30 courses in the 1988–89 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Introductory Note
More detailed course descriptions and course outlines are available upon request from the Pure Mathematics Department.
Topology of R", continuity, norms, metrics, completeness, Fourier series, and applications, for example, to O.D.E.’s, the heat problem, optimal approximation, the isoperimetric inequality.
Prereq: MATH 230B
For students in programs outside of Pure Mathematics.
Antireq: MATH 322A, PMATH 351A
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 geome- "
tries, geometrical constructions, errorcorrecting codes.
Prereq: MATH 234B
For students in programs outside of Pure Mathematics. .
Not available for credit to students in Honours Pure Mathematics programs.
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
Will be of interest to all math students.
Antireq: PMATH 440
Groups, rings, fields and applications. Prereq: MATH 234B PMATH 344 may be substituted for 334 whenever this is a requirement in an Honours program. Antireg: MATH 324, PMATH 334
Metric spaces, compactness, completeness, continuity, convergence, integration, function spaces.
Prereq: MATH 230B
PMATH 351A may be substituted for 331 whenever this is a requirement in an Honours program.
to Fourier series, differential equations and other topics.
Prereq: PMATH 351A _.
Analytic functions, Cauchy’s theorem, Laurent series, the residue theorem, integral evaluation, Mobius and other conformal maps.
Prereq: MATH 230B
PMATH 352 may be substituted for MATH 332B whenever this is a requirement in an Honours program.
Antireq: MATH 322B, 332B
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inversion in circles..
Prereq: MATH 224B
Will be of interest to all math students.
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: MATH 230B or consent of instructor Cross-listed as AM 362
Course Descriptions 16:109 Mathematics: Pure Mathematics
Intuitive set theory, metric spaces, point set topology.
Prereq: MATH 230A
Variable length coding. The Shannon entropy as 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 380A
Measures of conditional uncertainty (entropy). Maximizing conditional entropies. Applications to statistical physics, statistics, pattern recognition. Special entropies in questionnaire theory. Design of optimal questionnaires. Special entropies in dynamical systems. Basics in dynamical systems. Prereq: Consent of instructor Cross-listed as AM 380B
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.
Will be of interest to all math students.
Antireq: PMATH 432A
incompleteness theorem (in outline). Logicism, intuitionism, formalism. : Selected topics (some of intuitionistic logic, modal logic, the representation theorem for Boolean Algebras normally are treated).
Prereq: PMATH 430A.
Will be of interest to all math students.
Antireq: PMATH 432B
16:110 Course Descriptions Mathematics: Pure Mathematics
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: MATH 332B (or PMATH 362) Antireq: PMATH 340 ‘ Next offered in Winter 1988, 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’.
Prereq: PMATH 334 or 344 Next offered in Winter 1989, and each alternate Winter thereafter.
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prereq: MATH 234A
Not offered every year.
Continuation of the theory of rings and modules. Prereq: PMATH 334 or 344 Next offered in Fall 1988
Permutations, Cayley Theorem, Sylow
Theorem, Jordan-Hélder Theorem, nilpo-
tent and solvable groups, direct and
semidirect products, free groups. Prereq: PMATH 334 or 344
Field extensions and Galois theory. Prereq: PMATH 334 or 344
Lebesgue measure and integral for the real line, general measure and integration theory, convergence theorems, Fubini’s theorem, absolute continuity, Radon Nikodym theorem, LP-spaces.
Prereq: PMATH 331 or 351A, or consent of instructor.
Cross-listed as AM 462
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 351B or consent of instructor Cross-listed as AM 472
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 Lie Groups.
Prereq: PMATH 365 or consent of instructor
Cross-listed as AM 463
Grassman algebras, differential forms, Lie derivatives, isometries, Killing vector fields, applications to continuum mechanics, differentiable manifolds and applications of differential forms to physics.
Prereq: AM 362/PMATH 365 or consent of instructor
Cross-listed as AM 474
Topics from algebraic, combinatorial and geometric topology. Prereq: MATH 234B, PMATH 367
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. More detailed course descriptions and course outlines are available in the Statistics Undergraduate Studies Handbook.