34 courses in the 1981–82 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Note
More detailed course descriptions and course outlines are available upon request from the Pure Mathematics Department.
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Ideas and examples in geometry, number theory, algebra, and analysis. Modern theories are motivated by consideration of historically important topics such as angle trisection, solution by radicals, the real number system, non-Euclidean geometry, and computability of functions.
Prereq: None
Similar to, but independent of PMath 230a. Prereq: None
Groups, rings, fields and applications.
Prereq: Math 244b or consent of instructor.
N.B.: PMath 344 may be substituted for Math 334b whenever this is a requirement in an Honours programme.
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 230a/b
N.B.: P Math 351a may be substituted for Math 332a whenever this is a requirement in an Honours programme.
Continuation of PMath 351a.
Prereq: PMath 351a
Course Descriptions Pure Mathematics
Holomorphic functions, Cauchy’s integral theorem, Cauchy’s integral formulas, Taylor and Laurent expansions, classification of isolated singularities, the Residue theorem.
Prereq: Math 230a/b
N.B.: P Math 352a may be substituted for Math 332b whenever this is a requirement in an honours programme.
Continuation of PMath 352a.
Prereq: P Math 352a
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Curves in Euclidean 3-space (E°) and 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: Math 230a/b, or consent of instructor.
N.B.: Cross listed with AM 362.
Intuitive set theory, metric spaces, point set topology.
Prereq: Math 230a
A broad introduction to Mathematical Logic. The logic of sentences: truth-functions and axiomatic approaches (eg. Natural Deduction and Gentzen sequences). A brief introduction to the logic of predicates and to the foundations of mathematics. N.B.: This course will be of interest to all math students. Credit will only be granted for one of P Math 430a or 432a.
Continuation of P Math 430a. Gddel’s 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: P Math 430a
N.B.: This course will be-of interest to all math Students. Credit will only be granted for one of
P Math 430b or 432b.
First order languages and theories. This course is more specialized and at a more advanced level than P Math 430.
N.8.: Credit will only be granted for one of P Math 430a or 432a.
Offered alternate years.
Continuation of P Math 432a. A treatment of at least one of the following; set theory, model theory, undecidability.
Prereq: P Math 432a
N.B.: Credit will be granted for only one of P Math 430b or 432b.
Offered alternate years.
reciprocity, applications to Diophantine equations. Prereq: Third or fourth year standing or consent of instructor. N.B.: This course will be of interest to all honours math students.
Continuation of P Math 441a.
Prereq: Math 334b or P Math 344, and P Math 441a
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Continuation of the theory of rings and modules. Prereq: Math 334a/b or P Math 344
Offered in Fall 1982.
Course Descriptions 399
Pure Mathematics
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups. Prereq: Math 334b or P Math 344
Offered in Winter 1982 and Fall 1983.
Field extensions and Galois theory. Prereq: Math 334b or P Math 344 Offered in Fall 1981 and Winter 1983.
An introduction to integration and measure theory with emphasis on the real line.
Prereq: Math 332a or P Math 351a/b
Banach spaces and linear operators. Prereq: P Math 451a
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Differentiable manifolds, vector fields, linear connections, tensor fields, differential forms and structure equations.
Prereq: P Math 365/AM 362 or consent of instructor N.B.: Cross listed with AM 463.
Topics from pseudo-Riemannian and Riemannian geometry such as: isometries and Killing vector fields; sectional curvatures; submanifolds; normal co-ordinates; variation of geodesics and Jacobi fields; conformally related spaces.
Prereq: P Math/AM 463 or consent of instructor. N.B.: Cross listed with AM 474
Topics from algebraic, combinatorial and geometric topology.
Prereq: P Math 367
Offered in Winter 1982 and Fall 1982.
Cauchy's, Pexider's, and simitar equations. Equations for polynomials and trigonometric functions. Reduction to differential equations. Applications. Further topics, such as equations for functions of several variables, or equations for analytic functions, or equations on algebraic structures.
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