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Honours Mathematics and Computer Science (78 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

Program Requirements

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, COMP 204, COMP 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)

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 2021, Winter 2022

Instructors: Bélanger-Rioux, Rosalie; Bibby, Sean; Chinis, Jake (Fall) Fortier, Jérôme (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 150 Calculus A (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.

Terms: Fall 2021

Instructors: Roth, Charles (Fall)

• 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

• MATH 151 Calculus B (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.

Terms: Winter 2022

Instructors: Roth, Charles (Winter)

• 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

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

(36-39 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 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 2021, Winter 2022

Instructors: D'silva, Joseph (Fall) D'silva, Joseph (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 2021, Winter 2022

Instructors: Langer, Michael (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 252 Honours Algorithms and Data Structures (3 credits)

Offered by: Computer Science (Faculty of Science)

Overview

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.

Terms: Winter 2022

Instructors: Devroye, Luc P (Winter)

• 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 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 2021, Winter 2022

Instructors: Vybihal, Joseph P; Lin, Hsiu-Chin (Fall) Siddiqi, Kaleem (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 2021, Winter 2022

Instructors: Pientka, Brigitte (Fall) Si, Xujie (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 2021, Winter 2022

Instructors: Maheswaran, Muthucumaru (Fall) Balmau, Oana (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 2021, Winter 2022

Instructors: Panangaden, Prakash (Fall) Crepeau, Claude (Winter)

• COMP 362 Honours Algorithm Design (3 credits)

Offered by: Computer Science (Faculty of Science)

Overview

Computer Science (Sci) : Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.

Terms: Winter 2022

• 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.

• 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 2021, Winter 2022

Instructors: Allen, Patrick; Lumley, Allysa (Fall) Trudeau, Sidney (Winter)

• 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 2021

Instructors: Wise, Daniel (Fall)

• Fall

• 3 hours lecture; 1 hour tutorial

• Prerequisite: MATH 133 or equivalent

• MATH 251 Honours 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 maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.

Terms: Winter 2022

Instructors: Lipnowski, Michael (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶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.

Terms: Winter 2022

Instructors: Jakobson, Dmitry (Winter)

• MATH 350 Honours Discrete Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Fall 2021

Instructors: Norin, Sergey (Fall)

• 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

36-39 credits

0-3 credits selected from:

• 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 2021, Winter 2022

Instructors: Campbell, Jonathan (Fall) Patitsas, Elizabeth (Winter)

• 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

• COMP 204 Computer Programming for Life Sciences (3 credits) **

Offered by: Computer Science (Faculty of Science)

Overview

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.

Terms: Fall 2021, Winter 2022

Instructors: Becerra, David (Fall) Li, Yue (Winter)

• COMP 208 Computer Programming for Physical Sciences and Engineering (3 credits) **

Offered by: Computer Science (Faculty of Science)

Overview

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.

Terms: Fall 2021, Winter 2022

Instructors: Parekh, Deven (Fall) Vybihal, Joseph P (Winter)

• 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 (non-life) science or engineering fields.

** 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 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 2021

Instructors: Hundemer, Axel W (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Fall 2021

Instructors: Jaksic, Vojkan (Fall)

• Prerequisite(s): MATH 141

• Restriction(s): Not open to students who are taking or who have taken MATH 242.

*** It is strongly recommended that students take MATH 254.

3 credits selected from:

• MATH 248 Honours Vector Calculus (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Fall 2021

Instructors: Guan, Pengfei (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

Overview

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’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.

Terms: Winter 2022

Instructors: Guan, Pengfei (Winter)

18 credits in Mathematics, at least 9 credits selected from:

+ Not open to students who have taken MATH 354.

• MATH 356 Honours Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Fall 2021

Instructors: Paquette, Elliot (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.

Terms: Winter 2022

Instructors: Neslehova, Johanna (Winter)

• 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 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: Winter 2022

Instructors: There are no professors associated with this course for the 2021-2022 academic year.

• 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.

• MATH 454 Honours Analysis 3 (3 credits) +

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, 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. Fubini-Tonelli theorem.

Terms: Fall 2021

Instructors: Tosatti, Valentino (Fall)

• Prerequisite: MATH 255 or equivalent.

• Restriction: Not open to students who have taken MATH 354.

• MATH 455 Honours Analysis 4 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.

Terms: Winter 2022

Instructors: Vetois, Jerome (Winter)

• Prerequisite: MATH 454 or equivalent.

• Restriction(s): Not open to students who have taken MATH 355.

• MATH 456 Honours Algebra 3 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Fall 2021

Instructors: Goren, Eyal Z (Fall)

• MATH 457 Honours Algebra 4 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

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.

Terms: Winter 2022

Instructors: Pichot, Michael (Winter)

• Prerequisite: MATH 456 or equivalent

• Restriction(s): Not open to students who have taken MATH 371.

The remaining 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.

Faculty of Science—2021-2022 (last updated Apr. 7, 2021) (disclaimer)