Program Requirements
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.

MATH 133 Linear Algebra and Geometry (3 credits)
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; quadratic loci in two and three dimensions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jerome Fortier, Liangming Shen, Yann Batiste Pequignot, Damian Osajda (Fall) Jerome Fortier (Winter) Rebecca Patrias (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, MATH 130 or MATH 131, 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 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Sidney Trudeau, Jerome Fortier, Rebecca Patrias (Fall) Alexander Garver (Winter) Peter Zenz (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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Each Tutorial section is enrolment limited

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Corentin PerretGentilditMaillard, Jonah Gaster (Fall) Sidney Trudeau, Jerome Fortier, Thomas F Fox (Winter) Bogdan Nica (Summer)
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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Each Tutorial section is enrolment limited
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.

COMP 202 Foundations of Programming (3 credits) *
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 2018, Winter 2019, Summer 2019
Instructors: Giulia Alberini, Joseph P Vybihal (Fall) Giulia Alberini, TzuYang Yu (Winter) TzuYang Yu (Summer)
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 206 Introduction to Software Systems (3 credits)
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 2018, Winter 2019
Instructors: David Meger (Fall) Chad Zammar, Joseph P Vybihal (Winter)

COMP 250 Introduction to Computer Science (3 credits)
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 nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2018, Winter 2019
Instructors: Michael Langer, Giulia Alberini (Fall) Martin Robillard, Giulia Alberini (Winter)

COMP 251 Algorithms and Data Structures (3 credits)
Overview
Computer Science (Sci) : Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Terms: Fall 2018, Winter 2019
Instructors: Jérôme Waldispuhl (Fall) Luc P Devroye, Erin Leigh McLeish (Winter)
3 hours
Prerequisite: COMP 250
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 and 363, 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.

COMP 273 Introduction to Computer Systems (3 credits)
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 2018, Winter 2019
Instructors: Paul Kry (Fall) Kaleem Siddiqi (Winter)
3 hours
Corequisite: COMP 206.

COMP 302 Programming Languages and Paradigms (3 credits)
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 2018, Winter 2019
Instructors: Brigitte Pientka (Fall) Prakash Panangaden (Winter)
3 hours
Prerequisite: COMP 250

COMP 310 Operating Systems (3 credits)
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 2018, Winter 2019
Instructors: Muthucumaru Maheswaran (Fall) Joseph P Vybihal (Winter)
3 hours
Prerequisite: COMP 273

COMP 330 Theory of Computation (3 credits)
Overview
Computer Science (Sci) : Finite automata, regular languages, contextfree languages, pushdown automata, models of computation, computability theory, undecidability, reduction techniques.
Terms: Fall 2018
Instructors: Prakash Panangaden (Fall)
3 hours
Prerequisite: COMP 251.

COMP 360 Algorithm Design (3 credits)
Overview
Computer Science (Sci) : Advanced algorithm design and analysis. Linear programming, complexity and NPcompleteness, advanced algorithmic techniques.
Terms: Fall 2018, Winter 2019
Instructors: Bruce Alan Reed (Fall) Bruce Alan Reed (Winter)

MATH 222 Calculus 3 (3 credits)
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 2018, Winter 2019, Summer 2019
Instructors: Jeremy Macdonald, Dmitry Faifman (Fall) Lars Sektnan (Winter) Yann Batiste Pequignot (Summer)

MATH 235 Algebra 1 (3 credits)
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 2018
Instructors: Daniel Wise (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

MATH 236 Algebra 2 (3 credits)
Overview
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. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Terms: Winter 2019
Instructors: Bogdan Nica (Winter)
Winter
Prerequisite: MATH 235

MATH 242 Analysis 1 (3 credits)
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 2018
Instructors: Jerome Vetois (Fall)

MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: JeanChristophe Nave (Fall) Antony Raymond Humphries (Winter) Charles Roth (Summer)

MATH 317 Numerical Analysis (3 credits)
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: Fall 2018
Instructors: Peter Bartello (Fall)

MATH 318 Mathematical Logic (3 credits)
Overview
Mathematics & Statistics (Sci) : Propositional logic: truthtables, formal proof systems, completeness and compactness theorems, Boolean algebras; firstorder 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 2018
Instructors: Marcin Sabok (Fall)

MATH 323 Probability (3 credits)
Overview
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 2018, Winter 2019, Summer 2019
Instructors: David Stephens (Fall) David B Wolfson (Winter) Djivede Kelome (Summer)

MATH 340 Discrete Structures 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Terms: Winter 2019
Instructors: Jerome Fortier (Winter)
Complementary Courses (18 credits)
9 credits from the set of courses recommended for a major or honours program in Mathematics.
9 credits selected from Computer Science courses at the 300 level or above (except COMP 364 and COMP 396) and ECSE 508.