35 courses in the 1980–81 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.
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 P Math 230a. Prereq: None
Fundamentals of group, ring, field theory, and other algebraic structures.
Coreq: Math 231a
N.B.: P Math 341a may be substituted for Math 331a whenever this is a requirement in an honours programme.
Continuation of P Math 341a.
Prereq: P Math 341a
N.B.: P Math 341b may be substituted for Math 331b 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.8,: P Math 351a may be substituted for Math 332a whenever this is a requirement in an honours programme.
Continuation of P Math 351a. Prereq: P Math 351a
Course Descriptions 387 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 P Math 352a. Prereq: P Math 352a
Listed without a description.
Listed without a description.
The plane of complex numbers. The group of circlepreserving mappings and its subgroups. Connections with non-euclidean geometries (Laguerre, Minkowski).
Prereq: A knowledge of linear algebra.
N.B.: This course will be of interest to all math students.
Curves in Euclidean 3-space (E%) and the Serret- Frenet formulae; surfaces in E3 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/b
A broad introduction to Mathematical Logic. The logic of sentences: truth-functions and an axiomatic approach (Natural Deduction). The logic of predicates and quantifiers. 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. Gédel’s incompleteness theorem (in outline). Logicism, intuitionism, formalism. Selected topics (some of intuitionistic logic, modal logic, the represenation 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.B.; Credit will only be granted for one of P Math 430a or 432a.
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 only be granted for one of P Math 430b or 432b.
Elementary Theory of Numbers, quadratic 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 math students.
Continuation of P Math 441a. Coreq: Math 3310 or P Math 341b
Listed without a description.
Continuation of the theory of rings and modules. Prereq: Math 331a/b or P Math 341a/b
Offered in Winter 1981 and Fall 1982
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, niipotent and solvable groups, direct and semidirect products, free groups. Coreq: Math 331a/b or P Math 341alb
Offered in Fali 1980 and Winter 1982
Field extensions and Galois theory. Prereq: Math 331a/b or P Math 341a/b Offered in Fall 1987.
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 algebraic, combinatorial and geometric topology.
Prereq: P Math 367
Listed without a description.
Solutions of special functional equations. Theorems about genera! types of equations. General and restricted domains. Mathematical and other applications.
Course Descriptions 389