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Note: This is the 2023–2024 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Note: This is the 2023–2024 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
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.
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.
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 2023, Winter 2024, Summer 2024
Instructors: Trudeau, Sidney; Collins-Woodfin, Elizabeth; Branchereau, Romain (Fall) Gerbelli-Gauthier, Mathilde (Winter) Bellemare, Hugues (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, 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 2023, Winter 2024, Summer 2024
Instructors: Fortier, Jérôme; Cant, Dylan; Fu, Hao (Fall) Fortier, Jérôme (Winter) Sajjad, Alia (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, 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 2023, Winter 2024, Summer 2024
Instructors: Sroka, Marcin; Cairns, Hannah (Fall) Trudeau, Sidney; Macdonald, Jeremy; Mazakian, Hovsep (Winter) Mazakian, Hovsep; Abi Younes, Elio (Summer)
* 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.
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 2023, Winter 2024, Summer 2024
Instructors: M'hiri, Faten (Fall) M'hiri, Faten (Winter) Parekh, Deven (Summer)
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.
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 2023, Winter 2024
Instructors: Vybihal, Joseph P; Bérubé-Vallières, Mathieu (Fall) Vybihal, Joseph P; Errington, Jacob (Winter)
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 2023, Winter 2024
Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)
Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Terms: Fall 2023, Winter 2024
Instructors: Alberini, Giulia; Waldispuhl, Jérôme (Fall) Becerra, David (Winter)
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 2023, Winter 2024
Instructors: Elsaadawy, Mona (Fall) Vybihal, Joseph P (Winter)
3 hours
Corequisite: COMP 206.
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 2023, Winter 2024
Instructors: Errington, Jacob; Kopinsky, Max (Fall) Errington, Jacob (Winter)
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 2023, Winter 2024
Instructors: Maheswaran, Muthucumaru (Fall) Campbell, Jonathan (Winter)
3 hours
Prerequisite: COMP 273
Computer Science (Sci) : Finite automata, regular languages, context-free languages, push-down automata, models of computation, computability theory, undecidability, reduction techniques.
Terms: Fall 2023, Winter 2024
Instructors: Spinoso-Di Piano, Cesare; Crépeau, Claude (Fall) Crépeau, Claude; Dellas, John (Winter)
3 hours
Prerequisite: COMP 251.
Computer Science (Sci) : Advanced algorithm design and analysis. Linear programming, complexity and NP-completeness, advanced algorithmic techniques.
Terms: Fall 2023, Winter 2024
Instructors: Robere, Robert (Fall) Hatami, Hamed (Winter)
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 2023, Winter 2024, Summer 2024
Instructors: Sabok, Marcin; Allen, Patrick (Fall) Trudeau, Sidney (Winter) Bibby, Sean (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 2023
Instructors: Macdonald, Jeremy; Goren, Eyal Z (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 2024
Instructors: Macdonald, Jeremy (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 2023
Instructors: Hundemer, Axel W (Fall)
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2023, Winter 2024
Instructors: Hurtubise, Jacques Claude (Fall) Bélanger-Rioux, Rosalie (Winter)
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 2023
Instructors: Gantumur, Tsog (Fall)
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 2023
Instructors: Tserunyan, Anush (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 2023, Winter 2024, Summer 2024
Instructors: Sajjad, Alia; Nadarajah, Tharshanna (Fall) Sajjad, Alia; Nadarajah, Tharshanna (Winter) Kelome, Djivede (Summer)
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2024
Instructors: Norin, Sergey (Winter)
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.
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 2024
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.
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 2023
Instructors: Lee, Kiwon (Fall)
Prerequisite(s): MATH 133
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 2024
Instructors: Yang, Archer Yi (Winter)
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 2024
Instructors: Guan, Pengfei (Winter)
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2023, Winter 2024
Instructors: Nadarajah, Tharshanna (Fall) Russell, Oliver (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) : 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 2023
Instructors: Humphries, Tony (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: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2024
Instructors: Kelome, Djivede (Winter)
Winter
Prerequisite: MATH 141
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 2023
Instructors: Fortier, Jérôme (Fall)
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
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 2023
Instructors: Przytycki, Piotr (Fall)
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: Fall 2023
Instructors: Hoheisel, Tim (Fall)
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2023, Winter 2024, Summer 2024
Instructors: Przytycki, Piotr; Khadra, Anmar; Stephens, David; Steele, Russell; Miocevic, Milica; Choksi, Rustum; Dagdoug, Mohamed Mehdi; Asgharian, Masoud; Sajjad, Alia; Nadarajah, Tharshanna (Fall) Przytycki, Piotr; Nadarajah, Tharshanna; Khadra, Anmar; Steele, Russell (Winter) Correa, Jose Andres; Nadarajah, Tharshanna; Stephens, David; Jakobson, Dmitry (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) : 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 2023
Instructors: Hoheisel, Tim (Fall)
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 2023
Instructors: Nadarajah, Tharshanna (Fall)
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 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
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: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 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 2024
Instructors: Collins-Woodfin, Elizabeth (Winter)
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 2024
Instructors: Paquette, Courtney (Winter)
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: This course is not scheduled for the 2023-2024 academic year.
Instructors: There are no professors associated with this course for the 2023-2024 academic year.
9 credits selected from Computer Science courses at the 300 level or above (except COMP 364 and COMP 396) and ECSE 508.