40 courses in the 1979–80 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
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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
Fundamentals of group, ring, field theory, and other algebraic structures.
Coreq: Math 231a
N.B.: PMath 341a may be substituted for Math 331a whenever this is a requirement in an honours programme.
Continuation of PMath 341a
Prereq: PMath 341a
N.B.: PMath 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.B.: PMath 351a may be substituted for Math 332a whenever this is a requirement in an honours programme.
Continuation of PMath 351a. Prereq: PMath 3512
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.: PMath 352a may be substituted for Math 332b whenever this is a requirement in an honours programme.
Continuation of PMath 352a. Prereq: PMath 352a
Concurrent lines, collinear points, the Euler line, the Simson line, the nine-point circle. Cross ratio, projection, harmonic range, the quadrilateral and the quadrangle. Properties of circles.
Prereq: None
Course Descriptions 367 Pure Mathematics
Projective spaces over fields, collineations and correlations, quadric curves and surfaces. References to non-euclidean geometries.
Prereq: Math 231a/b
The plane of complex numbers. The group of circle-preserving mappings and its subgroups. Connections with non-euclidean geometries (Laguerre, Minkowski).
Prereq: Math 231a/b
Curves in Euclidean 3-space (£°) 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-dinemsional Riemannian spaces, covariant differentiation, geodesics, the curvature, Ricci and Einstein tensors.
Prereq: Math 230a/b, or consent of instructor.
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 Deductign). The logic of predicates and quantifiers. Foundations of Mathematics.
N.B.: Credit will only be granted for one of PMath 430a or 432a.
Continuation of PMath430a. Gédel’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: PMath 430a
N.B.: Credit will only be granted for one of PMath 430b or 432b.
First order languages and theories. This course is more specialized and at a more advanced level than PMath 430.
N.B.: Credit will only be granted for one of PMath 430a or 432a.
Continuation of P Math 432a. A treatment of at least one of the following: set theory, model theory, undecidability.
Prereq: PMath 432a
N.B.: Credit will only be granted for one of PMath 430b or 432b.
Elementary Theory of Numbers, quadratic reciprocity, applications to Diophantine equations.
Coreq: Math 331a/b or PMath 341a/b
Continuation of PMath 441ta. Prereq: PMath 441a
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Continuation of the theory of rings and modules. Prereq: Math 331a/b or PMath 341a/b -
Offered in Fall 1979 and Winter 19817.
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups.
Coreq: Math 331a/b or PMath 341a/b
Offered in Fall 1980.
Field extension and Galois theory. Prereq: Math 331a/b or PMath 341a/b Offered in Winter 1980 and Fall 1987.
An introduction to integration and measure theory with emphasis on the real line.
Prereq: Math 332a or PMath 351a/b
Course Descriptions Pure Mathematics
Continuation of PMath 45 ta. Prereq: PMath 451a
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Differentiable manifolds, vector fields, linear connections, tensor fields. differential forms and structure equations.
Prereq: PMath 365/AM 362 or consent of instructor
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Linear connections and Riemannian structures, geodesics and variations of geodesics, differential forms, integration theory and Stokes’ theorem. Prereq: PMath 463/AM 463, or consent of instructor
Topics from algebraic, combinatorial and geometric topology.
Prereq: PMath 367
Cauchy's, Pexider’s, and similar equations. Equations for polynomials and for trigonometric functions. Reduction to differential equations. General methods and theorems. Iteration. Applications. Further topics, such as equations for functions of several variables, or equations for analytic functions, or equations on algebraic structures.
Continuation of PMath 470a. Prereq: PMath 470a