Program Requirements
This program provides students with a solid training in both computer science and statistics together with the necessary mathematical background. As statistical endeavours involve ever increasing amounts of data, some students may want training in both disciplines.
Program Prerequisites
Students entering the Joint Major 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 72 credits of required courses.

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 2015, Winter 2016
Instructors: Djivede Kelome, William J Anderson (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 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 (51 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.
** Students take either COMP 350 or MATH 317, but not both.
*** Students take either MATH 223 or MATH 236, 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 2015, Winter 2016
Instructors: Michael Trevor Hallett (Fall) Yang Cai, Jackie Cheung (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 2015, Winter 2016
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 2015, Winter 2016
Instructors: Jérôme Waldispuhl, Mathieu Blanchette (Fall) Adrian Roshan Vetta (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 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 2015, Winter 2016
Instructors: Claude Crepeau (Fall) Claude Crepeau (Winter)
 3 hours
 Prerequisite: COMP 250 or COMP 203.
 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 2015, Winter 2016
Instructors: Paul Kry (Fall) Michael Langer (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 2015, Winter 2016
Instructors: Brigitte Pientka (Fall) Prakash Panangaden (Winter)
 3 hours
 Prerequisite: COMP 250

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 2015
Instructors: Prakash Panangaden (Fall)
 3 hours
 Prerequisite: COMP 251 and MATH 240.

COMP 350 Numerical Computing (3 credits) **
Overview
Computer Science (Sci) : Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Leastsquares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Terms: Fall 2015
Instructors: XiaoWen Chang (Fall)
 3 hours
 Prerequisites: MATH 222 and MATH 223 and one of: COMP 202, COMP 208, COMP 250; or equivalents.

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 2015, Winter 2016
Instructors: Hamed Hatami (Fall) Hamed Hatami (Winter)
 3 hours
 Prerequisite: Either COMP 251 or COMP 252, and either MATH 240 or MATH 235 or MATH 363.
 Restriction: Not open to students who have taken or are taking COMP 362.

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 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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

MATH 223 Linear Algebra (3 credits) ***
Overview
Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Terms: Fall 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs

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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.

MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248

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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

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 2015, Winter 2016
Instructors: William J Anderson (Fall)
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2015, Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.
Complementary Courses (21 credits)
12 credits in Mathematics selected from:
* Students take either MATH 340 or MATH 350, but not both.
** MATH 578 and COMP 540 cannot both be taken for program credit.

MATH 327 Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: This course is not scheduled for the 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Winter
 Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

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 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Not open to students who have taken or are taking MATH 343 or MATH 350.

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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2015, Winter 2016
Instructors: Djivede Kelome (Fall) Djivede Kelome (Winter)
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.

MATH 427 Statistical Quality Control (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Terms: Fall 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Prerequisites: MATH 323 + MATH 324

MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.

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 2016
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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: This course is not scheduled for the 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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: Fall 2015
Instructors: Russell Steele (Fall)
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425

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 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 Fall
 Prerequisites: MATH 247 or MATH 251; and MATH 387; or permission of the instructor.
9 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 2016
Instructors: Joelle Pineau (Winter)
 3 hours
 Prerequisites: (COMP 206 or ECSE 321), MATH 323 or equivalent 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 2015
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 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 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 2015
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: This course is not scheduled for the 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 academic year.
 3 hours
 Prerequisites: COMP 360 or COMP 362, MATH 323.

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 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 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 2015
Instructors: There are no professors associated with this course for the 20152016 academic year.
 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 20152016 academic year.
Instructors: There are no professors associated with this course for the 20152016 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 (except COMP 396, COMP 400, and COMP 431) and ECSE 508.