PMATH 230A Introduction to Pure Mathematics
Not offered 1982-83.
PMATH 230b introduction to Pure Mathematics Not offered 1982-83.
Pure Mathematics (PMATH)
34 courses in the 1982–83 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
PMATH 344 MATH 334 MATH 324
Listed without a description.
PMATH 351A MATH 332a MATH 322a
Listed without a description.
PMATH 352A MATH 332b }~= MATH 322b
Listed without a description.
PMATH 340 Elementary Number TheoryW 3C 0.5
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. This course will be of interest to all math students. Credit will be granted for only one of PMATH 340 and PMATH 44 1a.
PMATH 344 Abstract AlgebraF 3C 0.5
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.
PMATH 351A Real AnalysisF,S 3C 0.5
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.
PMATH 351B Real AnalysisW 3C 0.5
Continuation of PMATH 351a. Prereq: PMATH 351a.
PMATH 352A Complex AnalysisF,S 3C 0.5
Holomorphic functions, Cauchy's integral theorem, Cauchy's integral formulas, Taylor and Laurent expansions, Classification of isolated singularities, the Residue theorem.
Prereq: MATH 2306, PMATH 352a may be substituted for MATH 332b whenever this is a requirement in an Honours program.
PMATH 352B Complex AnalysisW 3C 0.5
Continuation of PMATH 352a. Prereq: PMATH 382a.
PMATH 360 GeometryF 3C 0.5
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inversion in circles.
Prereq: MATH 224b. This course will be of interest to all math students.
PMATH 365 Differential Geometry and Tensor AnalysisF,S 2C,1T 0.5
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; ndimensional 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 with AM 362.
PMATH 367 Set Theory and General TopologyW 3C 0.5
Intuitive set theory, metric spaces, point set topology.
Prereq: MATH 230a
PMATH 399 Readings in Pure Math
PMATH 430A Introduction 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 introduction to the logic of prédicates and to the foundations of mathematics. ‘ This course will be of interest to all math students. Credit will be granted for only one of PMATH 430a or 432a.
PMATH 430B Introduction 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: PMATH 430a. This course will be of interest to all math students. Credit will be granted for only one of PMATH 430b or 432b.
PMATH 432A Mathematical LogicF 3C 0.5
First order languages and theories. This course is more specialized and at a more advanced level than PMATH 439. - Credit will be granted for only one of PMATH 430a or 432a. Offered alternate years. Next offered Fall 1983.
PMATH 432B Mathematical LogicW 3C 0.5
Continuation of PMATH 432a. A treatment of at least one of the following; set theory, mode! theory, undecidability.
Prereq: PMATH 432a. Credit will be granted for only one of PMATH 430b or 432b. Offered alternate years. Next offered Winter 1984.
PMATH 441A Number TheoryF 2C 0.5
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 or PMATH 441a. Offered alternate years. Next offered Fall 1982.
PMATH 441B Number TheoryW 2C 0.5
Continuation of PMATH 441a.
Prereq: MATH 334 (or PMATH 344) and PMATH 44 1a. Offered alternate years. Next offered Winter 1983.
PMATH 443 Linear Algebra 2
Not offered 1982-83.
PMATH 445 Ring TheoryF 2C 0.5
Continuation of the theory of rings and modules. ‘
Prereq: MATH 334 or PMATH 344. Offered in Fall 1982 and Winter 1984.
Course Descriptions
Mathematics.
PMATH 446 Group TheoryF 2C 0.5
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups. Prereq: MATH 334 or PMATH 344. Offered in Fall 1983.
PMATH 447 Field TheoryW 2C 0.5.
Field extensions and Galois theory. Prereg: MATH 334 or PMATH 344. Offered in Winter 1983 and Fall 1984.
PMATH 451A Measure and IntegrationF 3C Q5
An introduction to integration and measure theory with emphasis on the real line.
Prereq: MATH 332a or PMATH 351a/b .
PMATH 451B Functional AnalysisW 3C 0.5
Banach spaces and linear operators. Prereq: PMATH 481a
PMATH 452A Complex Analysis 2a
Not offered 1982-83.
PMATH 452B Complex Analysis 2b
Not offered 1982-83.
PMATH 461 Finite Geometries
Not offered 1982-83.
PMATH 463 Differentiable ManifoldsF 2C,1T 0.5
Differentiable manifolds, vector fields, linear connections, tensor fields, differential forms and structure equations.
Prereq: PMATH 365/AM 362 or consent of instructor. Cross-listed with AM 463.
PMATH 465 Selected Topics in Differential GeometryW 2C,1T 0.5
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: PMATH/AM 463 or consent of instructor. Cross-listed with AM 474
PMATH 467 TopologyF 2C 0.5
Topics from algebraic, combinatorial and geometric topology.
Prereq: PMATH 367 and MATH 234b
PMATH 470A Functional EquationsF 2C 0.5
Cauchy's, Pexider’s, and similar equations. Equations for polynomials and trigonometric functions. Reduction to differential equations. Applications.
PMATH 470B Functional Equations
Not offered 1982-83.
PMATH 499 Readings in Pure Math
Statistics Course Descriptions