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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.
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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 2010, Winter 2011, Summer 2011
Instructors: Kelome, Djivede; Anderson, William J; Loveys, James G; Shahabi, Shahab; Clay, Adam (Fall) Kelome, Djivede; Anderson, William J (Winter) Palka, Karol (Summer)
- Prerequisite: a course in functions
- Restriction: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
- Restriction Note 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.
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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 2010, Winter 2011, Summer 2011
Instructors: Drury, Stephen W; Trudeau, Sidney; Shahabi, Shahab (Fall) Hundemer, Axel W (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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
- Each Tutorial section is enrolment limited
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MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Trudeau, Sidney (Fall) Sancho, Neville G F; Drury, Stephen W; Trudeau, Sidney (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 (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.
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COMP 202 Introduction to Computing 1 (3 credits) *
Overview
Computer Science (Sci) : Overview of components of microcomputers, the internet design and implementation of programs using a modern high-level language, an introduction to modular software design and debugging. Programming concepts are illustrated using a variety of application areas.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Petitpas, Mathieu; Frydrychowicz, Maja (Fall) Frydrychowicz, Maja; Pomerantz, Daniel (Winter) Pomerantz, Daniel (Summer)
- 3 hours
- Prerequisite: a CEGEP level mathematics course
- Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250
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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 2010, Winter 2011
Instructors: Vybihal, Joseph P (Fall) Vybihal, Joseph P; Dudek, Gregory L (Winter)
- 3 hours
- Prerequisite: COMP 202 or COMP 250
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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 2010, Winter 2011
Instructors: Precup, Doina (Fall) Langer, Michael (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.
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COMP 251 Data Structures and Algorithms (3 credits)
Overview
Computer Science (Sci) : Design and analysis of algorithms. Complexity of algorithms. Data structures. Introduction to graph algorithms and their analysis.
Terms: Fall 2010, Winter 2011
Instructors: Verbrugge, Clark (Fall) Crepeau, Claude (Winter)
- 3 hours
- Prerequisite: COMP 250 or COMP 203.
- Restrictions: Not open to students who have taken or are taking COMP 252.
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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 2010, Winter 2011
Instructors: Vybihal, Joseph P (Fall) Siddiqi, Kaleem (Winter)
- 3 hours
- Corequisite: COMP 206.
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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 2010, Winter 2011
Instructors: Pientka, Brigitte (Fall) Doherty, Jesse (Winter)
- 3 hours
- Prerequisite: COMP 250 or COMP 203
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COMP 330 Theoretical Aspects: Computer Science (3 credits)
Overview
Computer Science (Sci) : Mathematical models of computers, finite automata, Turing machines, counter machines, push-down machines, computational complexity.
Terms: Fall 2010
Instructors: Hatami, Hamed (Fall)
- 3 hours
- Prerequisite: COMP 251.
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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. Least-squares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Terms: Fall 2010
Instructors: Chang, Xiao-Wen (Fall)
- 3 hours
- Prerequisites: MATH 222 and MATH 223 and one of: COMP 202, COMP 208, COMP 250; or equivalents.
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COMP 360 Algorithm Design Techniques (3 credits)
Overview
Computer Science (Sci) : A study of techniques for the design and analysis of algorithms.
Terms: Fall 2010, Winter 2011
Instructors: Vetta, Adrian Roshan (Fall) Nguyen, The Phuong (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.
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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 2010, Winter 2011, Summer 2011
Instructors: Jonsson, Wilbur; Sancho, Neville G F (Fall) Jonsson, Wilbur (Winter)
- Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
- Restriction: Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227
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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 2010, Winter 2011
Instructors: Loveys, James G; Huang, Hongnian (Fall) Loveys, James G (Winter)
- 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
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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 2010
Instructors: Hahn, Heekyoung (Fall)
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
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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. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Terms: Winter 2011
Instructors: Hahn, Heekyoung (Winter)
- Winter
- Prerequisite: MATH 235
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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 2010
Instructors: Yassawi, Reem Adel (Fall)
- Fall
- Prerequisite: MATH 141
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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.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Jonsson, Wilbur (Fall) Jonsson, Wilbur (Winter) Roth, Charles (Summer)
- Prerequisites: MATH 133, MATH 222
- Restriction: Not open to students who have taken or are taking MATH 248
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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 2010
Instructors: Bartello, Peter (Fall)
- Fall
- Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.
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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 2010, Winter 2011, Summer 2011
Instructors: Anderson, William J (Fall) Partovi Nia, Vahid (Winter)
- 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
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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 2010, Winter 2011
Instructors: Asgharian-Dastenaei, Masoud (Fall) Anderson, William J (Winter)
- 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.
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MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2010
Instructors: Khalili Mahmoudabadi, Abbas (Fall)
- 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.
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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: Winter 2011
Instructors: Humphries, Antony Raymond (Winter)
- Winter
- Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
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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 2011
Instructors: Vetta, Adrian Roshan (Winter)
- 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.
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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: Winter 2011
Instructors: Reed, Bruce Alan (Winter)
- 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.
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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 2010
Instructors: Loveys, James G (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.
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MATH 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2010, Winter 2011
Instructors: Hundemer, Axel W; Kelome, Djivede (Fall) Kelome, Djivede (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.
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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 2011
Instructors: Addario-Berry, Dana Louis (Winter)
- Winter
- Prerequisite: MATH 323
- Restriction: Not open to students who have taken or are taking MATH 547.
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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. Quasi-likelihood. Sliced inverse regression. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.
Terms: Winter 2011
Instructors: Stephens, David (Winter)
- Winter
- Prerequisite: MATH 423 or EPIB 697
- Restriction: Not open to students who have taken MATH 426
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MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.
Terms: Fall 2010
Instructors: Genest, Christian (Fall)
- Fall
- Prerequisite: MATH 324 or equivalent
- Restriction: Not open to students who have taken MATH 424
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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 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 academic year.
- Prerequisite: MATH 324 or equivalent
- Restriction: Not open to students who have taken MATH 425
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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 2010
Instructors: Nave, Jean-Christophe (Fall)
- 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:
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COMP 423 Data Compression (3 credits)
Overview
Computer Science (Sci) : Information Theory. Huffman, arithmetic and dictionary codes. Context Modelling. Lossy compression and quantization. Signal processing. Applications to text, image, speech, audio and video data.
Terms: This course is not scheduled for the 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 academic year.
- 3 hours
- Prerequisites: COMP 251, MATH 223, MATH 323
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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 2011
Instructors: Pineau, Joelle (Winter)
- 3 hours
- Prerequisites: (COMP 206 or ECSE 321) and COMP 251
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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 2010
Instructors: Waldispuhl, Jerome (Fall)
- 3 hours
- Prerequisites: COMP 251 and MATH 323
- Restriction: Not open to students who have taken COMP 562. Not open to students who are taking or have taken COMP 561.
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COMP 490 Introduction to Probabilistic Analysis of Algorithms (3 credits)
Overview
Computer Science (Sci) : Fundamental tools from probability are used to analyze algorithms. Notions covered included independence, generating functions, probability inequalities, random walks and Markov chains. Analysis of probabilistic recurrences, Las Vegas algorithms, randomized approximation algorithms, random sampling methods, Monte Carlo techniques and algorithms for combinatorial search and graph theoretic problems.
Terms: This course is not scheduled for the 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 academic year.
- 3 hours
- Prerequisites: COMP 251 and MATH 323
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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 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 academic year.
- 3 hours
- Prerequisites: COMP 206, COMP 360, COMP 424 and MATH 323
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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: Winter 2011
Instructors: Chang, Xiao-Wen (Winter)
- 3 hours
- Prerequisite: MATH 327 or COMP 350
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COMP 547 Cryptography and Data Security (4 credits)
Overview
Computer Science (Sci) : This course presents an in-depth 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 2010
Instructors: Crepeau, Claude (Fall)
- 3 hours
- Prerequisites: COMP 360 or COMP 362, MATH 323.
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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 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 academic year.
- 3 hours
- Prerequisite: COMP 462.
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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 2010
Instructors: Naves, Guyslain (Fall)
- 3 hours
- Prerequisites: COMP 360 and MATH 223
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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 2010-2011 academic year.
Instructors: There are no professors associated with this course for the 2010-2011 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.
Faculty of Science—2010-2011 (last updated Jan. 19, 2011) (disclaimer)