32 courses in the 1989–90 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Topotogy of R", continuity, norms, metrics, completeness, Fourier series, and applications, for example, to ordinary differential equations, the heat problam, optimal approximation, the isoperimetric inequality. Prereq: MATH 230B or 237 Antireq: 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, 2448
Formerly MATH 234B
This course replaces MATH 2348 effective Winter, 1991.
An elementary approach to the theory of numbers; the Euclidean algorithm, congruence equations, multiplicative functions, solutions to Diophantine equations, continued fractions, and rational approximations to real numbers.
Prereq: MATH 224B or 225
Antireq: PMATH 440
This course will be of interest to all math students.
Groups, rings, fields and applications.
Prereq: MATH 134A, 234A or MATH 135, 235
PMATH 344 may be substituted for PMATH 334 whenever this 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 2308 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 351B
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 224B or 225 This course will be of interest to all math students.
the Serret-Frenet formulae; surfaces in E® 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 Einstein tensors. Applications of tensors in Relativity and Continuum Mechanics.
Prereq: AM 231 or MATH 230B, or consent of instructor.
Cross-listed as AM 333 .
Intuitive set theory, metric spaces, point sat 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 gommunications (TV, music, etc.). Determination of practical measures of information.
Prereq: Consent of instructor
Cross-listed as AM 381C
Course Descriptions 16:115 Mathematics: Pure Mathematics
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
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.
Antireq: PMATH 432
This course will be of interest to all math students.
incompleteness theorem (in outline). Lagicism, intuitionism, formalism. Selected topics (some of intuitionistic) logic, modal logic, the representation theorem for Boolean Algebras normally are treated).
Prereq: PMATH 430A
This course will be of interest to alt math students.
First order languages and theories. Antireq: PMATH 430A PMATH 432 is more specialized and presented at a more advanced level than PMATH 430A.
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.
16:116 Course Descriptions Mathematics: Pure Mathematics
An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichlet's unit theorem, solutions of Diophantine equations, Fermat's ‘last theorem’. Prereq: PMATH 334 or 344 Next offered in Winter 1991, and each alternate Winter thereafter.
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prereq: MATH 234A or 235
Not offered every year.
Continuation of the theory of rings and * modules. Prereq: PMATH 334 or 344
Permutations, Cayley Theorem, Sylow
Theorem, Jordan-Hélder Theorem.
nilpotent and solvable groups, direct
and semidirect products, free groups. Prereq: PMATH 334 or 344
Field extensions and Galois theory. Prereq: PMATH 334 or 344 Next offered in Fall 1990
Lebesgue measure and integral for the real 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
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, Submanifoids, Vector Bundies, Tensor and Exterior Algebras, Differential Forrns, Oriented Manifolds and Geometry, Homogeneous Spaces and Lie Groups. Prereq: PMATH 365 or consent o' instructor .
Some globai 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. Locai 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, combinatorial 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
Statistics
Course Descriptions
Courses not offered in the current academic year are listed at the end of this section.
Introductory Notes
1. The following courses are offered in conjunction with the Division of Mathematics for Industry and Commerce: STAT 331, 332, 333, 335, 371, 443
2. Mere detailed course descriptions and course outlines are available in the Statistics Undergraduate Studies Handbook.