Mathematics and Computer Science (Faculty of Arts)
The Joint Honours in Mathematics and Computer Science is available to students enrolled in both the Faculty of Arts and the Faculty of Science.
Note: Students entering a Mathematics program are normally expected to have completed MATH 133; MATH 139 or MATH 140; MATH 141; or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the program credits. If you are interested in the program, you must consult Honours adviser in both departments. For details, consult the program outline below.
DETAILED PROGRAM OUTLINE:
Program Requirement:
Students may complete this program with a minimum of 72 credits or a maximum of 78 credits depending if they are exempt from COMP 202/204/208 and/or MATH 222.
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
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2020
 Winter 2021
 Instructors
 Rosalie BélangerRioux, Piotr Przytycki
 Djivede A Kelome

MATH 150 Calculus A 4 Credits
 Fall
 Winter
 Summer
Offered in the: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: Not open to students who have taken CEGEP objective 00UN 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
 MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
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 Fall 2020
 Instructors
 Charles Roth

MATH 151 Calculus B 4 Credits
 Fall
 Winter
 Summer
Offered in the: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: Not open to students who have taken CEGEP objective 00UP 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
 Restriction: Not open to students who have taken MATH 152
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 Winter 2021
 Instructors
 Charles Roth
In particular, MATH 150/151 and MATH 140/141/222 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
(3639 credits)
* Students who have successfully completed MATH 150/151 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
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2020
 Winter 2021
 Instructors
 Joseph V D'silva
 Joseph V D'silva

COMP 250 Intro to Computer Science 3 Credits
 Fall
 Winter
 Summer
Offered in the: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 nonrecursive 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.
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 Fall 2020
 Winter 2021
 Instructors
 Giulia Alberini
 Giulia Alberini

COMP 252 Honours Algorithms&Data Struct 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Winter 2021
 Instructors
 Claude Crepeau

COMP 273 Intro to Computer Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 3 hours
 Corequisite: COMP 206.
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 Fall 2020
 Winter 2021
 Instructors
 Kaleem Siddiqi
 Paul Kry, HsiuChin Lin

COMP 302 Programming Lang & Paradigms 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2020
 Winter 2021
 Instructors
 Brigitte Pientka

COMP 310 Operating Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 3 hours
 Prerequisite: COMP 273
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 Fall 2020
 Winter 2021
 Instructors
 Muthucumaru Maheswaran
 Joseph P Vybihal

COMP 330 Theory of Computation 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Finite automata, regular languages, contextfree languages, pushdown automata, models of computation, computability theory, undecidability, reduction techniques.
Offered by: Computer Science
 3 hours
 Prerequisite: COMP 251.
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 Fall 2020
 Winter 2021
 Instructors
 Hamed Hatami
 Prakash Panangaden

COMP 362 Honours Algorithm Design 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Winter 2021
 Instructors
 Bruce Alan Reed

MATH 222 Calculus 3 3 Credits*
 Fall
 Winter
 Summer
Offered in the: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
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Djivede A Kelome, Jérôme Fortier
 Jerome Vetois

MATH 235 Algebra 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2020
 Instructors
 Daniel T Wise

MATH 251 Honours Algebra 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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 selfadjoint 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
 Symbols:
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 Winter 2021
 Instructors
 Michael Lipnowski

MATH 255 Honours Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, 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
 Symbols:
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 Winter 2021
 Instructors
 Vojkan Jaksic

MATH 350 Honours Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2020
 Instructors
 Sergey Norin
Complementary Courses
3639 credits
03 credits selected from:

COMP 202 Foundations of Programming 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250
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 Fall 2020
 Winter 2021
 Instructors
 Giulia Alberini
 Giulia Alberini

COMP 204 Comp. Programming for Life Sci 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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
 Prerequisite(s): BIOL 112. CEGEP level mathematics course.
 Restriction(s): Only one of COMP 204, COMP 202 and COMP 208 can be taken for credit.
 COMP 204 cannot be taken for credit with or after COMP 250, COMP 206, COMP 208, or COMP 364.
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 Fall 2020
 Winter 2021
 Instructors
 Mathieu Blanchette
 Yue Li

COMP 208 Computer Programming for PS&E 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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
 Prerequisite: MATH 141 or equivalent.
 Corequisite: MATH 133 or equivalent.
 Restrictions: Credit can be given only for one of COMP 202, COMP 204, or COMP 208. COMP 208 cannot be taken for credit with or after COMP 250 or COMP 206.
 COMP 202 is intended as a general introductory course, while COMP 208 is intended for students with sufficient math background and in (nonlife) science or engineering fields.
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 Fall 2020
 Winter 2021
 Instructors
 Joseph P Vybihal
** Students who have sufficient knowledge of computer programming are not required to take COMP 202/204/208.
3 credits selected from:

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2020
 Instructors
 Axel W Hundemer

MATH 254 Honours Analysis 1 3 Credits***
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2020
 Instructors
 Vojkan Jaksic
*** It is strongly recommended that students take MATH 254.
3 credits selected from:

MATH 248 Honours Vector Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2020
 Instructors
 Pengfei Guan

MATH 358 Honours Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Pointset 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’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 222, MATH 247 or MATH 251, MATH 255 or permission of the Department.
 Restrictions: Intended for students in Honours Mathematics programs, Not open to students who have taken or are taking MATH 314 or MATH 248
 Symbols:
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 Winter 2021
 Instructors
 Pengfei Guan
18 credits in Mathematics, at least 12 credits selected from:
+ Not open to students who have taken MATH 354.

MATH 356 Honours Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the: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, univariate 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
 Symbols:
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 Fall 2020
 Instructors
 Linan Chen

MATH 387 Honours Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 454 Honours Analysis 3 3 Credits+
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. FubiniTonelli theorem.
Offered by: Mathematics and Statistics
 Symbols:
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 Fall 2020
 Instructors
 Jerome Vetois

MATH 455 Honours Analysis 4 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Dmitry Jakobson

MATH 456 Honours Algebra 3 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 and either (MATH 247 or MATH 251).
 Restriction: Not open to students who have taken MATH 370.
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 Fall 2020
 Instructors
 Eyal Z Goren

MATH 457 Honours Algebra 4 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Michael Y Pichot