Major Mathematics and Computer Science (72 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

Program Requirements

The B.Sc.; Major in Mathematics and Computer Science emphasizes fundamental skills in mathematics and computer science, while exploring the interaction between the two fields.

Program Prerequisites

Students entering the Joint Major in Mathematics and Computer Science 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 72 credits of courses in the program specification.

  • 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 (54 credits)

* Students who have sufficient knowledge in a programming language do not need to take COMP 202 but can replace it with an additional Computer Science complementary course.

** Student cannot replace MATH 317 with COMP 350.

  • 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.

  • COMP 206 Introduction to Software Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.

    Terms: Fall 2024, Winter 2025

    Instructors: Errington, Jacob (Fall) Vybihal, Joseph P (Winter)

  • 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 251 Algorithms and Data Structures (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.

    Terms: Fall 2024, Winter 2025

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

    • 3 hours

    • Prerequisites: COMP 250; MATH 235 or MATH 240

    • COMP 251 uses mathematical proof techniques that are taught in the corequisite course(s). If possible, students should take the corequisite course prior to COMP 251.

    • COMP 251 uses basic counting techniques (permutations and combinations) that are covered in MATH 240 but not in MATH 235. These techniques will be reviewed for the benefit of MATH 235 students.

    • Restrictions: Not open to students who have taken or are taking COMP 252.

  • COMP 273 Introduction to Computer Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining.

    Terms: Fall 2024, Winter 2025

    Instructors: Elsaadawy, Mona (Fall) Kry, Paul (Winter)

  • COMP 302 Programming Languages and Paradigms (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Programming language design issues and programming paradigms. Binding and scoping, parameter passing, lambda abstraction, data abstraction, type checking. Functional and logic programming.

    Terms: Fall 2024, Winter 2025

    Instructors: Pientka, Brigitte (Fall) Errington, Jacob (Winter)

  • COMP 310 Operating Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Control and scheduling of large information processing systems. Operating system software - resource allocation, dispatching, processors, access methods, job control languages, main storage management. Batch processing, multiprogramming, multiprocessing, time sharing.

    Terms: Fall 2024, Winter 2025

    Instructors: Maheswaran, Muthucumaru (Fall) Liu, Xue (Winter)

  • COMP 330 Theory of Computation (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Finite automata, regular languages, context-free languages, push-down automata, models of computation, computability theory, undecidability, reduction techniques.

    Terms: Fall 2024, Winter 2025

    Instructors: Waldispuhl, Jérôme (Fall) Crépeau, Claude (Winter)

  • COMP 360 Algorithm Design (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Advanced algorithm design and analysis. Linear programming, complexity and NP-completeness, advanced algorithmic techniques.

    Terms: Fall 2024, Winter 2025

    Instructors: Robere, Robert (Fall) Hatami, Hamed (Winter)

  • 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 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 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 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 2024

    Instructors: Fortier, Jérôme (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 2024, Winter 2025

    Instructors: Sajjad, Alia (Fall) Nadarajah, Tharshanna (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

  • 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)

Complementary Courses (18 credits)

9 credits from the following.

Other MATH courses, at the undergraduate level, not included in this list may be chosen in consultation with an adviser.

  • 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

    Instructors: Nadarajah, Tharshanna (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 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 319 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 2025

    Instructors: Lin, Jessica (Winter)

  • 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 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 338 History and Philosophy of Mathematics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs.

    Terms: Fall 2024

    Instructors: Fortier, Jérôme (Fall)

  • 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: Winter 2025

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

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

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

  • 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 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 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 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)

  • 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 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 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 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)

  • 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 2025

    Instructors: Nave, Jean-Christophe (Winter)

9 credits selected from Computer Science courses at the 300 level or above (except COMP 364 and COMP 396) and ECSE 508.

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