35 courses in the 1987–88 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions Introductory Notes
1. With the exception of the courses listed at the end of this section, the following courses are offered on a regular basis. \
2. More detailed course descriptions and course outlines are available upon request from the Pure HMathe matics Department.
ideas and examples in geometry, number theory, algebra, and analysis. Modern theories are motivated by consideratian 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
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 230B
For 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, hemomorphisms, finite and infinite fields, potynomials and roots, field extensions, algebraic numbers, and applications, for example, to Latin squares, fijite geometries, geometrical constructic ns, errorcorrecting codes.
For students in programs outside of Pure Mathematics.
Not available for credit to siudents in Honours Pure Mathematics programs.
An elementary approach to the theory of numbers; the Euclidean algorithm, congruence equations, multiplicative functions, solutions t& Diophantine equations, continued fractions, and rational approximations to rea) numbers.
Prereq: MATH 2248
Will be of interes: to all math students.
Antireq: PMATH 440
Groups, rings, fields and applications. Prereq: MATH 2348 PMATH 344 may be substituted for 334 whenever this i's a requirement in an Honours program. ; Antirag: MATH 324, PMATH 334
Metric spaces, compactness, complete-
ness, continuity, convergence, integra: tion, function spaces.
Prereq: MATH 230B
PMATH 3514 may be substituted for 331 whenevé this is'a requirement in an Honours program.
Antireq: KYATH 322A, PMATH 331
po
Course Descriptions 16:109 Mathematics: Pure Mathematics
to Fourier series, differential equations and other topics.
Prereq: PMATH 351A
Analytic functions, Cauchy’s theorem, Laurent series, the residue theorem, integrat evaluation, Mobius and other conformal maps.
Prereq: MATH 230B
PMATH 352 may be substituted for MATH 3328 whenever this is a requirement in an Honours program.
Antireq: MATH 3228, 332B
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inversion in circles.
Prereq: MATH 2248
Wil be of interest fo all math students.
Serret-Frenet formulae; surfaces in E9 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
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. Chahnels. 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
16:110 Course Descriptions Mathematics: Pure Mathematics
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
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 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 ail math students.
Antireq: PMATH 432B
First order languages and theories. Antireg: PMATH 430A PMATH 432A is more specialized and presented at a more advanced level than PMATH 430A.
ment of at least one of the following: set theory, model theory, undecidability.
Prereq: PMATH 432A
Antireq: PMATH 430B
Next offered in Fall 1989, 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) Antireq: PMATH 340 Next offered in Winter 1988, and each alternate Winter thereafter.
An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichlet’s unit theorem, solutions of Diophantine equations, Fermat's ‘last theorem’. : Prereg: PMATH 334 or 344 Next offered in Winter 1989, and each altemate Winter thereafter. \
Continuation of linear algebra. Main topics: representations of endomorphisms, structdre of bilinear forms, multilinear products. Prereq: MATH 2344 - Not offered every year.
Continuation of the theory of rings and modules. Prereq: PMATH ‘p34 or 344 Next offered in Fall 1988
tent and solvable groups, direct and semidirect products, free groups.
Prereq: PMATH 334 or 344
'
Field extensjons and (Galois theory. Prereg: PMATH 334 or 344.
Lebesgue measure and irttegral for the real line, general measure and integration theory, convergence theorems, Fubini’s theorem’ absolute continuity. Radon Nikodym theorem, L-space®.
Prereq: PMATH 331 or 381A, or consent of instructor.
The Riemann mapping theorem and several topics such as analytic continuation, harmonic functions, elliptic functions, entire functions, univalent functions, special functions.
Prereq: PMATH 352
Banach spaces, linear operators, geom-
etry of Hilbert spaces, Hahn-Banach
theorem, open mapping theorem.
compact operators, applications. Prereq: PMATH 351B or consent of
instructor.
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: MATH 234B, PMATH 367
Cauchy‘s, Pexider’s, and similar equa-
tions. Equations for polynomials and
trigonometric functions. Reduction to
different equations. Applications. Ptereq: Consent of instructor
Not offered in 1987–88.
Not offered in 1987–88.
Not offered in 1987–88.