Statistics

Faculty List

Associate Chair:  L.C. Jeffrey (416-287-7265)
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.
STAB22H3 and STAB27H3 serve as a non-technical introduction to statistics. These courses are designed for students from disciplines where statistical methods are applied. STAB52H3 is a mathematical treatment of probability. STAB57H3 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.

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, Co-operative Programs and the Concurrent Teacher Education sections of this Calendar for further information.

Combining Statistics and Economics Programs
Students who wish to combine studies in statistics and economics should consult the Economics for Management section of this Calendar for information on the economics programs and restrictions on the order in which courses must be taken.

Service Learning and Outreach (Previously known as Science Engagement)
For experiential learning through community outreach and classroom in-reach, please see the Centre for Teaching and Learning section of this Calendar.

Statistics Programs

SPECIALIST PROGRAM IN QUANTITATIVE ANALYSIS (SCIENCE)

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 13.0 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
This program requires 13.0 credits including at least 4.0 credits at the C- or D-level of which at least 1.0 must be at the D-level.
Writing requirement (0.5 credits)
(Should be completed by the end of second year.)
One of:
ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), HLTA01H3, HUMA01H3, (HUMA11H3), (HUMA17H3), (LGGA99H3), LINA01H3, PHLA10H3, PHLA11H3, WSTA01H3.

First Year (3.0 credits specified)
CSCA08H3 Introduction to Computer Programming
CSCA48H3 Introduction to Computer Science
CSCA67H3 Discrete Mathematics for Computer Scientists
MATA23H3 Linear Algebra I
MATA31H3 Calculus I for Mathematical Sciences
MATA37H3 Calculus II for Mathematical Sciences

Second Year (4.0 credits specified)
CSCB07H3 Software Design
CSCB36H3 Introduction to the Theory of Computation
CSCB63H3 Design and Analysis of Data Structures
MATB24H3 Linear Algebra II
MATB41H3 Techniques of the Calculus of Several Variables I
MATB44H3 Differential Equations I
STAB52H3 Introduction to Probability
STAB57H3 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)
CSCC43H3 Introduction to Databases
CSCD11H3 Machine Learning and Data Mining
MATB42H3 Techniques of the Calculus of Several Variables II
[MATB61H3 Linear Programming and Optimization or CSCC73H3 Algorithm Design and Analysis]
MATC46H3 Differential Equations II
STAC52H3 Experimental Design
STAC62H3 Stochastic Processes
STAC67H3 Regression Analysis
STAD37H3 Multivariate Analysis
Plus 0.5 additional full credits from ACT, CSC, MAT or STA courses at the B-level or above.

Physical Sciences Stream (5.0 credits)
CSCC37H3 Introduction to Numerical Algorithms for Computational Mathematics
CSCD37H3 Analysis of Numerical Algorithms for Computational Mathematics
MATB42H3 Techniques of the Calculus of Several Variables II
MATB43H3 Introduction to Analysis
MATC34H3 Complex Variables
MATC35H3 Chaos, Fractals and Dynamics
MATC46H3 Differential Equations II
STAC62H3 Stochastic Processes
Plus 1.0 additional full credit from ACT, CSC, MAT or STA courses at the B-level or above, of which at least 0.5 credit must be at the D-level.

Mathematical Finance, Management and Economics Stream (5.0 credits)
ACTB40H3 Fundamentals of Investment and Credit
CSCC37H3 Introduction to Numerical Algorithms for Computational Mathematics
CSCD11H3 Machine Learning and Data Mining
MATB42H3 Techniques of the Calculus of Several Variables II
MATB61H3 Linear Programming and Optimization
MATC46H3 Differential Equations II
STAC62H3 Stochastic Processes
STAC67H3 Regression Analysis
STAC70H3 Statistics and Finance
STAD57H3 Time Series Analysis

Social and Health Sciences Stream (5.0 credits)
CSCC37H3 Introduction to Numerical Algorithms for Computational Mathematics
CSCC43H3 Introduction to Databases
MATB61H3 Linear Programming and Optimization
STAC52H3 Experimental Design
STAC62H3 Stochastic Processes
STAC67H3 Regression Analysis
STAD37H3 Multivariate Analysis
STAD57H3 Time Series Analysis
Plus 1.0 additional full credits from ACT, CSC, MAT or STA courses at the B-level or above.

Fourth year (0.5 credits)
One of:
CSCD94H3 Computer Science Project
MATD94H3 Mathematics Project
STAD94H3 Statistics Project

MAJOR PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: M. Samarakoon  Email: mahinda@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.
ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, ENGB51H3, GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), HLTA01H3, HUMA01H3, (HUMA11H3), (HUMA17H3),  (LGGA99H3), LINA01H3, PHLA10H3, PHLA11H3, WSTA01H3.

Program Requirements
This program requires 8.0 full credits.
First Year
[CSCA48H3 Introduction to Computer Science or PSCB57H3 Introduction to Scientific Computing]
MATA23H3 Linear Algebra I
[MATA30H3 Calculus I for Biological and Physical Sciences or MATA31H3 Calculus I for Mathematical Sciences] and
[MATA36H3 Calculus II for Physical Sciences or MATA37H3 Calculus II for Mathematical Sciences.]  Note: The sequence MATA31H3 and MATA37H3 is recommended. 
MATA31H3 is the pre-requisite for MATA37H3.
Second Year
MATB24H3 Linear Algebra II
MATB41H3 Techniques of the Calculus of Several Variables I
MATB42H3 Techniques of the Calculus of Several Variables II
STAB52H3 An Introduction to Probability*
STAB57H3 An Introduction to Statistics*
Third and Fourth Year
STAC67H3 Regression Analysis*
2.0 full credits from any C- or D- (or 300-400 on St. George) level courses in STA
1.0 full credit from ACTB40H3, ACTB47H3 or any C- or D- (or 300-400 on St. George) level courses in CSC, MAT or STA
* STAB52H3, STAB57H3, STAC67H3 - These courses must be taken at UTSC. No substitutes are permitted without permission of the program supervisor.

MINOR PROGRAM IN STATISTICS (SCIENCE)

Supervisor of Studies: M. Samarakoon Email: mahinda@utsc.utoronto.ca

Program Requirements
This program requires 4 full credits.
First Year (2.0 credits)
CSCA08H3 Introduction to Computer Programming
MATA23H3 Linear Algebra I
[MATA30H3 Calculus I for Biological and Physical Sciences or MATA31H3 Calculus I for Mathematical Sciences] and
[MATA36H3 Calculus II for Physical Sciences or MATA37H3 Calculus II for Mathematical Sciences.]  Note: The sequence MATA31H3 and MATA37H3 is recommended. 
MATA31H3 is the pre-requisite for MATA37H3.
Second Year (1.0 credit)
STAB52H3 An Introduction to Probability
STAB57H3 An Introduction to Statistics
Third and Fourth Year (1.0 credit)
STAC67H3 Regression Analysis

In addition 0.5 credits must be chosen from any C- or D-level STA course but not STAD29H3.

SPECIALIST PROGRAM IN MATHEMATICS (SCIENCE)

This program has a Statistics stream. For more information, see the Mathematics section of this Calendar.

SPECIALIST PROGRAM IN NATURAL SCIENCES (SCIENCE)

See the Physical Sciences section of this Calendar for more information.

Statistics Courses


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.
Prerequisite: [MATA30H3 & one of MATA35H3, MATA36H3 or MATA37H3] or [(MATA27H3) & a cumulative GPA of 2.5 or higher] Note: Students enrolled in or planning to enrol in any of the B.B.A. programs are strongly urged not to take ACTB40H3 because ACTB40H3 is an exclusion for MGTB09H3 (MGTC03H3), a required course in the B.B.A. degree. Students in any of the B.B.A programs will thus be forced to complete MGTB09H3 (MGTC03H3), even if they have credit for ACTB40H3, but will only be permitted to count one of ACTB40H3 and MGTB09H3 (MGTC03H3) towards the 20 credits required to graduate from UofT Scarborough.
Exclusion: ACT240H, MGTB09H3, (MGTC03H3).
Breadth Requirement: Quantitative Reasoning

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.
Prerequisite: ACTB40H3 & MATB41H3 & STAB52H3
Exclusion: ACT247H
Breadth Requirement: Quantitative Reasoning

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: ANTC35H3, ECMB11H3, POLB11H3, PSYB07H3, SOCB06H3, STAB52H3, STAB57H3, STA220H, STA250H
Breadth Requirement: Quantitative Reasoning

STAB27H3    Statistics II

This course follows STAB22H3, 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.
Prerequisite: STAB22H3
Exclusion: ECMB12H3, STAB57H3, STA221H, STA250H
Breadth Requirement: Quantitative Reasoning

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.
Prerequisite: MATA33H3 or MATA36H3 or MATA37H3
Exclusion: STAB22H3, STA107H, STA257H
Breadth Requirement: Quantitative Reasoning

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.
Prerequisite: STAB52H3
Exclusion: STA261H
Breadth Requirement: Quantitative Reasoning

STAC52H3    Experimental Design

The statistical aspects of collecting and analyzing experimental data. Complete randomization and restricted randomization schemes.
Prerequisite: STAB27H3 or STAB57H3
Exclusion: STA332H
Breadth Requirement: Quantitative Reasoning

STAC62H3    Stochastic Processes

This course continues the development of probability theory begun in STAB52H3. Topics covered include Poisson processes, Gaussian processes, Markov processes, renewal theory, queuing theory, martingales and stochastic differential equations.
Prerequisite: STAB57H3
Breadth Requirement: Quantitative Reasoning

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.
Prerequisite: STAB57H3
Exclusion: STA302H
Breadth Requirement: Quantitative Reasoning

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: ACTB40H3 & STAC67H3
Breadth Requirement: Quantitative Reasoning

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.
Prerequisite: STAB27H3
Exclusion: All C-level/300-level & D-level/400-level STA courses or equivalents except STA322H.
Breadth Requirement: Quantitative Reasoning

STAD37H3    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.
Prerequisite: STAC67H3
Exclusion: STA437H, (STAC42H3)
Breadth Requirement: Quantitative Reasoning

STAD57H3    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.
Prerequisite: STAC62H3
Exclusion: STA457H, (STAC57H3)
Breadth Requirement: Quantitative Reasoning

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.