Introduction to the topological concepts that underlie analysis. Included are metric spaces, topological spaces, separation, compactness, convergence, completeness and connectedness. Prerequisite: Grade of C or higher in MATH 222 and MATH 225. MATH 380 recommended.
Prerequisite(s) / Corequisite(s):
Grade of C or higher in MATH 222 and MATH 225. MATH 380 recommended.
Course Rotation for Day Program:
Offered even Fall.
Most current editions of the following:
By Willard, Stephen (Dover Publications) Recommended
Introduction to Topology
By Gamelin, Theodore and Greene, Robert (Dover Publications) Recommended
To generalize the concept of distance.
To examine the extent to which analytical concept can be developed in terms of topology.
To study examples which counter our Euclidean-based intuition.
To communicate mathematically, formally and informally, both verbally and in writing.
Determine if sets are open, closed or neither with respect to various topologies.
Find the closure, limit points, boundary and interior of sets with respect to various topologies.
Determine if spaces meet the criteria to be metric spaces of topological spaces.
Determine if functions defined on topological spaces are continuous.
Determine if sequences defined on topological space are convergent.
Determine if a topological space is compact, complete, connected, or separable.
Recommended maximum class size for this course: 20
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical
outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.