28 courses in the 1990–91 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
PMATH 344Abstract Algebra 2F,S 3C 0.5
Field theory, examples of fields, field of fractions, algebraic extensions, construction of roots, separable extensions, splitting fields, classification of finite fields. Finite non-Abelian groups, Sylow theorems. Introduction to Galois theory..
Prereq: PMATH 343 or PMATH 336 with consent of instructor
An introduction to affine, projective and non-Euclidean forms of geometry. Conic sections in the projective plane. Inversion in circles. Theorems of Desargues, Pappus, and Pascal. Prereq: MATH 224B or 225 This course will be of interest to all math students.
PMATH 365Elementary Differential Geometry and Tensor AnalysisF,S 3C 0.5
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:AM 231 or MATH 2308, or consent of instructor
PMATH 380AIntroduction to Information TheoryF,S 3C 0.5
Variable length coding. The Shannon entropy as a measure of uncertainty and expected information. Minimai 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. an Ls
PMATH 380BApplications of Information TheoryW 3C 0.5
Measures of information: probabilistic, mixed and nonprobabilistic. Measures of uncertainty (entropies). Entropies for continuous random variables. The maximum entropy principle and its applications to: statistical mechanics, optimal discretization and quantization of random variables, image representation and pattern recognition. Applications to questionnaires. Optimal questionnaires.
PMATH 430AIntroduction to Mathematical Logic 1F,W,S 3C 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 predicates and to the foundations of mathematics.
PMATH 430BIntroduction to Mathematical Logic 2 Continuation of PMATH 430A. Gédel's3C 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).
An introduction to elementary and analytic number theory; primitive roots, law of quadratic reciprocity, Gaussian sums, Riemann zeta-function, distribution of prime numbers.
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 in Winter 1991, and each alternate Winter thereafter.
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.
Some global aspects of surface theory, the Euler-Poincaré characteristic, the global interpretation of Gaussian curvature via the Gauss-Bonnet formula. Submanifolds of E", induced Rieman- - nian metrics, extrinsic and intrinsic curvatures, Gauss-Codazzi equations. Local Lie groups of transformations on - R’, infinitesimal generators, the Lie derivative. An introduction to differentiable manifolds, the tangent and cotangent bundles, affine connections and the Riemann curvature tensor. The above topics will be illustrated by applications to continuum mechanics and mathematical physics.
Courses not offered in the current academic year are listed at the end c**his section.
C100 3C 05 Introduction to the Study of Leisure and Recreation and Leisure Services 1 overview of the field of recreation t phasizing the understanding of le:sure phenomena as well as an introduction to various leisure service ‘ ources.
| 3200 3C 0.5
Theories of Piay
A critical analysis of definitions, {cepts and assumptions of classical, tant and modern theories of play with implications for research strategies, programming and planning for play.
f 3201 3C 0.5 { slology of Leisure Nature and extent of leisure phenomena in contemporary society. 1 amination of institutional and formal « anizational aspects, social role, social research strategies employed in the study of leisure.