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Note: This is the 2018–2019 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Note: This is the 2018–2019 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
(45 or 48 credits)
This program provides training in statistics, with a solid mathematical core, and basic training in computing. With strong performance in an appropriate selection of courses, this program can lead to "A.Stat." professional accreditation from the Statistical Society of Canada, which is regarded as the entry level requirement for Statisticians practising in Canada.
Students may complete this program with a minimum of 45 credits or a maximum of 48 credits depending on whether or not they are required to take MATH 203.
Students entering the Core Science Component in Statistics are normally expected to have completed the courses below or their equivalents. Otherwise they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.
Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Fortier, Jerome; Shen, Liangming; Pequignot, Yann Batiste; Osajda, Damian (Fall) Fortier, Jerome (Winter) Patrias, Rebecca (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Trudeau, Sidney; Fortier, Jerome; Patrias, Rebecca (Fall) Garver, Alexander (Winter) Zenz, Peter (Summer)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Perret-Gentil-dit-Maillard, Corentin; Gaster, Jonah (Fall) Trudeau, Sidney; Fortier, Jerome; Fox, Thomas F (Winter) Nica, Bogdan; Xu, Peter (Summer)
Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited
In addition, a student who has not completed the equivalent of MATH 203 on entering the program must consult an academic adviser and take MATH 203 in the first semester, increasing the total number of program credits from 45 to 48.
* Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of complementary courses.
** Students who have sufficient knowledge in a programming language do not need to take COMP 202, but must replace it by either COMP 250 or COMP 350.
***MATH 236 is an equivalent prerequisiste to MATH 223 for required and complementary Computer Science courses listed below.
+ Students have to take MATH 204 prior to MATH 324.
Computer Science (Sci) : Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Alberini, Giulia; Vybihal, Joseph P (Fall) Alberini, Giulia; Yu, Tzu-Yang; Zammar, Chad (Winter) Yu, Tzu-Yang (Summer)
3 hours
Prerequisite: a CEGEP level mathematics course
Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250
Mathematics & Statistics (Sci) : The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Terms: Winter 2019
Instructors: Genest, Christian (Winter)
Winter
Prerequisite: MATH 203 or equivalent. No calculus prerequisites
Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Macdonald, Jeremy; Faifman, Dmitry (Fall) Sektnan, Lars (Winter) Pequignot, Yann Batiste (Summer)
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2018
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Terms: Winter 2019
Instructors: Nica, Bogdan (Winter)
Winter
Prerequisite: MATH 235
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2018
Instructors: Vetois, Jerome (Fall)
Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Stephens, David (Fall) Wolfson, David B (Winter) Kelome, Djivede (Summer)
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2018, Winter 2019
Instructors: Khalili Mahmoudabadi, Abbas (Fall) Asgharian-Dastenaei, Masoud (Winter)
Fall and Winter
Prerequisite: MATH 323 or equivalent
Restriction: Not open to students who have taken or are taking MATH 357
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
Mathematics & Statistics (Sci) : Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2018
Instructors: Yang, Yi (Fall)
18 or 21 credits
0-3 credits from:
Mathematics & Statistics (Sci) : Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions).
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Wolfson, David B; Khalili Mahmoudabadi, Abbas (Fall) Wolfson, David B (Winter) Correa, Jose Andres (Summer)
No calculus prerequisites
Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar. Students should consult for information regarding transfer credits for this course.
At least 6 credits selected from:
* Students can take either MATH 317 or COMP 350, but not both.
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2018, Winter 2019
Instructors: Langer, Michael; Alberini, Giulia (Fall) Robillard, Martin; Alberini, Giulia (Winter)
Computer Science (Sci) : Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Least-squares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Terms: Fall 2018
Instructors: Chang, Xiao-Wen (Fall)
Mathematics & Statistics (Sci) : Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Terms: Winter 2019
Instructors: Hundemer, Axel W (Winter)
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2018, Winter 2019
Instructors: Roth, Charles (Fall) Drury, Stephen W (Winter)
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Nave, Jean-Christophe (Fall) Humphries, Antony Raymond (Winter) Roth, Charles (Summer)
Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2018
Instructors: Nica, Bogdan (Fall)
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2018
Instructors: Bartello, Peter (Fall)
Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2018
Instructors: Lessard, Jean-Philippe (Fall)
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: Winter 2019
Instructors: Panayotov, Ivo (Winter)
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2019
Instructors: Kelome, Djivede (Winter)
Winter
Prerequisite: MATH 141
Mathematics & Statistics (Sci) : Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Terms: Winter 2019
Instructors: Fortier, Jerome (Winter)
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Fall 2018
Instructors: Vetta, Adrian Roshan (Fall)
Mathematics & Statistics (Sci) : An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.
Terms: Fall 2018
Instructors: Nguyen, Van Quang (Fall)
Mathematics & Statistics (Sci) : Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Terms: Winter 2019
Instructors: Kelome, Djivede (Winter)
At least 9 credits selected from:
*Students can take either MATH 410 or MATH 420, but not both.
Communication (CCE) : Production of written and oral assignments designed to communicate scientific problems and findings to varied audiences. Analysis of the disciplinary conventions of scientific discourse in terms of audience, purpose, organization, and style; comparative rhetorical analysis of academic and popular genres, including abstracts, lab reports, research papers, print and online journalism.
Terms: Fall 2018, Winter 2019
Instructors: Dechief, Diane (Fall) Dechief, Diane (Winter)
Computer Science (Sci) : Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Terms: Fall 2018, Winter 2019
Instructors: Chandar, Sarath (Fall) Hamilton, William (Winter)
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Kelome, Djivede; Neslehova, Johanna; Lessard, Jean-Philippe; Stephens, David; Steele, Russell; Tsogtgerel, Gantumur (Fall) Kelome, Djivede; Stephens, David; Jakobson, Dmitry; Genest, Christian; Steele, Russell; Tsogtgerel, Gantumur; Asgharian-Dastenaei, Masoud; Kamran, Niky (Winter) Kelome, Djivede; Steele, Russell; Yang, Yi (Summer)
Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
Requires departmental approval.
Mathematics & Statistics (Sci) : Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Neslehova, Johanna; Stephens, David (Fall) Neslehova, Johanna (Winter) Neslehova, Johanna; Stephens, David; Steele, Russell (Summer)
Fall and Winter and Summer
Requires approval by the chair before registration
Please see regulations concerning Project Courses under Faculty Degree Requirements
Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Terms: This course is not scheduled for the 2018-2019 academic year.
Instructors: There are no professors associated with this course for the 2018-2019 academic year.
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2019
Instructors: Steele, Russell (Winter)
Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasi-likelihood. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Terms: Winter 2019
Instructors: Neslehova, Johanna (Winter)
Mathematics & Statistics (Sci) : Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.
Terms: Fall 2018
Instructors: Genest, Christian (Fall)
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: Winter 2019
Instructors: Steele, Russell (Winter)
Mathematics & Statistics (Sci) : Life tables and distributions; force of mortality; premium, net premium, and reserve valuation for life insurance and annuity contracts (discrete and continuous case); cash flow analysis for portfolios of life insurance and annuities; asset liability management; numerical techniques for multiple decrement and state models; portfolio valuation of aggregate risks.
Terms: This course is not scheduled for the 2018-2019 academic year.
Instructors: There are no professors associated with this course for the 2018-2019 academic year.
Mathematics & Statistics (Sci) : Stochastic models and inference for loss severity and claim frequency distributions; computational techniques for the aggregation of independent risks (Panjer's algorithm, FFT, etc.); risk measures and quantitative risk management applications; models and inference for multivariate data, heavy-tail distributions, and extremes; dynamic risk models based on stochastic processes and ruin theory.
Terms: This course is not scheduled for the 2018-2019 academic year.
Instructors: There are no professors associated with this course for the 2018-2019 academic year.
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: Fall 2018
Instructors: Steele, Russell (Fall)
Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Terms: Fall 2018
Instructors: Asgharian-Dastenaei, Masoud (Fall)
Fall
Prerequisite: MATH 357 or equivalent
Mathematics & Statistics (Sci) : Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Terms: Winter 2019
Instructors: Khalili Mahmoudabadi, Abbas (Winter)
Winter
Prerequisite: MATH 556
Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.
Terms: Winter 2019
Instructors: Neslehova, Johanna; Stephens, David (Winter)
Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
Restriction(s): Requires permission of the Department of Mathematics and Statistics.