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.