinary program designed for students interested in applying mathematical ideas and analysis to problems in the biological sciences, social and health sciences, physical sciences, and in finance and risk management. After completing this program students will be well prepared to pursue professional careers as quantitative analysts, go on to professional masters programs in such areas of application or to pursue research degrees in the areas in these fields that require a strong training in quantitative methods.
The program requires 13 credits in total. Students will be required to complete a culminating project course in their final year of studies that applies the computational, mathematical, or statistical skills they have acquired. It is strongly recommended that they complete the equivalent of a minor in an area of application. Suggested areas are: Mathematical Finance, Biological Sciences, Physical Sciences, and Social and Health Sciences. The program has streams corresponding to these. Students should select an area of application in consultation with the Supervisor of Studies. For the project course the student needs a supervisor in the appropriate department, also selected in consultation with the Supervisor of Studies.
The Specialist Program in Quantitative Analysis is eligible for inclusion in the Co operative Program in Physical Sciences and in the Concurrent Teacher Education Program (CTEP). Please refer to the Physical Sciences section, the Co operative Programs section and the Concurrent Teacher Education section of this Calendar for further information.
Program Requirements:
Writing requirement (0.5 credits)
(Should be completed by the end of second year.)
One of:
ANTA01H , ANTA02H , CLAA02H , ENGA10H , ENGA11H , ENGB06H , ENGB07H , ENGB08H , ENGB09H , ENGB17H , ENGB19H , ENGB50H , ENGB51H , GGRA02H , GGRA03H , GGRB05H , (GGRB06H), HISA01H , HLTA01H , HUMA11H , HUMA17H , HUMA19H , (LGGA99H), LINA01H , PHLA10H , PHLA11H , WSTA01H .
First Year (3.0 credits specified)
CSCA08H Introduction to Computer Programming
CSCA48H Introduction to Computer Science
CSCA65H Mathematical Expression and Reasoning for Computer Science
MATA23H Linear Algebra I
MATA30H Calculus I
MATA37H Calculus II for Mathematical Scientists
Second Year (4.0 credits specified)
CSCB07H Software Design
CSCB36H Introduction to the Theory of Computation
CSCB63H Design and Analysis of Data Structures
MATB24H Linear Algebra II
MATB41H Techniques of the Calculus of Several Variables I
MATB44H Differential Equations I
STAB52H Introduction to Probability
STAB57H Introduction to Statistics
Second, Third and Fourth Years
Students should choose a stream during their second year of studies which fits with the area of application that interests them.
Biological and Life Sciences Stream (5.0 credits)
CSCC43H Introduction to Databases
CSCD11H Machine Learning and Data Mining
MATB42H Techniques of the Calculus of Several Variables II
MATB61H Linear Programming and Optimization
or
CSCC73H Algorithm Design and Analysis
MATC46H Differential Equations II
STAC42H Multivariate Analysis
STAC52H Experimental Design
STAC62H Stochastic Processes
STAC67H Regression Analysis
Plus 0.5 additional full credits from ACT, CSC, MAT or STA courses at the B or above level.
Physical Sciences Stream (5.0 credits)
CSCC50H Numerical Algebra and Optimization
CSCC51H Numerical Approximation, Integration and Ordinary Differential Equations
MATB42H Techniques of the Calculus of Several Variables II
MATB43H Introduction to Analysis
MATC34H Complex Variables
MATC35H Chaos, Fractals and Dynamics
MATC46H Differential Equations II
STAC62H Stochastic Processes
Plus 1.0 additional full credits from ACT, CSC, MAT or STA courses at the B or above level.
Mathematical Finance, Management and Economics Stream (5.0 credits)
ACTB40H Fundamentals of Investment and Credit
CSCC36H Numerical Methods
CSCD11H Machine Learning and Data Mining
MATB42H Techniques of the Calculus of Several Variables II
MATB61H Linear Programming and Optimization
MATC46H Differential Equations II
STAC57H Time Series Analysis
STAC62H Stochastic Processes
STAC67H Regression Analysis
STAC70H Statistics and Finance
Social and Health Sciences Stream (5.0 credits)
CSCC36H Numerical Methods
CSCC43H Introduction to Databases
MATB61H Linear Programming and Optimization
STAC42H Multivariate Analysis
STAC52H Experimental Design
STAC57H Time Series Analysis
STAC62H Stochastic Processes
STAC67H Regression Analysis
Plus 1.0 additional full credits from ACT, CSC, MAT or STA courses at the B or above level.
Fourth year (0.5 credits)
One of:
CSCD94H Computer Science Project
MATD94H Mathematics Project
STAD94H Statistics Project
MAJOR PROGRAM IN STATISTICS
Supervisor of Studies: A. Hashim Email: hashim@utsc.utoronto.ca
Recommended Writing Course: Students are urged to take a course from the following list of courses by the end of their second year.
ANTA01H , ANTA02H , CLAA02H , ENGA10H , ENGA11H , ENGB06H , ENGB07H , ENGB08H , ENGB09H , ENGB17H , ENGB19H , ENGB50H , ENGB51H , GGRA02H , GGRA03H , GGRB05H , (GGRB06H), HISA01H , HLTA01H , LINA01H , HUMA11H , HUMA17H , HUMA19H , (LGGA99H), PHLA10H , PHLA11H , WSTA01H .
Program Requirements:
This program requires 8.0 full credits.
First Year
CSCA48H Introduction to Computer Science
or
PSCB57H Introduction to Scientific Computing
MATA23H Linear Algebra I
MATA30H Calculus I
[MATA36H Calculus II for Physical Sciences
or
MATA37H Calculus II for Mathematical Sciences (recommended)]
Second Year
MATB24H Linear Algebra II
MATB41H Techniques of the Calculus of Several Variables I
MATB42H Techniques of the Calculus of Several Variables II
STAB52H An Introduction to Probability
STAB57H An Introduction to Statistics
Third and Fourth Year
STAC67H Regression Analysis (This course must be taken at UTSC. No substitutes are permitted without permission of the program supervisor.)
2.0 full credits from any C (or 300-400 on St. George) level courses in STA
1.0 full credit from ACTB40H , ACTB47H or any C (or 300-400 on St. George) level courses in CSC, MAT or STA
SPECIALIST PROGRAM IN COMPUTER SCIENCE
This program has a Statistics stream. For more information, see the Computer Science section of this Calendar.
SPECIALIST PROGRAM IN MATHEMATICS AND ITS APPLICATIONS
This program has a Statistics stream. For more information, see the Mathematics section of this Calendar.
SPECIALIST PROGRAM IN NATURAL SCIENCES
(See the Physical Sciences section of this Calendar.)
ACTB40H3 Fundamentals of Investment and Credit
This course is concerned with the concept of financial interest. Topics covered include: interest, discount and present values, as applied to determine prices and values of annuities, mortgages, bonds, equities, loan repayment schedules and consumer finance payments in general, yield rates on investments given the costs on investments.
Exclusion: ACT240H, MGTB09H , (MGTC03H).
Prerequisite: [MATA30H & one of MATA35H , MATA36H or MATA37H ] or [(MATA27H) & a cumulative GPA of 2.5 or higher]
Note: Students enrolled in or planning to enrol in any of the BBA programs are strongly urged not to take ACTB40H because ACTB40H is an exclusion for MGTB09H (MGTC03H), a required course in the BBA degree. Students in any of the BBA programs will thus be forced to complete MGTB09H (MGTC03H), even if they have credit for ACTB40H , but will only be permitted to count one of ACTB40H and MGTB09H (MGTC03H) towards the 20 credits required to graduate from U of T Scarborough.
ACTB47H3 Introductory Life Contingencies
This course provides an introduction to insurance and annuity concepts from a mathematical point of view. Topics covered include: probability theory applied to survival and to cost and risks of life assurances, life annuities, and pensions, analysis of survival distributions, international actuarial notation, annual benefit premium.
Exclusion: ACT247H
Prerequisite: ACTB40H & MATB41H & STAB52H
STAB22H3 Statistics I
This course is a basic introduction to statistical reasoning and methodology, with a minimal amount of mathematics and calculation. The course covers descriptive statistics, populations, sampling, confidence intervals, tests of significance, correlation, regression and experimental design. A computer package is used for calculations.
Exclusion: ANTC35H , ECMB09Y , ECMB11H , PSYB07H , SOCB06H , STAB52H , STAB57H , STA220H, STA250H
STAB27H3 Statistics II
This course follows STAB22H , and gives an introduction to regression and analysis of variance techniques as they are used in practice. The emphasis is on the use of software to perform the calculations and the interpretation of output from the software. The course reviews statistical inference, then treats simple and multiple regression and the analysis of some standard experimental designs.
Exclusion: ECMB12H , STAB57H , STA221H, STA250H
Prerequisite: STAB22H
STAB52H3 An Introduction to Probability
A mathematical treatment of probability. The topics covered include: the probability model, density and distribution functions, computer generation of random variables, conditional probability, expectation, sampling distributions, weak law of large numbers, central limit theorem, Monte Carlo methods, Markov chains, Poisson processes, simulation, applications. A computer package will be used.
Exclusion: STAB22H , STA107H, STA257H
Prerequisite: MATA33H or MATA36H or MATA37H
STAB57H3 An Introduction to Statistics
A mathematical treatment of the theory of statistics. The topics covered include: the statistical model, data collection, descriptive statistics, estimation, confidence intervals and P-values, likelihood inference methods, distribution-free methods, bookstrapping, Bayesian methods, relationship among variables, contingency tables, regression, ANOVA, logistic regression, applications. A computer package will be used.
Exclusion: STA261H
Prerequisite: STAB52H
STAC42H3 Multivariate Analysis
Linear algebra for statistics. Multivariate distributions, the multivariate normal and some associated distribution theory. Multivariate regression analysis. Canonical correlation analysis. Principal components analysis. Factor analysis. Cluster and discriminant analysis. Multidimensional scaling. Instruction in the use of SAS.
Exclusion: STA437H
Prerequisite: STAC67H
STAC52H3 Experimental Design
The statistical aspects of collecting and analyzing experimental data. Complete randomization and restricted randomization schemes.
Exclusion: STA332H
Prerequisite: STAC67H
STAC57H3 Time Series Analysis
An overview of methods and problems in the analysis of time series data. Topics covered include descriptive methods, filtering and smoothing time series, identification and estimation of times series models, forecasting, seasonal adjustment, spectral estimation. Instruction in the use of SAS.
Exclusion: STA457H
Prerequisite: STAC62H
STAC62H3 Stochastic Processes
This course continues the development of probability theory begun in STAB52H . Topics covered include Poisson processes, Gaussian processes, Markov processes, renewal theory, queuing theory, martingales and stochastic differential equations.
Prerequisite: STAB57H
STAC67H3 Regression Analysis
Orthogonal projections. Univariate normal distribution theory. The linear model and its statistical analysis, residual analysis, influence analysis, collinearity analysis, model selection procedures. Analysis of designs. Random effects. Models for categorical data. Nonlinear models. Instruction in the use of SAS.
Exclusion: STA302H
Prerequisite: STAB57H
STAC70H3 Statistics and Finance
The course discusses the use of statistical methods in finance. Topics covered include returns, random walks and the efficient market hypothesis, portfolio theory, the capital asset pricing model, options pricing, value-at-risk, time series and GARCH models.
Prerequisite: ACTB40H & STAC67H
STAD29H3 Statistics for Life & Social Scientists
The course discusses many advanced statistical methods used in the life and social sciences. Emphasis is on learning how to become a critical interpreter of these methodologies while keeping mathematical requirements low. Topics covered include multiple regression, logistic regression, discriminant and cluster analysis, principal components and factor analysis.
Exclusion: All C-level/300-level & D-level/400-level STA courses or equivalents except STA322H.
Prerequisite: STAB27H
STAD94H3 Statistics Project
A significant project in any area of statistics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a statistics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken. Students must obtain consent from the Supervisor of Studies before registering for this course.
SCIB01H3 Science Engagement Outreach
SCIB02H3 Science Engagement In-Reach
(See the Science Engagement section of this Calendar for full course descriptions.)
