# Liberal Program - Core Science Component Statistics (48 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

### Program Requirements

(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.

#### Program Prerequisites

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.

• MATH 133 Linear Algebra and Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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. Linear transformations. Eigenvalues and diagonalization.

Terms: Fall 2024, Winter 2025

Instructors: Macdonald, Jeremy (Fall) Roth, Charles (Winter)

• 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, except by permission of the Department of Mathematics and Statistics.

• Restriction C: Not open to students who are taking or have taken MATH 134.

• MATH 140 Calculus 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

Terms: Fall 2024, Winter 2025

Instructors: Sabok, Marcin; Trudeau, Sidney (Fall)

• 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, except by permission of the Department of Mathematics and Statistics

• Each Tutorial section is enrolment limited

• MATH 141 Calculus 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

Terms: Fall 2024, Winter 2025

Instructors: Trudeau, Sidney (Winter)

• Prerequisites: MATH 139 or MATH 140 or MATH 150.

• 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, except by permission of the Department of Mathematics and Statistics.

• Each Tutorial section is enrolment limited

#### Required Courses (27 credits)

* 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.

• COMP 202 Foundations of Programming (3 credits) **

Offered by: Computer Science (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: M'hiri, Faten (Fall) M'hiri, Faten (Winter)

• 3 hours

• Prerequisite: a CEGEP level mathematics course

• Restrictions: Not open to students who have taken or are taking COMP 204, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.

• COMP 202 is intended as a general introductory course, while COMP 204 is intended for students in life sciences, and COMP 208 is intended for students in physical sciences and engineering.

• MATH 204 Principles of Statistics 2 (3 credits) +

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

• 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.

• MATH 222 Calculus 3 (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: Pym, Brent (Fall)

• MATH 235 Algebra 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• Fall

• 3 hours lecture; 1 hour tutorial

• Prerequisite: MATH 133 or equivalent

• MATH 236 Algebra 2 (3 credits) ***

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

Instructors: Macdonald, Jeremy (Winter)

• MATH 242 Analysis 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: Jakobson, Dmitry (Fall)

• Fall

• Prerequisite: MATH 141

• Restriction(s): Not open to students who are taking or who have taken MATH 254.

• MATH 323 Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024, Winter 2025

• Prerequisites: MATH 141 or equivalent.

• Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus

• Restriction: Not open to students who have taken or are taking MATH 356

• MATH 324 Statistics (3 credits) +

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

Terms: Fall 2024, Winter 2025

Instructors: Nadarajah, Tharshanna (Fall) Asgharian, 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.

• MATH 423 Applied Regression (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.

Terms: Fall 2024

Instructors: Steele, Russell (Fall)

#### Complementary Courses (18 or 21 credits)

0-3 credits from:

• MATH 203 Principles of Statistics 1 (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: Stephens, David; Correa, Jose Andres (Fall) Sajjad, Alia (Winter)

• 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 http://www.mcgill.ca/students/transfercredit for information regarding transfer credits for this course.

A student who has not completed the equivalent of MATH 203 on entering the program must consult and academic adviser and take MATH 203 in the first semester, increasing the total number of program credits from 45 to 48.

At least 6 credits selected from:

* If chosen, students can take either MATH 317 or COMP 350, but not both.

• COMP 250 Introduction to Computer Science (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)

• 3 hours

• Prerequisites: Familiarity with a high level programming language and CEGEP level Math.

• Students with limited programming experience should take COMP 202 or equivalent before COMP 250. See COMP 202 Course Description for a list of topics.

• COMP 350 Numerical Computing (3 credits) *

Offered by: Computer Science (Faculty of Science)

### Overview

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 2024

Instructors: Chang, Xiao-Wen (Fall)

• MATH 209 Fundamentals of Statistical Modeling and Inference (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Introduction to statistical modelling, likelihood principle andmaximum likelihood estimation, Bayesian principle andBayesian estimation, with emphasis on their application instatistical analysis and data science.

Terms: Winter 2025

Instructors: Lee, Kiwon (Winter)

• MATH 243 Analysis 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

Instructors: Hundemer, Axel W (Winter)

• MATH 314 Advanced Calculus (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 315 Ordinary Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

Terms: Fall 2024, Winter 2025

Instructors: Paquette, Courtney (Fall) Kamnitzer, Joel (Winter)

• Prerequisite: MATH 222.

• Corequisite: MATH 133.

• Restriction: Not open to students who have taken or are taking MATH 325.

• MATH 316 Complex Variables (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: Kamran, Niky (Fall)

• MATH 317 Numerical Analysis (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 326 Nonlinear Dynamics and Chaos (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: Humphries, Tony (Fall)

• MATH 327 Matrix Numerical Analysis (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 329 Theory of Interest (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

Terms: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 340 Discrete Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.

Terms: Winter 2025

Instructors: Norin, Sergey (Winter)

• MATH 350 Honours Discrete Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.

Terms: Fall 2024

Instructors: Norin, Sergey (Fall)

• Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.

• Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.

• Intended for students in mathematics or computer science honours programs.

• MATH 378 Nonlinear Optimization (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.

Terms: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 417 Linear Optimization (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: Hoheisel, Tim (Fall)

• MATH 430 Mathematical Finance (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

Instructors: Kelome, Djivede (Winter)

• MATH 463 Convex Optimization (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.

Terms: Winter 2025

Instructors: Paquette, Courtney (Winter)

At least 9 credits selected from:

*If chosen, students can take at most one of MATH 410, MATH 420, MATH 527D1/D2, and WCOM 314.

• COMP 551 Applied Machine Learning (4 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: Prémont-Schwarz, Isabeau; Rabbany, Reihaneh (Fall) Li, Yue (Winter)

• MATH 208 Introduction to Statistical Computing (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Basic data management. Data visualization. Exploratory data analysis and descriptive statistics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.

Terms: Fall 2024

Instructors: Lee, Kiwon (Fall)

• MATH 308 Fundamentals of Statistical Learning (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.

Terms: Winter 2025

Instructors: Yang, Archer Yi (Winter)

• MATH 410 Majors Project (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : A supervised project.

Terms: Fall 2024, Winter 2025

Instructors: Kelome, Djivede (Fall) Kelome, Djivede (Winter)

• 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.

• MATH 420 Independent Study (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024, Winter 2025

Instructors: Kelome, Djivede (Fall) Kelome, Djivede (Winter)

• Fall and Winter and Summer

• Requires approval by the chair before registration

• Please see regulations concerning Project Courses under Faculty Degree Requirements

• MATH 427 Statistical Quality Control (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 447 Introduction to Stochastic Processes (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

Instructors: Paquette, Elliot (Winter)

• Winter

• Prerequisite: MATH 323

• Restriction: Not open to students who have taken or are taking MATH 547.

• MATH 462 Honours Mathematics for Machine Learning (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Foundations of optimization and convex analysis, stochastic gradient descent. Divergences, loss functions, empirical loss minimization and parameter estimation. Reproducing kernel Hilbert spaces. Multiple linear regression in the context of machine learning. Classification with support vector machines. Dimensionality reduction, Johnson-Lindenstrauss Lemma. Concentration of measure and learning bounds.

Terms: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 510 Quantitative Risk Management (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Basics concepts in quantitative risk management: typesof financial risk, loss distribution, risk measures,regulatory framework. Empirical properties of financialdata, models for stochastic volatility. Extreme-valuetheory models for maxima and threshold exceedances.Multivariate models, copulas, and dependence measures.Risk aggregation.

Terms: Winter 2025

Instructors: Neslehova, Johanna (Winter)

• MATH 523 Generalized Linear Models (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.

Terms: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 524 Nonparametric Statistics (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

Instructors: Genest, Christian (Fall)

• Fall

• Prerequisite: MATH 324 or equivalent

• Restriction: Not open to students who have taken MATH 424

• MATH 525 Sampling Theory and Applications (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2025

Instructors: Dagdoug, Mohamed Mehdi (Winter)

• Prerequisite: MATH 324 or equivalent

• Restriction: Not open to students who have taken MATH 425

• MATH 527D1 Statistical Data Science Practicum (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI).

Terms: Fall 2024

Instructors: Correa, Jose Andres; Kolaczyk, Eric (Fall)

• MATH 527D2 Statistical Data Science Practicum (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : See MATH 527D1 for course description.

Terms: Winter 2025

Instructors: Correa, Jose Andres; Kolaczyk, Eric (Winter)

• MATH 545 Introduction to Time Series Analysis (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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: Winter 2025

Instructors: Stephens, David (Winter)

• MATH 556 Mathematical Statistics 1 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 2024

• Fall

• Prerequisite: MATH 357 or equivalent

• MATH 557 Mathematical Statistics 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.

Terms: Winter 2025

Instructors: Genest, Christian (Winter)

• MATH 558 Design of Experiments (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Row-column designs. Latin squares. Model and analysis for fixed row and column effects. Split-plot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues.

Terms: Winter 2025

• MATH 559 Bayesian Theory and Methods (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Subjective probability, Bayesian statistical inference and decision making, de Finetti’s representation. Bayesian parametric methods, optimal decisions, conjugate models, methods of prior specification and elicitation, approximation methods. Hierarchical models. Computational approaches to inference, Markov chain Monte Carlo methods, Metropolis—Hastings. Nonparametric Bayesian inference.

Terms: This course is not scheduled for the 2024-2025 academic year.

Instructors: There are no professors associated with this course for the 2024-2025 academic year.

• MATH 598 Topics in Probability and Statistics (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.

Terms: Fall 2024, Winter 2025

Instructors: Addario-Berry, Louigi Dana; Neslehova, Johanna (Fall) Asgharian, Masoud (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.

• WCOM 314 Communicating Science (3 credits) *

Offered by: McGill Writing Centre (Faculty of Arts)

### Overview

WCOM : Production of written and oral assignments (in English) 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 2024, Winter 2025

Instructors: Kubler, Kyle (Fall) Kubler, Kyle (Winter)

• Restriction: Not open to students who have taken CCOM 314.

Faculty of Science—2024-2025 (last updated Apr. 3, 2024) (disclaimer)