36 courses in the 1984–85 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Course Descriptions
Introductory Notes
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, optimai approximation, the isoperimetric inequality.
Prereq: MATH 230a (MATH 230b Oesirable)
Will be ‘of particular interest to students in programs outside of Pure Mathematics.
Credit will be granted for only 1 of MATH 3222, PMATH 331, 351a.
Not available for credit to students in Honours Pure Mathematics Programs.
Rings, ideats, factor rings, homomorphisms, finite and infinite fietds, polynomials and roots, field extensions, algebraic numbers, and applications, for example, to Latin squares, finite geometries, geometrical constructions, error-correcting codes.
Prereq: MATH 234b
Will be of particular interest to students in programs outside of Pure Mathematics.
An elementary approach to the theory of numbers. Topics will include the Euclidean algorithm, unique factorization, congruences and the Euler phi function, and solutions to Diophantine equations. Prereq: MATH 224b : Will be of interest to ali math students. Credit will be granted for only 1 of PMATH 340, 441a.
Groups, rings, fields and applications. Prereq: MATH 244b, or consent of instructor PMATH 344 may be substituted for 334 whenever this is a requirement in an Honours program.
Theory of functions of real variables. The notions of compactness, connectedness and uniformity are used in a study of continuity, differentiation, and integration.
Prereq: MATH 230b
PMATH 351a may be substituted for 331 whenever this is a requirement in an Honours program.
Holomorphic functions, Cauchy's integral theorem, Cauchy’s integral formulas, Taylor and Laurent expansions, classification of isolated singularities, the residue theorem.
Prereq: MATH 230b
PMATH 352a may be substituted for MATH 332b whenever this is a requirement in an Honours program.
PMATH 365Ditterential Geometry and Tensor Analysis Curves in Euclidean 3-space (E°) andF,S 2C,1T 0.5
the Serret-Frenet formulae; surfaces in E3 and their intrinsic geometry, Gaussian curvature and the Gauss- Bonnet theorem. Coordinate transformations and tensors in ndimensions; n-dimensional Riemannian spaces, covariant uiiferentiation, 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.
PMATH 380AIntroduction to Information Theory with Applications3C 0.5
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.
PMATH 380BInformation Theory with Applications3C 0.5
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. Cross-listed as AM 380b..
PMATH 430AIntroduction to Mathematical LogicF,W,S 2C,1T 0.5
A broad introduction to Mathematical Logic. The logic of sentences: truthfunctions and axiomatic approaches (eg. Natural Deduction and Gentzen sequences), A brief intraduétion to the logic of predicates and to the foundations of mathematics.
Will be of interest to all math students.
Credit will be granted for only 1 of PMATH 430a, 432a.
PMATH 430BIntroduction to Mathematical Logic Continuation of PMATH 430a. Gédel'sW 2C,1T 0.5
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: PMATH430a.
Will be of interest to all math students.
Credit will be granted for only 1 of PMATH 430b, 432b.
First order languages and theories. This course is more specialized and at a more advanced Jevel than PMATH 430. Credit will be granted for only 1 of PMATH 430a, 432a. Offered in Winter 1985 and each alternate Winter thereafter.
PMATH 465Topics in Differential GeometryW 2C\1T 0.5
Grassman algebras, differential forms, Lie derivatives, isometries, Killing vector fields, applications to continuum mechanics, differentiable manifolds and applications of differential forms to physics. ‘