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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 390
Course Title: Introduction to Topology
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

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.
Text(s): Most current editions of the following:

General Topology
By Willard, Stephen (Dover Publications)
Introduction to Topology
By Gamelin, Theodore and Greene, Robert (Dover Publications)
Course Objectives
  • 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.
    Measurable Learning
  • 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.
    Topical Outline:
  • Metric spaces
  • Topological spaces
  • Convergence
  • Completeness
  • Compactness
  • Connectedness
  • Separation

    Recommended maximum class size for this course: 20

    Library Resources:

    Online databases are available at You may access them using your CougarTrack login and password when prompted.

    Prepared by: Suzanne Tourville Date: November 7, 2013
    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.

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