Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
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
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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.
 Terms
 Instructors
 Rosalie BélangerRioux, Gavin Ball, Florian Aigner, Piotr Przytycki
 Djivede A Kelome

MATH 140
Calculus 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics
 Each Tutorial section is enrolment limited
 Terms
 Instructors
 Sidney Trudeau, Tyrone Ghaswala, Michael Albanese
 Jérôme Fortier

MATH 141
Calculus 2
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics.
 Each Tutorial section is enrolment limited
 Terms
 Instructors
 Jérôme Fortier, Marcin Sabok
 Sidney Trudeau
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.
Both courses are equivalent as prerequisites for required and complementary Computer Science courses listed below.

COMP 202
Foundations of Programming
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 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
 Terms
 Instructors
 Giulia Alberini, Jonathan C Campbell
 Giulia Alberini

COMP 206
Intro to Software Systems
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 Terms
 Instructors
 Joseph V D'silva
 Joseph P Vybihal, Joseph V D'silva

COMP 250
Intro to Computer Science
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 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.
 Terms
 Instructors
 Giulia Alberini
 Giulia Alberini

COMP 251
Algorithms and Data Structures
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Introduction to algorithm design and analysis. Graph algorithms, greedy algorithms, data structures, dynamic programming, maximum flows.
Offered by: Computer Science
 3 hours
 Prerequisite: COMP 250
 Corequisite(s): MATH 235 or MATH 240.
 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 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.
 Terms
 Instructors
 Jérôme Waldispuhl, David C Becerra
 David C Becerra

COMP 273
Intro to Computer Systems
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Number representations, combinational and sequential digital circuits, MIPS instructions and architecture datapath and control, caches, virtual memory, interrupts and exceptions, pipelining.
Offered by: Computer Science
 Terms
 Instructors
 Kaleem Siddiqi
 Paul Kry, HsiuChin Lin

COMP 302
Programming Lang & Paradigms
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 330
Theory of Computation
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Finite automata, regular languages, contextfree languages, pushdown automata, models of computation, computability theory, undecidability, reduction techniques.
Offered by: Computer Science
 Terms
 Instructors
 Hamed Hatami
 Prakash Panangaden

COMP 350
Numerical Computing
3 Credits**
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 360
Algorithm Design
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Advanced algorithm design and analysis. Linear programming, complexity and NPcompleteness, advanced algorithmic techniques.
Offered by: Computer Science
 Terms
 Instructors
 Bruce Alan Reed, Bettina Kemme, Seyyed Aliasghar Hosseini
 Robert Robere

MATH 222
Calculus 3
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Djivede A Kelome, Jérôme Fortier
 Jerome Vetois

MATH 223
Linear Algebra
3 Credits***
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent

MATH 236
Algebra 2
3 Credits***
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 242
Analysis 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 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
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 317
Numerical Analysis
3 Credits**
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics

MATH 323
Probability
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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
 Terms
 Instructors
 David B Wolfson, Alia Sajjad
 David B Wolfson, Alia Sajjad

MATH 324
Statistics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 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.
 Terms
 Instructors
 Masoud AsgharianDastenaei
 Yi Yang

MATH 423
Applied Regression
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Multiple regression estimators and their properties. Hypothesis tests and confidence
intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.
Offered by: Mathematics and Statistics
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 208
Intro to Statistical Computing
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Basic data management. Data visualization. Exploratory data analysis and descriptive statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
Offered by: Mathematics and Statistics

MATH 308
Fundls of Statistical Learning
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.
Offered by: Mathematics and Statistics

MATH 327
Matrix Numerical Analysis
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 340
Discrete Mathematics
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Offered by: Mathematics and Statistics

MATH 350
Honours Discrete Mathematics
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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.

MATH 352
Problem Seminar
1 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
 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.
 Terms
 Instructors
 Djivede A Kelome, Anmar Khadra, Russell Steele, Rustum Choksi

MATH 427
Statistical Quality Control
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 447
Intro. to Stochastic Processes
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.

MATH 523
Generalized Linear Models
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, loglinear models. Multinomial models. Overdispersion and Quasilikelihood.
Applications to experimental and observational data.
Offered by: Mathematics and Statistics

MATH 524
Nonparametric Statistics
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424

MATH 525
Sampling Theory & Applications
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425

MATH 545
Intro to Time Series Analysis
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 578
Numerical Analysis 1
4 Credits**
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 594
Topics in Mathematics&Stats
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): This course covers a topic in mathematics and/or statistics.
Offered by: Mathematics and Statistics
 Prerequisites: At least 30 credits in required or complementary courses from the Honours Mathematics, Honours Applied Mathematics, or Honours Probability and Statistics programs. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
 Restrictions: Requires permission of the Department of Mathematics and Statistics
9 credits in Computer Science selected as follows:
At least 6 credits selected from:

COMP 424
Artificial Intelligence
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning.
Offered by: Computer Science

COMP 462
Computational Biology Methods
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 526
Probabilistic Reasoning and AI
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Belief networks, Utility theory, Markov Decision Processes and Learning Algorithms.
Offered by: Computer Science
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

COMP 540
Matrix Computations
4 Credits**
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 547
Cryptography & Data Security
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 551
Applied Machine Learning
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Offered by: Computer Science
 Prerequisite(s): MATH 323 or ECSE 205 or ECSE 305 or equivalent
 Restriction(s): Not open to students who have taken or are taking COMP 451.
 Some background in Artificial Intelligence is recommended, e.g. COMP424 or ECSE526, but not required.
 Terms
 Instructors
 Mohsen Ravanbakhsh
 Reihaneh Rabbany

COMP 564
Adv Comput'l Bio Meth&Research
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Computer Science (Sci): Fundamental concepts and techniques in computational structural biology, system
biology. Techniques include dynamic programming algorithms for RNA structure
analysis, molecular dynamics and machine learning techniques for protein structure
prediction, and graphical models for gene regulatory and proteinprotein interaction
networks analysis. Practical sessions with stateoftheart software.
Offered by: Computer Science

COMP 566
Discrete Optimization 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

COMP 567
Discrete Optimization 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year