Program Requirements
Revision, August 2012. Start of revision.
Students may complete this program with a minimum of 72 credits or a maximum of 75 credits depending on whether or not they are exempt from taking COMP 202.
Program Prerequisites
Students must consult an Honours adviser in both departments. Students entering the Joint Honours 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 7275 credits of courses in the program.

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 2012, Winter 2013, Summer 2013
Instructors: Djivede Kelome, William J Anderson, Eric Cormier, Michael Bailey (Fall) William J Anderson, Alexey Eremin (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, 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 2012, Winter 2013, Summer 2013
Instructors: Sidney Trudeau, Stephen W Drury, William G Brown, Thomas F Fox (Fall)
 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 2012, Winter 2013, Summer 2013
Instructors: Antonio Lei (Fall) Sidney Trudeau, Stephen W Drury, Thomas F Fox (Winter)
 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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
 Each Tutorial section is enrolment limited
Required Courses (45 credits)
* Students who have sufficient knowledge in a programming language are not required to take COMP 202.

COMP 202 Foundations of Programming (3 credits) *
Overview
Computer Science (Sci) : Introduction to programming in a modern highlevel language, modular software design and debugging. Programming concepts are illustrated using a variety of application areas.
Terms: Fall 2012, Winter 2013, Summer 2013
Instructors: Daniel Pomerantz, Xue Liu, Ioannis Rekleitis (Fall) Jorg Andreas Kienzle, Daniel Pomerantz (Winter) Daniel Pomerantz (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 2012, Winter 2013
Instructors: Joseph P Vybihal, Gregory L Dudek (Fall) Wenbo He, Gregory L Dudek (Winter)
 3 hours
 Prerequisite: COMP 202 or COMP 250

COMP 250 Introduction to Computer Science (3 credits)
Overview
Computer Science (Sci) : An introduction to the design of computer algorithms, including basic data structures, analysis of algorithms, and establishing correctness of programs. Overview of topics in computer science.
Terms: Fall 2012, Winter 2013
Instructors: Michael Langer (Fall) Mathieu Blanchette (Winter)
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Restrictions: COMP 203 and COMP 250 are considered to be equivalent from a prerequisite point of view, and cannot both be taken for credit.

COMP 252 Honours Algorithms and Data Structures (3 credits)
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 2013
Instructors: Patrick Hayden (Winter)
 3 hours
 Prerequisite: COMP 250 and MATH 240
 Restrictions: Open only to students registered in following programs: Honours in Computer Science, Joint Honours in Mathematics and Computer Science, Honours in Applied Mathematics, Honours in Mathematics. Not open to students who have taken or are taking COMP 251.
 Note: COMP 252 can be used instead of COMP 251 to satisfy prerequisites.

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 2012, Winter 2013
Instructors: Joseph P Vybihal, Xue Liu (Fall) Joseph P Vybihal (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 2012, Winter 2013
Instructors: Brigitte Pientka (Fall)
 3 hours
 Prerequisite: COMP 250 or COMP 203

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 2012, Winter 2013
Instructors: Xue Liu (Fall) Muthucumaru Maheswaran (Winter)
 3 hours
 Prerequisite: COMP 273

COMP 330 Theory of Computation (3 credits)
Overview
Computer Science (Sci) : Mathematical models of computers, finite automata, Turing machines, counter machines, pushdown machines, computational complexity.
Terms: Fall 2012
Instructors: Claude Crepeau (Fall)
 3 hours
 Prerequisite: COMP 251.

COMP 362 Honours Algorithm Design (3 credits)
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 2013
Instructors: Bruce Alan Reed (Winter)
 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 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 2012
Instructors: Henri Darmon (Fall)
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent

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 2012
Instructors: Suresh Eswarathasan, Ivo Klemes (Fall)
 Fall
 Prerequisite: MATH 141

MATH 248 Honours Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2012
Instructors: Axel W Hundemer (Fall)
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Mathematics, Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 314

MATH 251 Honours Algebra 2 (3 credits)
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 selfadjoint operators.
Terms: Winter 2013
Instructors: Jessica Banks (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)
Overview
Mathematics & Statistics (Sci) : Series of functions including power series. Riemann integration in one variable. Elementary functions.
Terms: Winter 2013
Instructors: Sidney Trudeau (Winter)
 Winter
 Prerequisites: MATH 242 or permission of the Department

MATH 350 Graph Theory and Combinatorics (3 credits)
Overview
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Fall 2012
Instructors: Sergey Norin (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 343 or MATH 340.
 Intended for students in mathematics or computer science honours programs.
Complementary Courses (30 credits)
18 credits in Mathematics, at least 12 credits selected from:
* Students with appropriate background in probability may substitute MATH 587 for MATH 356 and must then also register for MATH 355.

MATH 354 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.
Terms: Fall 2012
Instructors: Dmitry Jakobson (Fall)
 Fall
 Prerequisite: MATH 255 or equivalent

MATH 355 Honours Analysis 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces, L_2 spaces, Fourier series. Fourier integrals (if time allows).
Terms: Winter 2013
Instructors: John A Toth (Winter)
 Winter
 Prerequisite: MATH 354 or equivalent.

MATH 356 Honours Probability (3 credits) *
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, univariate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2012
Instructors: Abbas Khalili Mahmoudabadi (Fall)
 Fall
 Prerequisite: MATH 255 or MATH 243
 Restriction: Not open to students who have taken or are taking MATH 323

MATH 370 Honours Algebra 3 (3 credits)
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 2012
Instructors: Michael Pichot (Fall)
 Fall
 Prerequisite: MATH 251

MATH 371 Honours Algebra 4 (3 credits)
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 2013
Instructors: Michael Pichot (Winter)
 Winter
 Prerequisite: MATH 370

MATH 387 Honours 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: This course is not scheduled for the 20122013 academic year.
Instructors: There are no professors associated with this course for the 20122013 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 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: Fall 2012
Instructors: David Stephens (Fall)
 Prerequisite: MATH 324 or MATH 357 or equivalent
The remaining credits should be selected from honours 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, COMP 396 and COMP 431. ECSE 508 may also be taken.
Revision, August 2012. End of revision.