Bachelor of Science (B.Sc.) - Major Mathematics and Computer Science(72 Credits)
Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
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.
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MATH 133
Linear Algebra and Geometry
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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.
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Sidney Trudeau, Elizabeth W Collins-Woodfin, Romain Branchereau
- Mathilde Gerbelli-Gauthier
-
MATH 140
Calculus 1
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
- 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
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Jérôme Fortier, Dylan J Cant, Hao Fu
- Jérôme Fortier
-
MATH 141
Calculus 2
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
- 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
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Hannah A Cairns, Marcin Sroka
- Sidney Trudeau, Jeremy Macdonald, Hovsep Mazakian
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.
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COMP 202
Foundations of Programming
3 Credits*
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Computer Science
- 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.
- Terms
- Instructors
- Faten M'hiri
- Faten M'hiri
-
COMP 206
Intro to Software Systems
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Computer Science
- Terms
- Instructors
- Joseph P Vybihal, Mathieu Bérubé-Vallières
- Joseph P Vybihal, Jacob T Errington
-
COMP 250
Intro to Computer Science
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Computer Science
- 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.
- Terms
- Instructors
- Giulia Alberini
- Giulia Alberini
-
COMP 251
Algorithms and Data Structures
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Offered by: Computer Science
- 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.
- Terms
- Instructors
- Giulia Alberini, Jérôme Waldispuhl
- David C Becerra
-
COMP 273
Intro to Computer Systems
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining.
Offered by: Computer Science
- Terms
- Instructors
- Mona E Elsaadawy
- Joseph P Vybihal
-
COMP 302
Programming Lang & Paradigms
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Computer Science
- Terms
- Instructors
- Jacob T Errington, Max Kopinsky
- Jacob T Errington
-
COMP 310
Operating Systems
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Computer Science
- Terms
- Instructors
- Muthucumaru Maheswaran
- Oana Balmau, Jonathan C Campbell
-
COMP 330
Theory of Computation
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Finite automata, regular languages, context-free languages, push-down automata, models of computation, computability theory, undecidability, reduction techniques.
Offered by: Computer Science
- Terms
- Instructors
- Cesare Spinoso-Di Piano, Claude Crepeau
- Claude Crepeau
-
COMP 360
Algorithm Design
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Advanced algorithm design and analysis. Linear programming, complexity and NP-completeness, advanced algorithmic techniques.
Offered by: Computer Science
- Terms
- Instructors
- Robert Robere
- Hamed Hatami
-
MATH 222
Calculus 3
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Patrick Allen, Marcin Sabok
- Sidney Trudeau
-
MATH 235
Algebra 1
3 Credits
Offered in the:
- Fall
- Winter
- 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.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
- Terms
- Instructors
- Eyal Z Goren, Jeremy Macdonald
-
MATH 236
Algebra 2
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 242
Analysis 1
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
- Fall
- Prerequisite: MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 254.
-
MATH 315
Ordinary Differential Eqns
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Jacques Claude Hurtubise
- Rosalie Bélanger-Rioux
-
MATH 317
Numerical Analysis
3 Credits**
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics
-
MATH 318
Mathematical Logic
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 323
Probability
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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
- Terms
- Fall 2023
- Winter 2024
- Summer 2024
- Instructors
- Alia Sajjad, Tharshanna Nadarajah
- Alia Sajjad, Tharshanna Nadarajah
-
MATH 340
Discrete Mathematics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Offered by: Mathematics and Statistics
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 in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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
Intro to Statistical Computing
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 308
Fundls of Statistical Learning
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 319
Partial Differential Equations
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 324
Statistics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
- 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.
- Terms
- Instructors
- Tharshanna Nadarajah
- Oliver Russell
-
MATH 326
Nonlinear Dynamics and Chaos
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 327
Matrix Numerical Analysis
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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
-
MATH 329
Theory of Interest
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
-
MATH 338
History & Philosophy of Math
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 346
Number Theory
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Offered by: Mathematics and Statistics
- Winter
- Prerequisite: MATH 235 or consent of instructor
- Restriction: Not open to students who have taken or are taking MATH 377.
- 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
-
MATH 348
Euclidean Geometry
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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 in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 410
Majors Project
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
- 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.
- Terms
- Instructors
- Russell Steele, Masoud Asgharian, Mohamed Mehdi Dagdoug, David A Stephens, Milica Miocevic, Anmar Khadra, Rustum Choksi, Piotr Przytycki, Alia Sajjad, Tharshanna Nadarajah
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MATH 417
Linear Optimization
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 423
Applied Regression
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 427
Statistical Quality Control
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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
-
MATH 430
Mathematical Finance
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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
-
MATH 447
Intro. to Stochastic Processes
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- Winter
- Prerequisite: MATH 323
- Restriction: Not open to students who have taken or are taking MATH 547.
- Terms
- Instructors
- Elizabeth W Collins-Woodfin
-
MATH 463
Convex Optimization
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
-
MATH 478
Comput. Meth. in Applied Math
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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
Offered by: Mathematics and Statistics
- 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.