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Honours Mathematics and Computer Science (75 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

Program Requirements

Students may complete this program with a minimum of 72 credits or a maximum of 75 credits depending on whether or not they are exempt from taking COMP 202.

Program Prerequisites

Students must consult an Honours adviser in both departments. Students entering the Joint Honours in Mathematics 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 72-75 credits of courses in the program.

  • MATH 133 Linear Algebra and Geometry (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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: Djivede Kelome, William J Anderson, James G Loveys, Shahab Shahabi, Adam Clay (Fall) Djivede Kelome, William J Anderson (Winter) Karol Palka (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.

  • MATH 140 Calculus 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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: Stephen W Drury, Sidney Trudeau, Shahab Shahabi (Fall) Axel W Hundemer (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

  • MATH 141 Calculus 2 (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

    Terms: Fall 2010, Winter 2011, Summer 2011

    Instructors: Sidney Trudeau (Fall) Neville G F Sancho, Stephen W Drury, Sidney Trudeau (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 (45 credits)

* Students who have sufficient knowledge in a programming language are not required to take COMP 202.

  • COMP 202 Introduction to Computing 1 (3 credits) *

    Offered by: Computer Science (Faculty of Science)

    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: Mathieu Petitpas, Maja Frydrychowicz (Fall) Maja Frydrychowicz, Daniel Pomerantz (Winter) Daniel Pomerantz (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

  • COMP 206 Introduction to Software Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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: Joseph P Vybihal (Fall) Joseph P Vybihal, Gregory L Dudek (Winter)

  • COMP 250 Introduction to Computer Science (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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: Doina Precup (Fall) Michael Langer (Winter)

    • 3 hours

    • Prerequisites: Familiarity with a high level programming language and CEGEP level Math.

    • Restrictions: COMP 203 and COMP 250 are considered to be equivalent from a prerequisite point of view, and cannot both be taken for credit.

  • COMP 252 Algorithms and Data Structures (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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 2011

    Instructors: Luc P Devroye (Winter)

    • 3 hours

    • Prerequisite: COMP 250 and MATH 240

    • Restrictions: Open only to students registered in following programs: Honours in Computer Science, Joint Honours in Mathematics and Computer Science, Honours in Applied Mathematics, Honours in Mathematics. Not open to students who have taken or are taking COMP 251.

    • Note: COMP 252 can be used instead of COMP 251 to satisfy prerequisites.

  • COMP 273 Introduction to Computer Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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: Joseph P Vybihal (Fall) Kaleem Siddiqi (Winter)

  • COMP 302 Programming Languages and Paradigms (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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: Brigitte Pientka (Fall) Jesse Doherty (Winter)

  • COMP 310 Operating Systems (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Control and scheduling of large information processing systems. Operating system software - resource allocation, dispatching, processors, access methods, job control languages, main storage management. Batch processing, multiprogramming, multiprocessing, time sharing.

    Terms: Fall 2010, Winter 2011

    Instructors: Carl Tropper (Fall) Andraws Swidan (Winter)

  • COMP 330 Theoretical Aspects: Computer Science (3 credits)

    Offered by: Computer Science (Faculty of Science)

    Overview

    Computer Science (Sci) : Mathematical models of computers, finite automata, Turing machines, counter machines, push-down machines, computational complexity.

    Terms: Fall 2010

    Instructors: Hamed Hatami (Fall)

  • COMP 362 Honours Algorithm Design (3 credits)

    Offered by: Computer Science (Faculty of Science)

    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: Fall 2010

    Instructors: Mohit Singh (Fall)

    • 3 hours

    • Prerequisite: COMP 252

    • Restriction: Not open to students who have taken or are taking COMP 360.

    • Note: COMP 362 can be used instead of COMP 360 to satisfy prerequisites.

  • MATH 235 Algebra 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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: Heekyoung Hahn (Fall)

    • Fall

    • 3 hours lecture; 1 hour tutorial

    • Prerequisite: MATH 133 or equivalent

  • MATH 242 Analysis 1 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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: Reem Adel Yassawi (Fall)

  • MATH 248 Honours Advanced Calculus (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.

    Terms: Fall 2010

    Instructors: Pengfei Guan (Fall)

    • Fall and Winter and Summer

    • Prerequisites: MATH 133 and MATH 222 or consent of Department.

    • Restriction: Intended for Honours Mathematics, Physics and Engineering students

    • Restriction: Not open to students who have taken or are taking MATH 314

  • MATH 251 Honours Algebra 2 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 self-adjoint operators.

    Terms: Winter 2011

    Instructors: James G Loveys (Winter)

    • Winter

    • Prerequisites: MATH 235 or permission of the Department

    • Restriction: Not open to students who are taking or have taken MATH 247

  • MATH 255 Honours Analysis 2 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Series of functions including power series. Riemann integration in one variable. Elementary functions.

    Terms: Winter 2011

    Instructors: Vojkan Jaksic (Winter)

    • Winter

    • Prerequisites: MATH 242 or permission of the Department

  • MATH 350 Graph Theory and Combinatorics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.

    Terms: Winter 2011

    Instructors: Bruce Alan Reed (Winter)

Complementary Courses (30 credits)

18 credits in Mathematics, at least 12 credits selected from:

* Students with appropriate background in probability may substitute MATH 587 for MATH 356 and must then also register for MATH 355.

  • MATH 354 Honours Analysis 3 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.

    Terms: Fall 2010

    Instructors: Dmitry Jakobson (Fall)

    • Fall

    • Prerequisite: MATH 255 or equivalent

  • MATH 355 Honours Analysis 4 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces, L_2 spaces, Fourier series. Fourier integrals (if time allows).

    Terms: Winter 2011

    Instructors: Dmitry Jakobson (Winter)

    • Winter

    • Prerequisite: MATH 354 or equivalent.

  • MATH 356 Honours Probability (3 credits) *

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Basic combinatorial probability. Introductory distribution theory of univariate and multivariate distributions with special reference to the Binomial, Poisson, Gamma and Normal distributions. Characteristic functions. Weak law of large numbers. Central limit theorem.

    Terms: Fall 2010

    Instructors: Johanna Neslehova (Fall)

  • MATH 370 Honours Algebra 3 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.

    Terms: Fall 2010

    Instructors: Jayce Getz (Fall)

  • MATH 371 Honours Algebra 4 (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.

    Terms: Winter 2011

    Instructors: Jayce Getz (Winter)

  • MATH 387 Honours Numerical Analysis (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

    Terms: This course is not scheduled for the 2010-2011 academic year.

    Instructors: There are no professors associated with this course for the 2010-2011 academic year.

    • Taught in alternate years

    • Winter (even years)

    • Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.

    • Corequisites: MATH 255 or MATH 243.

    • Restriction: Intended primarily for Honours students.

The remaining credits should be selected from honours courses given by the Department of Mathematics and Statistics.

12 credits in Computer Science, selected from Computer Science courses at the 300 level or above excluding COMP 364, COMP 396 and COMP 431. ECSE 508 may also be taken.

Faculty of Science—2010-2011 (last updated Jan. 19, 2011) (disclaimer)