34 courses in the 1983–84 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Introductory Notes
More detailed course descriptions and course outlines are available upon request from the Pure Mathematics Department.
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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 all math students. Credit will be granted for only one of PMATH 340, 44174..
Groups, rings, fields and applications. Prereq: MATH 244b, or consent of instructor.
PMATH 344 may be substituted for MATH 334 whenever this is a requirement in an Honours program. Offered in Fall 1983, 1984. Offered in Winter from 1985 on.
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 MATH 332a whenever this is a requirement in an Honours program.
Continuation of PMATH 351a. Prereq: PMATH 351a.
Holomorphic functions, Cauchy's integral theorem, Cauchy's integral tormulas, 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.
Course Descriptions
Mathematics.
Pure Mathematics
Continuation of PMATH 352a. Prereq: PMATH 352a.
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.
Curves in Euclidean 3-space (E%) and the Serret-Frenet formutae; surfaces in £3 and their intrinsic geometry, Gaussian curvature and the Gauss- Bonnet theorem. Coordinate transformations and tensors in ndimensions; 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.
Intuitive set theory, metric spaces, point set topology.
Prereq: MATH 230a
A broad introduction to Mathematical Logic. The logic of sentences: truthfunctions and axiomatic approaches (eg. Naturat 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. Credit will be granted for only one of PMATH 430a, 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. Credit will be granted tor only one of PMATH 430b, 432b.
First order languages and theories. This course is more specialized and ata more advanced level than PMATH 430. Credit will be granted for only one of PMATH 430a, 432a. , Oftered in Fall 1983 and Winter 1985.
Continuation of PMATH 432a. A treatment of at least one of the following; set theory, model theory, undecidability.
Prereq: PMATH 432a.
Credit will be granted for only one of PMATH 430b, 432b.
Offered in Winter 1984 and Fall 1985.
Elementary Theory of Numbers, quadratic reciprocity, applications to Diophantine equations.
Prereq: Third or fourth year standing or consent of instructor.
Credit will be granted for only one of PMATH 340, 441a.
Offered in Fall 1984 and Winter 1986.
Continuation of PMATH 441a.
Prereq: MATH 334 (or PMATH 344) and PMATH 441a.
Next offered Fall 1986.
Continuation of the theory of rings and modules.
Prereq: MATH 334 or PMATH 344. Offered in Winter 1984 and Fall 1985.
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups. Preraq: MATH 334 or PMATH 344. Offered in Fail 1983 and Winter 1985.
Field extensions and Galois theory. Prereq: MATH 334 or PMATH 344. Offered in Fall 1984.
An introduction to integration and measure theory with emphasis on the real line.
Prereq: MATH 332a or PMATH 351a
Banach spaces and linear operators. Prereg: PMATH 451a
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: PMATH 367 and MATH 234b
Not Offered 1983-84.
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