33 courses in the 1991–92 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
HONOURS SEMINARS
Consult departmental listings for topics and pre-requisites for 1991-92. Open to third and fourth year Honours Psychology or Make-Up Psychology Students, or by consent of the instructor.
A broad introduction to Mathematical Logic. The logic of sentences: truthfunctions and axiomatic approaches (eg. Natural Deduction and Gentzen
Sequences). A brief introduction to the
logic of predicates and to the foundations of mathematics.
This course will be of interest to all math students.
Topology of R", continuity, norms, metrics, completeness, Fourier series, and applications, for example, to ordinary differential equations, the heat problem, optimal approximation, the isoperimetric inequality. Prereg: MATH 230B or 237 Antireg: MATH 322A, PMATH 351 Cross-listed as AM 331 For students in programs outside of Pure Mathematics. Not available for credit to students in Honours Pure Mathematics programs.
Complex numbers; continuity, differentiability, analyticity of functions; the Cauchy-Riemann equations; solution of Laplace's equation; conformal mapping by elementary functions, and applications; contour integration, the Cauchy and allied theorems; Taylor and Laurent expansions, uniform convergence and power series; the residue calculus, and applications.
Prereq: MATH 230B or 237
Antireq: MATH 322B, 332B, PMATH 352
Cross-listed as AM 332
Formerly MATH 332B
Not available for credit to students in Honours Pure Mathematics programs.
Rings, ideals, factor rings, homomorphisms, finite and infinite fields, polynomials and roots, field extensions, algebraic numbers, and applications, for example, to Latin squares, finite geometries, geometrical constructions, error-correcting codes.
Prereq: MATH 134A, 234A or MATH 135, 235
For students in programs outside of Pure Mathematics.
Not available for credit to students in Honours Pure Mathematics programs.
Groups, subgroups, normal subgroups, quotient groups, morphisms. Products of groups. Permutation groups. Symmetry groups.
Prereq: MATH 135, 235
Antireq: MATH 2248, 234B, 244B, PMATH 343
Formerly MATH 2348
Course Descriptions Pure Mathematics
An elementary approach to the theory of numbers; the Euclidean algorithm, congruence equations, multiplicative functions, solutions to Diophantine equations, continued fractions, and tational approximations to real numbers.
Prereq: MATH 224B or 225
Antireq: PMATH 440
This course will be of interest to all math students.
Introduction to group theory, permutations, homomorphisms, subgroups, and normal subgroups, factor groups, Lagrange’s theorem, finite Abelian groups. Rings, ideals, modules, domains, Principal Ideal Domains, Euclidean algorithms, Unique Factorization Domains, finitely generated modules over Principal Ideal Domains, applications to finite Abelian groups and Jordan canonical form.
Prereq: MATH 235
PMATH 343 may be substituted for PMATH 336 whenever the latter is a requirement in an Honours program.
Field theory, examples of fields, field of fractions, algebraic extensions, construction of roots, separable extensions, splitting fields, classification of finite fields. Finite non-Abelian groups, Sylow theorems. Introduction to Galois theory.
Prereq: PMATH 343 or PMATH 336 with consent of instructor
PMATH 344 may be substituted for PMATH 334 whenever the latter is a requirement in an Honours program.
Metric spaces, compactness, completeness, continuity, convergence, integration, function spaces.
Prereq: MATH 230B or 237, or consent of instructor
Antireq: AM 331, MATH 322A, PMATH 331
Formerly PMATH 351A
PMATH 351 may be substituted for AM/PMATH 331 whenever this is a requirement in an Honours program.
Analytic functions, Cauchy's theorem, Laurent series, the residue theorem, integral evaluation, Mébius and other conformal maps.
Prereq: MATH 230B or 237, or consent of instructor
Antireq: AM/PMATH 332, MATH 322B, 332B
PMATH 352 may be substituted for AM/PMATH 332 or MATH 332B whenever these are requirements in an Honours program.
Fourier series, differential equations and other topics.
Prereq: PMATH 351
Formerly PMATH 3518
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inversion in circles. Theorems of Desargues, Pappus, and Pascal. Prereq: MATH 2248 or 225, or consent of instructor This course will be of interest to all math students.
the Serret-Frenet formulae; surfaces in ES and their intrinsic geometry, Gaussian curvature and the Gauss-Bonnet theorem. Coordinate transformations and tensors in n-dimensions; n-dimensional Riemannian spaces, covariant differentiation, geodesics, the curvature, Ricci and Einsteirt tensors. Applications of tensors in Relativity and Continuum Mechanics.
Prereq: AM 231 or MATH 230B, or consent of instrucior
Cross-listed as AM 333
Intuitive set theory, metric spaces, point set topology.
Prereq: MATH 230A or 237
Variable length coding. The Shannon entropy as a measure of uncertainty and expected information. Minimal average length coding; the Shannon entropy as lower bound. Source entropy. Channels. Transinformation. Capacity. Applications to problem solving, Information transmission, logics, science, linguistics and communications (TV, music, etc.). Determination of practical measures of information.
Prereq: Consent of instructor
Cross-listed as AM 381C
Measures of information: probabilistic, mixed and nonprobabilistic. Measures of uncertainty (entropies). Entropies for continuous random variables. The maximum entropy principle and its applications to: statistical mechanics, optimal discretization and quantization of random variables, image representation and pattern recognition. Applications to questionnaires. Optimal questionnaires.
Prereq: Consent of instructor
Cross-listed as AM 481C
First order languages and theories.
An introduction to elementary and analytic number theory; primitive roots, law of quadratic reciprocity, Gaussian sums, Riemann zeta-function, distribution of prime numbers.
Prereq: AM/PMATH 332 or MATH 332B or PMATH 352
Antireq: PMATH 340
Next offered in Winter 1990, and each alternate Winter thereafter.
An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichlet’s unit theorem, solutions of Diophantine equations, Fermat's ‘last theorem’. Prereg: PMATH 334 or 344 Next offered in Winter 1991, and each alternate Winter thereafter.
Course Descriptions Pure Mathematics
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prereq: MATH 234A or 235
Not offered every year.
Jacobson structure theory, density theorem, Jacobson radical, Maschke's theorem. Artinian rings, Artin- Wedderburn theorem, modules over semi-simple Artinian rings. Division rings. Representations of finite groups.
Prereq: PMATH 344
Next offered in Fall 1991.
Continuation of the theory of rings and modules.
Prereq: PMATH 334 or 344
This course will not be offered after Winter 1991.
Permutations, Cayley Theorem, Sylow
Theorem, Jordan-Hélder Theorem.
nilpotent and solvable groups, direct
and semidirect products, free groups. Prereq: PMATH 334 or 344
Prime ideals, Krull dimension, integral elements, localization, discrete valuations, Dedekind domains, Noetherian domains. Algebraic and transcendental field extensians, algebraic closure. Introduction to algebraic geometry. Prereq: PMATH 344
Lebesgue measure and integral for the teal line, general measure and integration theory, convergence theorems, Fubini's theorem, absolute continuity, Radon Nikodym theorem, L?-spaces. Prereq: AM/PMATH 331 or PMATH 351 Cross-listed as AM 431
The Riemann mapping theorem and several topics such as analytic continuation, harmonic functions, elliptic functions, entire functions, univalent functions, special functions.
Prereq: PMATH 352
16:131
Banach spaces, linear operators, geometry of Hilbert spaces, Hahn- Banach theorem, open mapping theorem, compact operators, applications.
Prereq: PMATH 353 or AM 431/PMATH 451
Cross-listed as AM 432
Topics chosen from: Charts and atlases, Manifolds and Diffeomorphisms, Tangent Spaces, Submanifolds, Vector Bundles, Tensor and Exterior Algebras, Differential Forms, Oriented Manifolds and Geometry, Homogeneous Spaces and Lle Groups. Prereq: PMATH 365 or consent of instructor
Some global aspects of surface theory, the Euler-Poincaré characteristic, the global interpretation of Gaussian curvature via the Gauss-Bonnet formula. Submanifolds of E°, induced Riemannian metrics, extrinsic and intrinsic curvatures, Gauss-Codazzi equations. Local Lie groups of transformations on R®, infinitesimal generators, the Lie derivative. An introduction to differentiable manifolds, the tangent and cotangent bundles, affine connections and the Riemann curvature tensor. The above topics will be illustrated by applications to continuum mechanics and mathematical physics.
Prereq: AM 333/PMATH 365 or consent of instructor
Cross-listed as AM 433
Topics from algebraic, combinatoriat and geometric topology.
Cauchy's, Pexider’s, and similar equa-
tions. Equations for polynomials and
trigonometric functions. Reduction to
different equations. Applications. Prereq: Consent of instructor
Recreation and Leisure Studies
Undergraduate Officer A. Gilbert, BMH 2212, ext. 3015