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.