Math. 655 Syllabus



Grading Policy

Grades in the course will be determined on the following basis:

Homeworks and class pariticipation 100 points
Quizes 100 points
Take-home final 200 points



Syllabus and Calendar

The following syllabus is somewhat tentative. It is possible that there might be some slippage and some topics might be omitted. The precise quiz dates will be announced at least one week in advance.

Week of Topics Covered
Sept. 24 Euler's formula, informal discussion of topology
Sept. 29 Metric spaces, continuity, topological spaces: definitions and examples
Oct. 6 Connectedness, path connectedness
Oct. 13 Quiz 1, compactness
Oct. 20 Space-filling curves, countability, separation axioms
Oct. 27 Function spaces, completeness, Banach fixed-point theorem, applications
Nov. 3 Tietze extension theorem, Urysohn metrization theorem, Quiz 3
Nov. 10 Identification (quotient) spaces, topological groups, orbit spaces
Nov. 17 Quiz 4, projective spaces, manifolds
Nov. 24 Classification of 1-manifolds, classification of surfaces
Dec. 1 Classification of surfaces contd., Quiz 5