33 courses in the 1986–87 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Mathematics Electives -
Course Descriptions
Courses not offered in the current academic year are listed at the end of this section.
introductory Note.
MTHEL courses are not restricted to students in the Faculty of Mathematics. When taken by Mathematics students, MTHEL courses count as nonmathematics electives.
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-Euciidean geometry, and computability of functions.
Prereq: None
Not offered every year
230A.
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
Will be of particular interest to students in programs outside of Pure Mathematics.
Antireq: MATH 322A, PMATH 351A
Not available for credit to students in Honours Pure Mathematics Programs.
Rings, ideals, 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, errorcorrecting codes.
Prereq: MATH 23438
Will be of particular interest to students in programs outside of Pure Mathematics.
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 2248.
Will be of interest to all math studenis.
Antireq: PMATH 440
Groups, rings, fields and applications. Prereg: MATH 234B PMATH 344 may be substituted for 334 whenever this is a requirement in an Honours program. : ‘ Antireq: MATH 324, PMATH 334
‘
Metric spaces, compactness, completeness, continuity, convergence, integration, function spaces. Prereq: MATH 2308 : PMATH 351A may be substituted for 331 whenever this is a requirement in an Honours program. Antireg: MATH 322A, PMATH 337°
Real Analysis Ii . Applications of PMATH 351A concepts to Fourier series, differential equations and other topics.
Prereq: PMATH 351A
- PMATH 352 FS 3C 05 © Compiex Analysis Analytic functions, Cauchy's theorem, Laurent series, the residue theorem, integral evaluation, Mobius and other conformal maps. : \ PMATH 352 may be substituted for MATH 3328 whenever this is a requirement in an Honours program. Antireq: MATH 3228, 3328
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inver sion in circles.
Prereq: MATH 2248
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 ss, theorem. Coordinate transformations and tensors in n-dimensions; r-dimensional Riemannian spaces, covariant differentiation, geodesics, the curvature, Ricci ‘and Einstein tensors, Applications of tensors in Relativity and Continuum Mechanics.
Prereq: MATH 2308 or consant of instructor 5
Cross-listed as AM 362.
Intuitive set theory, metric spaces, point
set topology. Prereq: MATH 230A
‘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 entro-. piés. 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.
A broad introduction to Mathematical. Logic. The logic of sentences: truthfunctions and axiomatic approaches (eg. Natural Deduction and Gentzen sequences). A brief introduction to thelogic of predicates and {to the foundations of mathematics.
Will be of interest.to all math
students.
Antireq: PMATH 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.
Antireq: PMATH 4328
‘
Course whorensivanse 16.107
pure Methemetics
First order lariquages and theories.
Antireq: PMATH 430A
PMATH 432A is more specialized. and presented al a more advanced level than PMATH 430A.
Next offered in Winter 1987 and each alternate Winter thereafter.
Mathematical Logic : Continuation of PMATH 432A. A ‘traatment of at least one of the following: set theory, model theory, undecidability. Prereq: PMATH 432A an Antireg: PMATH 4308 Next offered in Fall 1987 and each. altemate Fall thereafter.
An introduction to elementary and analytic number theory; primitive roots, jaw of quadratic reciprocity, Gaussian. sums, Riemann zeta-function, distribution of prime numbers. Prereq: MATH 3328 (or PMATH 382) Antireq: PMATH 340 ; Offered in Winter 1966, and each alternate Winter thereafter.
An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichiet’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. ‘
Continuation of linear algebra. Main topics: representations of endomorp-
- hisms; structure of bilinear forms, multi
near products. | Prereq: MATH 234A Not offered every year.
Continuation of the theory of rings and modules.
Prereq: PMATH 334 or 344
Permutations, Cayley Theorem, Sylow
Theorem, Jordan-Hdkier Theorem, nitpo-
tent and solvable groups, direct and
semidirect products, free groups. Prereq: PMATH 334 or 344
Course Descriptions | Mathematics: Stalietics. .
Field extensions and’ Galois theory. Prereq: PMATH 334 or 344 Next offerad in Fall 1987
Measure and integration Lebesgue measure and integral for the’ real line, general measure and integration theory, convergence theorems, Fubini‘s theorem, absolute continuity, Racion Nikodym theorem, LP-spaces.
Prereq: PMATH 331 or 351A or. consent of instructor.
The Riemann mapping theorem and several topics such as analytic continuation, harmonic furictions, elliptic functions, entire functions, univalent func- - tions, special functions. Prereq: PMATH 352
Banach spaces, linear operators, geom-
atry of Hilbert spaces, Hahn-Banach
theorem, open mapping theorem.
compact operators, applications. Prereq: PMATH 3518 or consent of
instructor
Grassman algebras, differential forms, Lie derivatives, isomatries, Killing vector fields, applications to continuum - mechanics, differentiable manifolds and applications of differential forms to physics.
Prereq: AM 362/PMATH 366 or consent, of instructor
Cross-listed as AM 474.
Topics from algebraic, combinatorial and geometric topology. Prereq: PMATH 367, MATH 2348
Cauchy's, Pexider’s, and similar equa-
tions. Equations for polynomials and
trigonometric functions. Reduction to
different equations. Applications. Prereq: Consent of instructor
" PMATH 499 Reedinge in Pure Mathematics
Not offered in 1986–87.
Not offered in 1986–87.
Not offered in 1986–87.