Request for the Approval of a Topics
Course
Course Title and Number (include cross-listing): MATH 471 Topics:
Introduction to Topology
Credits: 4 credits.
Are you seeking Distribution Credit? No.
In What Major(s) can this course be used? Mathematics.
Course Description: This course will serve as an introduction to the topology
of Euclidean spaces and manifolds, with an emphasis on basic sets (disks,
spheres, annuli, Cantor sets) in lower dimensional space. Continuous maps,
homeomorphisms, and embeddings will be studied in conjunction with
connectedness and paths, convergence and compactness, manifolds, homotopy,
contractible sets, the Brouwer fixed-point theorem, and covering spaces. At the
end of the course, each student will complete an individual project based on a
research article that examines one of the major areas (e.g. physical knot
theory) in the modern study of topology.
Required Texts: Topology: A First Course,
Munkres, James R., Prentice-Hall Incorporated, 1975 and selected articles from
journals.
Prerequisites: Calculus II
Staffing Implications (Please be specific. Every
course must have staffing implications, even if those implications are small.) An instructor (Trautwein)
will teach this course as part of his regular fall teaching load.
Rationale: This course has been offered in the past as an
independent study. The demand to offer topics courses in the Mathematics
Department has increased over the past two years and such courses have been
successful in attracting students.