Major Concentration Mathematics (36 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Arts and Science

Program Requirements

Students who have done well in MATH 242 and MATH 235 at the end of their first term should consider, in consultation with their adviser and the instructors of the courses involved, the possibility of entering into an Honours program in Mathematics, in Applied Mathematics, in Probability and Statistics, or a Joint Honours program in Mathematics and another discipline.

Program Prerequisites

Students who have not completed the program prerequisite courses listed below or their equivalents will be required to make up any deficiencies in these courses over and above the 36 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; quadratic loci in two and three dimensions.

    Terms: Fall 2019, Winter 2020

    Instructors: Rosalie Bélanger-Rioux, Zayd Omar, Michael Albanese (Fall)

    • 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.

  • 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 2019, Winter 2020

    Instructors: Sidney Trudeau, Isabella Negrini, Aled Walker (Fall) Jérôme Fortier (Winter)

    • 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

  • 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 2019, Winter 2020

    Instructors: Asad Haris, Sidney Trudeau, Brahim Abdenbi (Fall) Sidney Trudeau, Jeremy Macdonald (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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.

    • Each Tutorial section is enrolment limited

Guidelines for Course Selection

Where appropriate, Honours-level courses may be substituted for their Majors-level counterparts. Students planning to undertake graduate studies in mathematics are urged to make such substitutions.

Students interested in computer science should consider the courses MATH 317, MATH 318, MATH 327, MATH 340, MATH 407, MATH 417, and take the Minor Concentration Computer Science.

Students interested in probability and statistics should consider either taking the Minor Concentration Statistics under option C, or else including some or all of the courses MATH 423, MATH 447, MATH 523, MATH 524, and MATH 525.

Students interested in applied mathematics should consider the courses MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407 and MATH 417.

Students interested in careers in business, industry or government should consider the courses MATH 317, MATH 319, MATH 327, MATH 407, MATH 417, MATH 423, MATH 447, MATH 523, and MATH 525.

Required Courses (21 credits)

  • 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 2019, Winter 2020

    Instructors: Jeremy Macdonald, Broderick Causley (Fall) Jérôme Fortier (Winter)

  • 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 2019

    Instructors: Daniel Wise (Fall)

    • 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 2020

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

  • 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 2019

    Instructors: Jerome Vetois (Fall)

    • Fall

    • Prerequisite: MATH 141

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

  • 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 2020

    Instructors: Axel W Hundemer (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 2019, Winter 2020

    Instructors: Charles Roth (Fall)

  • 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 2019, Winter 2020

    Instructors: Jose Andres Correa, Shomoita Alam (Fall) Djivede Kelome, David B Wolfson (Winter)

    • 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

Complementary Courses (15 credits)

15 credits selected as follows:

At least 9 credits from:

* Note: Either MATH 249 or MATH 316 may be taken but not both.

  • MATH 249 Honours Complex Variables (3 credits) *

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Functions of a complex variable; Cauchy-Riemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; Schwarz-Christoffel transformation; Poisson's integral formulas; applications.

    Terms: Winter 2020

    Instructors: Jerome Vetois (Winter)

    • Winter

    • Prerequisite(s): MATH 248 or MATH 358 or equivalent.

    • Restriction: Intended for Honours Physics and Engineering students

    • Restriction: Not open to students who have taken or are taking MATH 316

  • 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 2019, Winter 2020

    Instructors: Jean-Christophe Nave (Fall) Rosalie Bélanger-Rioux (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 2019

    Instructors: Brent Pym (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 2019

    Instructors: Peter Bartello (Fall)

  • 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 2019, Winter 2020

    Instructors: Masoud Asgharian-Dastenaei (Fall)

    • 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 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 2020

    Instructors: Jérôme Fortier (Winter)

  • MATH 423 Regression and Analysis of Variance (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2019

    Instructors: Yi Yang (Fall)

Remaining credits from:

  • 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 2020

    Instructors: Christian Genest (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.

  • 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 statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.

    Terms: Fall 2019

    Instructors: Russell Steele (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: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

  • MATH 318 Mathematical Logic (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.

    Terms: Fall 2019

    Instructors: Marcin Sabok (Fall)

  • MATH 319 Introduction to Partial Differential Equations (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

    Terms: Winter 2020

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

  • MATH 320 Differential Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The Gauss-Codazzi equations, rigidity.

    Terms: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 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 2019

    Instructors: Antony Raymond Humphries (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 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

  • MATH 346 Number Theory (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

    Terms: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

    • Winter

    • Prerequisite: MATH 235 or consent of instructor

    • Restriction: Not open to students who have taken or are taking MATH 377.

  • MATH 348 Euclidean Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.

    Terms: Fall 2019

    Instructors: Michael Lipnowski (Fall)

    • Prerequisite: MATH 133 or equivalent or permission of instructor.

    • Restriction: Not open to students who have taken MATH 398.

  • MATH 352 Problem Seminar (1 credit)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.

    Terms: Fall 2019

    Instructors: Sergey Norin (Fall)

    • Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.

    • Prerequisite: Enrolment in a math related program or permission of the instructor.

  • MATH 407 Dynamic Programming (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.

    Terms: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

  • MATH 410 Majors Project (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : A supervised project.

    Terms: Fall 2019, Winter 2020

    Instructors: Djivede Kelome, Russell Steele, Johanna Neslehova, David B Wolfson, Antony Raymond Humphries (Fall) Djivede Kelome (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 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 2019

    Instructors: Van Quang Nguyen, Jacques Claude Hurtubise (Fall)

  • 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: Fall 2019

    Instructors: Christian Genest (Fall)

  • 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 2020

    Instructors: Russell Steele (Winter)

    • Winter

    • Prerequisite: MATH 323

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

  • MATH 478 Computational Methods in Applied Mathematics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, Navier-Stokes equations

    Terms: Winter 2020

    Instructors: Jean-Christophe Nave (Winter)

  • MATH 523 Generalized Linear Models (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    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 2020

    Instructors: Johanna Neslehova (Winter)

    • Winter

    • Prerequisite: MATH 423

    • Restriction: Not open to students who have taken MATH 426

  • 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: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

    • 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: This course is not scheduled for the 2019-2020 academic year.

    Instructors: There are no professors associated with this course for the 2019-2020 academic year.

    • Prerequisite: MATH 324 or equivalent

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

Bachelor of Arts & Science—2019-2020 (last updated Aug. 20, 2019) (disclaimer)