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. Linear transformations. Eigenvalues and diagonalization.
Terms: Fall 2021, Winter 2022
Instructors: BélangerRioux, Rosalie; Bibby, Sean; Chinis, Jake (Fall) Fortier, Jérôme (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, 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 2021, Winter 2022
Instructors: Trudeau, Sidney; Nazari Zahraei Motlagh, Erfan; Sabbagh, Magid (Fall) Kelome, Djivede (Winter)
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

MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2021, Winter 2022
Instructors: Macdonald, Jeremy; Albanese, Michael (Fall) Fortier, Jérôme (Winter)
Required Courses (46 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 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 2021, Winter 2022
Instructors: Campbell, Jonathan (Fall) Patitsas, Elizabeth (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 2021, Winter 2022
Instructors: D'silva, Joseph (Fall) D'silva, Joseph (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 2021, Winter 2022
Instructors: Langer, Michael (Fall) Alberini, Giulia (Winter)

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 2022
Instructors: Devroye, Luc P (Winter)
3 hours
Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.

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 2021, Winter 2022
Instructors: Vybihal, Joseph P; Lin, HsiuChin (Fall) Siddiqi, Kaleem (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 2021, Winter 2022
Instructors: Pientka, Brigitte (Fall) Si, Xujie (Winter)

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 2021, Winter 2022
Instructors: Panangaden, Prakash (Fall) Crepeau, Claude (Winter)
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 2022
Instructors: Vetta, Adrian Roshan (Winter)

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 2021
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

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 2022
Instructors: Hoheisel, Tim (Winter)

MATH 248 Honours Vector Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Terms: Fall 2021
Instructors: Guan, Pengfei (Fall)

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 2022
Instructors: Lipnowski, Michael (Winter)

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 2022
Instructors: Jakobson, Dmitry (Winter)

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 2021
Instructors: Paquette, Elliot (Fall)

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 2022
Instructors: Neslehova, Johanna (Winter)

MATH 533 Regression and Analysis of Variance (4 credits)
Overview
Mathematics & Statistics (Sci) : Multivariate normal and chisquared distributions; quadratic forms. Multiple linear regression estimators and their properties. General linear hypothesis tests. Prediction and confidence intervals. Asymptotic properties of least squares estimators. Weighted least squares. Variable selection and regularization. Selected advanced topics in regression. Applications to experimental and observational data.
Terms: Fall 2021
Instructors: Khalili Mahmoudabadi, Abbas (Fall)
Complementary Courses (33 credits)
18 credits in Mathematics selected as follows:
3 credits selected from:

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 2021
Instructors: Hundemer, Axel W (Fall)

MATH 254 Honours Analysis 1 (3 credits) *
Overview
Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Terms: Fall 2021
Instructors: Jaksic, Vojkan (Fall)
* It is strongly recommended that students take MATH 254.
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: Winter 2022
Instructors: There are no professors associated with this course for the 20212022 academic year.

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: This course is not scheduled for the 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.
At least 8 credits selected from:

MATH 523 Generalized Linear Models (4 credits)
Overview
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.
Terms: Winter 2022
Instructors: Neslehova, Johanna (Winter)

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 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.

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 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.

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 2021
Instructors: Khalili Mahmoudabadi, Abbas (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 2022
Instructors: Genest, Christian (Winter)
Winter
Prerequisite: MATH 556

MATH 558 Design of Experiments (4 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Rowcolumn designs. Latin squares. Model and analysis for fixed row and column effects. Splitplot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues.
Terms: Winter 2022
Instructors: Sajjad, Alia (Winter)
The remaining Mathematics credits selected from:
** MATH 578 and COMP 540 cannot both be taken for program credit.

MATH 350 Honours Discrete Mathematics
(3 credits)
Overview
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.
Terms: Fall 2021
Instructors: Norin, Sergey (Fall)

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 2021
Instructors: Norin, Sergey (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 454 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 2021
Instructors: Tosatti, Valentino (Fall)

MATH 462 Honours Mathematics for Machine Learning (3 credits)
Overview
Mathematics & Statistics (Sci) : Foundations of optimization and convex analysis, stochastic gradient descent. Divergences, loss functions, empirical loss minimization and parameter estimation. Reproducing kernel Hilbert spaces. Multiple linear regression in the context of machine learning. Classification with support vector machines. Dimensionality reduction, JohnsonLindenstrauss Lemma. Concentration of measure and learning bounds.
Terms: Fall 2021
Instructors: Oberman, Adam (Fall)

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: Winter 2022
Instructors: Steele, Russell (Winter)

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 2021
Instructors: Nave, JeanChristophe (Fall)

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 2021
Instructors: Chen, Linan (Fall)

MATH 594 Topics in Mathematics and Statistics
(4 credits)
Overview
Mathematics & Statistics (Sci) : This course covers a topic in mathematics and/or statistics.
Terms: Fall 2021, Winter 2022
Instructors: Jaksic, Vojkan (Fall) Tserunyan, Anush (Winter)
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
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 2022
Instructors: Cheung, Jackie (Winter)

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 2021
Instructors: There are no professors associated with this course for the 20212022 academic year.

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 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.

COMP 540 Matrix Computations (4 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: Winter 2022
Instructors: Chang, XiaoWen (Winter)

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: Fall 2021
Instructors: Crepeau, Claude (Fall)

COMP 551 Applied Machine Learning (4 credits)
Overview
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.
Terms: Fall 2021, Winter 2022
Instructors: Ravanbakhsh, Siamak (Fall) Rabbany, Reihaneh (Winter)

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 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.

COMP 564 Advanced Computational Biology Methods and Research (3 credits)
Overview
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.
Terms: Winter 2022
Instructors: Waldispuhl, Jérôme (Winter)

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: This course is not scheduled for the 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.

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 20212022 academic year.
Instructors: There are no professors associated with this course for the 20212022 academic year.
The remaining Computer Science credits are selected from COMP courses at the 300 level or above excluding COMP 396.