Note: This is the 2010–2011 edition of the eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or click here to jump to the newest eCalendar.
Program Requirements
Students who wish to study at the Honours level in two Arts disciplines may apply to combine Joint Honours Program components from two Arts disciplines. For a list of available Joint Honours programs, see "Overview of Programs Offered" and "Joint Honours Programs."
To remain in the Joint Honours program and receive the Joint Honours degree, a student must maintain the standards set by each discipline, as well as by the Faculty. In the Mathematics courses of the program a GPA of 3.00 and a CGPA of 3.00 must be maintained. Students who have difficulty in maintaining the required level should change to another program before entering their final year.
Program Prerequisites
Students who have not completed the program prerequisite courses listed below or their equivalents will be required to make up any deficiencies in these courses over and above the 36 credits required for the program.
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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
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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
Required Courses (15 credits)
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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 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 248 Honours Advanced Calculus (3 credits)
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: Guan, Pengfei (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
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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 self-adjoint operators.
Terms: Winter 2011
Instructors: Loveys, James G (Winter)
- Winter
- Prerequisites: MATH 235 or permission of the Department
- Restriction: Not open to students who are taking or have taken MATH 247
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MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Series of functions including power series. Riemann integration in one variable. Elementary functions.
Terms: Winter 2011
Instructors: Jaksic, Vojkan (Winter)
- Winter
- Prerequisites: MATH 242 or permission of the Department
Complementary Courses
21 credits with at 15 credits selected from the list below. The remaining credits are to be chosen from the full list of available Honours courses in Mathematics and Statistics.
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MATH 325 Honours Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Fall 2010, Winter 2011
Instructors: Humphries, Antony Raymond (Fall) Klemes, Ivo (Winter)
- Fall and Winter
- (3-0-6)
- Prerequisite: MATH 222.
- Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
- Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315
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MATH 354 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.
Terms: Fall 2010
Instructors: Jakobson, Dmitry (Fall)
- Fall
- Prerequisite: MATH 255 or equivalent
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MATH 355 Honours Analysis 4 (3 credits)
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: Jakobson, Dmitry (Winter)
- Winter
- Prerequisite: MATH 354 or equivalent.
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MATH 356 Honours Probability (3 credits)
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: Neslehova, Johanna (Fall)
- Fall
- Prerequisite: MATH 255 or MATH 243
- Restriction: Not open to students who have taken or are taking MATH 323
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MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2011
Instructors: Asgharian-Dastenaei, Masoud (Winter)
- Winter
- Prerequisite: MATH 356 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 324
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MATH 366 Honours Complex Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
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 248.
- Corequisite: MATH 354.
- Restriction: Not open to students who have taken or are taking MATH 466, MATH 249, MATH 316, MATH 381.
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MATH 370 Honours Algebra 3 (3 credits)
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: Getz, Jayce (Fall)
- Fall
- Prerequisite: MATH 251
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MATH 371 Honours Algebra 4 (3 credits)
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: Getz, Jayce (Winter)
- Winter
- Prerequisite: MATH 370
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MATH 380 Honours Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
Terms: Winter 2011
Instructors: Guan, Pengfei (Winter)
- Winter
- Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314
Faculty of Arts—2010-2011 (last updated Jan. 19, 2011) (disclaimer)