32 courses in the 1985–86 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Courses not offered in the current academic year are listed at the end of thie section.
Introductory 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
Not offered every year
PMATH 2305 2C,1T 05 introduction to Pure Mathematics Similar to, but independent of, PMATH 2Wa.
Prereq: None
Not offered every year
Topology of R", continuity, norms, metrics, completeness, Fourier series, and applications, for example, to 0.D.E.’s, the heat problem, optimal approximation, the isoperimetric inequality.
Prereq: MATH 230a (MATH 230b desirable)
Will be of particular interest to students in programs outside of Pure Mathematics. .
Credit will be granted for only 1 of MATH 3224, PMATH 331, 351a.
Not available for credit to students in Honours Pure Mathematics Programs.
Rings, ideais, factor rings, homomorphisms, finite and infinite fields, polynomials and roots, field extensions, algebraic numbers, and applications, for example, to Latin squares, finite geometries, geometrical constructions, error-correcting codes.
Prereq: MATH 234b
Will be of particular interest to students in programs outside of Pure Mathematics.
Credit will be granted for only 1 of
Not available for credit to students in Honours Pure Mathematics programs.
An elementary approach to the theory of numbers; the Euclidean algorithm, congruence equations, multiplicative functions, solutions to Diophantine equations, continued fractions, and rational approximations to real numbers.
Prereq: MATH 224b
Will be of interest to alt math students.
Credit will be granted for only 1 of PMATH 340, 440.
Groups, rings, fields and applications. Prereq: MATH 234b PMATH 344 may be substituted for 334 whenever this is a requirement in an Honours program. Credit will be granted for only 1 of MATH 324, PMATH 334, 344.
Metric spaces, compactness, completeness, continuity, convergence, integration, function spaces.
Prereq: MATH 230b
PMATH 351a may be substituted for 331 whenever this is a requirement in an Honours program.
Credit willbe granted for only 1 of MATH 322a, PMATH 331, 351a.
to Fourier series, differential equations and other topics.
Prereq: PMATH 351a
16.105
Analytic functions, Cauchy’s theorem, Laurent series, the residue. theorem, integral evaluation, Mébius and other conformal maps.
Prereq: MATH 230b
PMATH 352 may be substituted for MATH 332b whenever this is a requirement in an Honours program.
Credit will be granted for only 1 of MATH 322b, 332b, PMATH 352
Formerly: 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.
Analysis . 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 230b or consent of instructor
Cross-listed as AM 362.
Intuitive set theory, metric spaces, point set topology.
Prereq: MATH 230a
PMATH 38a 3C 05 Introduction to Information Theory with Applications Variable length coding. The Shannon entropy as measure of uncertainty and expected information. Minimal average length coding; the Shannon entropy as lower bound. Source entropy. Channels. Transinformation. Capacity. Applications to problem solving, information transmission, logics science, linguistics and ~ communications (TV, music, etc.). Determination of practical measures of information. Prereq: Consent of instructor Cross-listed as AM 380a.
Measures of conditional uncertainty (entropy). Maximizing conditional entropies. Applications to statistical physics, statistics, pattern recognition. Special entropies in questionnaire theory. Design of optimal questionnaires. Special entropies in dynamical systems. Basics in dynamical systems. Prereq: Consent of instructor Cross-listed as AM 380b.
PMATH 399 ; Readings in Pure Mathematics
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 predicates and to the foundations of mathematics.
Will be of interest to all math studenis.
Credit will be granted for only 1 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 aif math students.
Credit will be granted for only 1 of PMATH 430b, 432b.
First order languages and theories.
Credit will be granted for only 1 of PMATH 430a, 432a.
PMATH 432a is more specialized and presented at a more advanced level than PMATH 430a.
Next offered in Winter 1987 and each alternate Winter thereafter.
Continuation of PMATH 432a. A treat: ment of at least one of the following: set theory, modet theory, undecidability.
Prereq: PMATH 432a
Credit will be granted for only 1 of PMATH 430b, 432b.
Next offered in Fall 1985 and each alternate Fall thereafter.
An introduction to elementary and analytic number theory; primitive roots, law of quadratic reciprocity, Gaussian sums, Riemann zeta-function. distribution of prime numbers.
Prereq: MATH 332b (or PMATH 352)
Creait will be granted for only 1 of PMATH 340, 440.
Offered in Winter 1986, and each alternate Winter thereafter.
Formerly: PMATH 441a
An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichlet’s unit theorem, solutions of Diophantine equations, Fermat's ‘last theorem’.
Prereq: PMATH 334 or 344
Next offered Fall 1986, and each alternate Fall thereafter.
Formerly: PMATH 4416
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products. Prereq: MATH 234a Not offered every year.
Continuation of the theory of rings and modules. Prereq: PMATH 334 or 344
tent and solvable groups, direct and semidirect products, free groups. Prereq: PMATH 334 or 344 Next offered in Fall 1986.
Field extensions and Galois theory. Prereq: PMATH 334 or 344
Lebesgue measure and integral for the real line, general measure and integration theory, convergence theorems, Fubini’s theorem, absolute continuity, Radon Nikodym theorem, LP-spaces. Prereq: PMATH 331 or 351a or consent of instructor. Formerly: PMATH 451a
Course Descriptions Mathematics: Pure Mathematics
The Riemann mapping theorem and several topics such as analytic continuation, harmonic functions, elliptic functions, entire functions, univalent functions, special functions.
Prereq: PMATH 352
Formerly: PMATH 352b
Banach spaces, linear operators, geometry of Hilbert spaces, Hahn-Banach theorem, open mapping theorem, compact operators, applications. Prereq: PMATH 3516 or consent of instructor Formerly: PMATH 451b
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, MATH 234b
Cauchy’s, Pexider’s, and similar equations. Equations for polynomials and trigonometric functions. Reduction to different equations. Applications.
Not offered in 1985–86.
Not offered in 1985–86.
Not offered in 1985–86.