Math 554: Foundations of Topology 2

From MathWiki
Revision as of 11:07, 14 November 2019 by Ls5 (Talk | contribs) (Catalog Information)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Catalog Information

Title

Foundations of Topology 2.

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

W

Prerequisite

Math 553 or instructor's consent.

Description

Fundamental group, retractions and fixed points, homotopy types, separation theorems, classification of surfaces, Seifert-van Kampen Theorem, classification of covering spaces, and applications to group theory.

Desired Learning Outcomes

Students should gain a familiarity with surfaces, fundamental group, and covering spaces.

Minimal learning outcomes

  1. The Fundamenatal Group
  2. The topology of the plane
    • Jordan Curve Theorem
  3. Seifert-van Kampen Theorem
  4. Classification of Surfaces
  5. Classification of Covering Spaces
  6. Group Theory
    • Free groups
    • Free abelian groups
    • Presentations of groups
    • Subgroups of free groups

Textbooks

Possible textbooks for this course include (but are not limited to):

Additional topics

Courses for which this course is prerequisite