Program Requirements
This is a challenging program providing students with a solid training in both computer science and statistics suitable for entry into graduate school in either discipline.
Students may complete this program with a minimum of 76 credits or a maximum of 79 credits depending on whether or not they are exempt from taking COMP 202.
Program Prerequisites
Students entering the Joint Honours in Statistics 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 7679 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 2014, Winter 2015
Instructors: Djivede Kelome, Michael Brandenbursky, Christopher Cornwell, Sidney Trudeau (Fall) Djivede Kelome (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 2014, Winter 2015
Instructors: Axel W Hundemer, Stephen W Drury, Ronan Conlon (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 2014, Winter 2015
Instructors: Thomas F Fox (Fall) Axel W Hundemer (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 (49 credits)
* Students who have sufficient knowledge in a programming language are not required to take COMP 202.
** Students take either MATH 251 or MATH 247, but not both.

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 2014, Winter 2015
Instructors: Melanie LymanAbramovitch, Jonathan Tremblay (Fall) Jonathan Tremblay, Bentley Oakes (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 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 2014, Winter 2015
Instructors: Joseph P Vybihal (Fall) Joseph P Vybihal (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 2014, Winter 2015
Instructors: Mathieu Blanchette, Jérôme Waldispuhl, Hamed Hatami (Fall) Martin Robillard (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 2015
Instructors: Luc P Devroye (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 2014, Winter 2015
Instructors: Joseph P Vybihal (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 2014, Winter 2015
Instructors: Brigitte Pientka (Fall) Nathan Friedman (Winter)
 3 hours
 Prerequisite: COMP 250

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 2014
Instructors: Prakash Panangaden (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 2015
Instructors: Hamed Hatami (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 2014
Instructors: Payman L Kassaei (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 2014
Instructors: Axel W Hundemer (Fall)
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.

MATH 247 Honours Applied Linear Algebra (3 credits) **
Overview
Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Terms: Winter 2015
Instructors: Piotr Przytycki (Winter)
 Winter
 Prerequisite: MATH 133 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251

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 2014
Instructors: Pengfei Guan (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 2015
Instructors: Piotr Przytycki (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) : 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.
Terms: Winter 2015
Instructors: Vojkan Jaksic (Winter)
 Winter
 Prerequisites: MATH 242 or MATH 254 or permission of the Department

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 2014
Instructors: Abbas Khalili Mahmoudabadi (Fall)
 Fall
 Prerequisite(s): MATH 133 or MATH 134, and MATH 222 or permisson of the Department.
 Corequisite(s): MATH 242 or MATH 254

MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chisquared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2015
Instructors: David B Wolfson (Winter)
 Winter
 Prerequisite: MATH 356 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 324

MATH 533 Honours Regression and Analysis of Variance (4 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 423 but will be assessed at the 500 level.
Terms: Fall 2014
Instructors: David Stephens (Fall)
 Prerequisites: MATH 357, MATH 247 or MATH 251.
 Restriction: Not open to have taken or are taking MATH 423.
 Note: An additional project or projects assigned by the instructor that require a more detailed treatment of the major results and concepts covered in MATH 423.
Complementary Courses (30 credits)
15 credits in Mathematics selected as follows:
3 credits selected from:

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 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 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 397 Honours Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 327 plus additional work involving theoretical assignments and/or a project. The final examination for this course may be different from that of MATH 327.
Terms: Winter 2015
Instructors: Antony Raymond Humphries (Winter)
 Winter
 Prerequisites: MATH 251 or MATH 247, COMP 202 or permission of the instructor.
At least 8 credits selected from:

MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Terms: Winter 2015
Instructors: Russell Steele (Winter)
 Winter
 Prerequisite: MATH 423
 Restriction: Not open to students who have taken MATH 426

MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Terms: Fall 2014
Instructors: Christian Genest (Fall)
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424

MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425

MATH 556 Mathematical Statistics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Terms: Fall 2014
Instructors: David Stephens (Fall)
 Fall
 Prerequisite: MATH 357 or equivalent

MATH 557 Mathematical Statistics 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Terms: Winter 2015
Instructors: Abbas Khalili Mahmoudabadi (Winter)
 Winter
 Prerequisite: MATH 556
Revision, June 2014. Start of revision.
The remaining Mathematics credits selected from:
** MATH 578 and COMP 540 cannot both be taken for program credit.

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 2014
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.

MATH 352 Problem Seminar (1 credit)
Overview
Mathematics & Statistics (Sci) : Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Terms: Fall 2014
Instructors: Sergey Norin (Fall)
 Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
 Prerequisite: Enrolment in a math related program or permission of the instructor.

MATH 354 Honours Analysis 3 (3 credits)
Overview
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.
Terms: Fall 2014
Instructors: Stephen W Drury (Fall)
 Fall
 Prerequisite: MATH 255 or equivalent

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: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 Prerequisite: MATH 324 or MATH 357 or equivalent

MATH 578 Numerical Analysis 1 (4 credits) **
Overview
Mathematics & Statistics (Sci) : Development, analysis and effective use of numerical methods to solve problems arising in applications. Topics include direct and iterative methods for the solution of linear equations (including preconditioning), eigenvalue problems, interpolation, approximation, quadrature, solution of nonlinear systems.
Terms: Fall 2014
Instructors: JeanChristophe Nave (Fall)
 Fall
 Prerequisites: MATH 247 or MATH 251; and MATH 387; or permission of the instructor.

MATH 587 Advanced Probability Theory 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.
Terms: Fall 2014
Instructors: Linan Chen (Fall)
 Fall
 Prerequisite(s): MATH 356 and MATH 255 or MATH 243 or equivalent.
Revision, June 2014. End of revision.
15 credits in Computer Science selected as follows:
At least 6 credits selected from:

COMP 424 Artificial Intelligence (3 credits)
Overview
Computer Science (Sci) : Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning.
Terms: Winter 2015
Instructors: Joelle Pineau (Winter)
 3 hours
 Prerequisites: (COMP 206 or ECSE 321) and COMP 251

COMP 462 Computational Biology Methods (3 credits)
Overview
Computer Science (Sci) : Application of computer science techniques to problems arising in biology and medicine, techniques for modeling evolution, aligning molecular sequences, predicting structure of a molecule and other problems from computational biology.
Terms: Fall 2014
Instructors: Mathieu Blanchette (Fall)
 3 hours
 Prerequisites: COMP 251, and MATH 323 or MATH 203 or BIOL 309
 Restriction: Not open to students who have taken COMP 562. Not open to students who are taking or have taken COMP 561.

COMP 526 Probabilistic Reasoning and AI (3 credits)
Overview
Computer Science (Sci) : Belief networks, Utility theory, Markov Decision Processes and Learning Algorithms.
Terms: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 3 hours
 Prerequisites: COMP 206, COMP 360, COMP 424 and MATH 323

COMP 540 Matrix Computations (3 credits) **
Overview
Computer Science (Sci) : Designing and programming reliable numerical algorithms. Stability of algorithms and condition of problems. Reliable and efficient algorithms for solution of equations, linear least squares problems, the singular value decomposition, the eigenproblem and related problems. Perturbation analysis of problems. Algorithms for structured matrices.
Terms: Fall 2014
Instructors: XiaoWen Chang (Fall)
 3 hours
 Prerequisite: MATH 327 or COMP 350

COMP 547 Cryptography and Data Security (4 credits)
Overview
Computer Science (Sci) : This course presents an indepth study of modern cryptography and data security. The basic information theoretic and computational properties of classical and modern cryptographic systems are presented, followed by a cryptanalytic examination of several important systems. We will study the applications of cryptography to the security of systems.
Terms: Winter 2015
Instructors: Claude Crepeau (Winter)
 3 hours
 Prerequisites: COMP 360 or COMP 362, MATH 323.

COMP 552 Combinatorial Optimization (4 credits)
Overview
Computer Science (Sci) : Algorithmic and structural approaches in combinatorial optimization with a focus upon theory and applications. Topics include: polyhedral methods, network optimization, the ellipsoid method, graph algorithms, matroid theory and submodular functions.
Terms: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 4 hours
 Prerequisite: Math 350 or COMP 362 (or equivalent).
 Restriction: This course is reserved for undergraduate honours students and graduate students. Not open to students who have taken or are taking MATH 552.

COMP 564 Computational Gene Regulation (3 credits)
Overview
Computer Science (Sci) : This course examines computational problems related to gene regulation at the mRNA and protein levels. With respect to mRNA expression, topics include microarray analysis, SNP detection, and the inference of genetic networks. With respect to protein expression, topics include peptide sequencing, peptide identification, and the interpretation of interaction maps.
Terms: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 3 hours
 Prerequisite: COMP 462.

COMP 566 Discrete Optimization 1 (3 credits)
Overview
Computer Science (Sci) : Use of computer in solving problems in discrete optimization. Linear programming and extensions. Network simplex method. Applications of linear programming. Vertex enumeration. Geometry of linear programming. Implementation issues and robustness. Students will do a project on an application of their choice.
Terms: Fall 2014
Instructors: Jacques Ferland (Fall)
 3 hours
 Prerequisites: COMP 360 and MATH 223

COMP 567 Discrete Optimization 2 (3 credits)
Overview
Computer Science (Sci) : Formulation, solution and applications of integer programs. Branch and bound, cutting plane, and column generation algorithms. Combinatorial optimization. Polyhedral methods. A large emphasis will be placed on modelling. Students will select and present a case study of an application of integer programming in an area of their choice.
Terms: This course is not scheduled for the 20142015 academic year.
Instructors: There are no professors associated with this course for the 20142015 academic year.
 3 hours
 Prerequisites: COMP 566 or MATH 417
The remaining Computer Science credits are selected from COMP courses at the 300 level or above excluding COMP 396 and COMP 431.