Bachelor of Science (B.Sc.) - Honours Mathematics and Computer Science(78 Credits)
Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
The B.Sc.; Honours in Mathematics and Computer Science provides a rigorous training, at the honours level, in mathematics and computer science, while exploring the interaction between the two fields. This program may be completed with a minimum of 72 credits or a maximum of 78 credits.
Program Prerequisites
Students must consult an Honours adviser in both departments to ensure that they have sufficient background to enter the program. The minimum requirements are the following courses or their equivalencies:
-
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(s): 1) Not open to students who have taken CEGEP objective 00UQ or equivalent. 2) Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
- Terms
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Jeremy Macdonald, Antoine Giard, Miguel Ayala, Romain Branchereau
- Th茅o Pinet
-
MATH 150
Calculus A
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture, 2 hours tutorial
- Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
- Restriction(s): 1) Not open to students who have taken or are taking MATH 139 or MATH 140 or CEGEP objective 00UN or equivalent. 2) Not open to students who have taken or are taking MATH 122,except by permission of the Department of Mathematics and Statistics.
- MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
-
MATH 151
Calculus B
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Offered by: Mathematics and Statistics
- Winter
- 3 hours lecture; 2 hours tutorial
- Each Tutorial section is enrolment limited
- Prerequisite: MATH 150
- Restriction(s): 1) Not open to students who have taken or are taking MATH 141 or CEGEP objective 00UP or equivalent. 2) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematic sand Statistics.
In particular, MATH 150/MATH151 and MATH 140/MATH 141/MATH 222 are considered equivalent.
To be awarded the Honours degree, the student must have, at time of graduation, a CGPA of at least 3.00 in the required and complementary Mathematics courses of the program, as well as an overall CGPA of at least 3.00.
Required Courses
(33-36 credits)
* Students who have successfully completed MATH 150/MATH 151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.
-
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
- Jacob T Errington
- Joseph P Vybihal, Max Kopinsky
-
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). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.
Offered by: Computer Science
- Terms
- Instructors
- Giulia Alberini
- Giulia Alberini
-
COMP 252
Honours Algorithms&Data Struct
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): The design and analysis of data structures and algorithms. The description of various computational problems and the algorithms that can be used to solve them, along with their associated data structures. Proving the correctness of algorithms and determining their computational complexity.
Offered by: Computer Science
- 3 hours
- Prerequisite: COMP 250 and either MATH 235 or MATH 240
- Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
- COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.
-
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
- Paul Kry
-
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
- Brigitte Pientka
- 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
- Max Kopinsky
- Max Kopinsky
-
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
- J茅r么me Waldispuhl
- Mathieu B茅rub茅-Valli猫res
-
COMP 362
Honours Algorithm Design
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.
Offered by: Computer Science
- 3 hours
- Prerequisite: COMP 252
- Restriction: Not open to students who have taken or are taking COMP 360.
- Note: COMP 362 can be used instead of COMP 360 to satisfy prerequisites.
- 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 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 2024
- Winter 2025
- Summer 2025
- Instructors
- Brent Pym, Damien Tageddine
- Hovsep Mazakian
-
MATH 251
Honours Algebra 2
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and
quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.
Offered by: Mathematics and Statistics
- Winter
- Prerequisites: MATH 235 or permission of the Department
- Restriction: Not open to students who are taking or have taken MATH 247
-
MATH 255
Honours Analysis 2
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, H脙露lder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Offered by: Mathematics and Statistics
-
MATH 350
Honours Discrete Mathematics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Offered by: Mathematics and Statistics
- Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
- Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.
- Intended for students in mathematics or computer science honours programs.
Complementary Courses
39-42 credits
0-3 credits selected from:
-
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
- 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.
- To take COMP 202, students should have a solid understanding of pre-calculus fundamentals such as polynomial, trigonometric, exponential, and logarithmic functions.
- Terms
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Faten M'hiri
- Faten M'hiri
-
COMP 204
Comp. Programming for Life Sci
3 Credits**
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Computer Science (Sci): Computer programming in a high level language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms, modular software design, libraries, file input/output, debugging. Emphasis on applications in the life sciences.
Offered by: Computer Science
- Co-requisite: BIOL 112
- Restrictions: Not open to students who have taken or are taking COMP 202, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
- To take COMP 204, students should have a solid understanding of pre-calculus fundamentals such as polynomial, trigonometric, exponential, and logarithmic functions.
- Terms
- Instructors
- David C Becerra
- Kaleem Siddiqi
-
COMP 208
Computer Programming for PS&E
3 Credits**
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Programming and problem solving in a high level computer language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms such as searching and sorting. Modular software design, libraries, file input and output, debugging. Emphasis on applications in Physical Sciences
and Engineering, such as root finding, numerical integration, diffusion, Monte Carlo methods.
Offered by: Computer Science
- 3 hours
- Corequisite: MATH 133 and MATH 141, or equivalents.
- Restrictions: Not open to students who have taken or are taking COMP 202, COMP 204, orGEOG 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 208 is intended for students with sufficient math background and in (non-life) science or engineering fields.
- Terms
- Instructors
- Michael Langer, Isabeau Pr茅mont-Schwarz
- Chad Zammar, Isabeau Pr茅mont-Schwarz
** Students who have sufficient knowledge of computer programming are not required to take COMP 202/COMP 204/COMP 208.
3 credits selected from:
-
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 254
Honours Analysis 1
3 Credits***
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Offered by: Mathematics and Statistics
- Prerequisite(s): MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 242.
3 credits selected from:
-
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; homomorphisms and quotient groups.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 245.
-
MATH 245
Honours Algebra 1
3 Credits***
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Honours level: Sets, functions, and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. In-depth study of rings, ideals, and quotient rings; fields and construction of fields from polynomial rings; groups, subgroups, and cosets, homomorphisms, and quotient groups.
Offered by: Mathematics and Statistics
- Prerequisites: Prerequisites: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 235.
*** It is strongly recommended that students take both MATH 245 and MATH 254.
3 credits selected from:
-
MATH 248
Honours Vector Calculus
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Partial derivatives and differentiation of functions in several variables; Jacobians;
maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Offered by: Mathematics and Statistics
- Fall and Winter and Summer
- Prerequisites: MATH 133 and MATH 222 or consent of Department.
- Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
- Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
-
MATH 358
Honours Advanced Calculus
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini鈥檚 theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes鈥� theorem and the divergence theorem.
Offered by: Mathematics and Statistics
9-18 credits selected from:
+ Not open to students who have taken MATH 354.
-
MATH 356
Honours Probability
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Offered by: Mathematics and Statistics
- Fall
- Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.
- Restriction: Not open to students who have taken or are taking MATH 323
-
MATH 357
Honours Statistics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sampling distributions. Point estimation. Minimum variance unbiased estimators,
sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.
Offered by: Mathematics and Statistics
- Winter
- Prerequisite: MATH 356 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 324
-
MATH 387
Honours 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
- Taught in alternate years
- Winter (even years)
- Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.
- Corequisites: MATH 255 or MATH 243.
- Restriction: Intended primarily for Honours students.
- 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 454
Honours Analysis 3
3 Credits+
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov鈥檚 theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.
Offered by: Mathematics and Statistics
- Prerequisite(s): MATH 255
- Restriction: Not open to students who have taken MATH 354.
-
MATH 455
Honours Analysis 4
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval鈥檚 identity, Poisson summation formula.
Offered by: Mathematics and Statistics
- Prerequisite: MATH 454 or equivalent.
- Restriction(s): Not open to students who have taken MATH 355.
-
MATH 456
Honours Algebra 3
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Groups, quotient groups and the isomorphism theorems. Group actions. Groups of prime order and the class equation. Sylow's theorems. Simplicity of the alternating group. Semidirect products. Principal ideal domains and unique factorization domains. Modules over a ring. Finitely generated modules over a principal ideal domain with applications to canonical forms.
Offered by: Mathematics and Statistics
-
MATH 457
Honours Algebra 4
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Representations of finite groups. Maschke's theorem. Schur's lemma. Characters, their orthogonality, and character tables. Field extensions. Finite and cyclotomic fields. Galois extensions and Galois groups. The fundamental theorem of Galois theory. Solvability by radicals.
Offered by: Mathematics and Statistics
0-9 credits should be selected from honours courses and 500-level courses given by the Department of Mathematics and Statistics.
12 credits in Computer Science, selected from Computer Science courses at the 300 level or above excluding COMP 364 and COMP 396. ECSE 508 may also be taken.