Math 205: Topology
Time: MWF, 11:55AM  12:45PM
Location: Physics 235
Instructor: Paul Bendich
Office Hours: Physics 210, Mondays 34, Fridays 12
Main Textbooks: we will using two textbooks, both by James R. Munkres.
They are
Topology: A First Course, and Elements of Algebraic Topology ,
and are referred to as "T" and "AT" in the syllabus below. We will also use
some supplementary handouts of my own creation.
Date  Topics  Chapters  Assignments 

Aug. 29  Overview, Introduction, Motivating Examples   
Aug. 31  Preliminaries: Set Therory, Logic, Functions  T: 1  HW 
Sept. 2  Topological Spaces: Definition and Basic Examples  T: 21  HW 
Sept. 4  Topological Spaces: Bases  T: 22  HW 
Sept. 7  Product Topology, Subspace Topology  T: 24 25  HW 
Sept. 9  Limit Points, Closure  T: 26  HW 
Sept. 12  Continuous Functions I  T: 27  HW 
Sept. 14  Continuous Functions II  T: 27  HW 
Sept. 16  Metric Spaces I  T: 29  
Sept. 19  Metric Spaces II  T: 210  HW 
Sept. 21  Quoitent Topology  T: 211  HW 
Sept. 23  Connectedness I  T: 31  HW 
Sept. 26  Connectedness II  T: 32, 33  HW 
Sept. 28  Compactness I  T: 35  HW 
Sept. 30  Compactness II  T: 36  HW 
Oct. 3  Compactness III  T: 37  HW 
Oct. 5  Simplicial Complexes I  AT: 1,2,3  
Oct. 7  Simplicial Complexes II  AT: 1,2,3  
Oct. 12  (Linear) Algebra Review  handout, AT: 4  
Oct. 14  Simplicial Homology: Definition  AT: 5  
Oct. 17  Homology: Examples  AT: 6  
Oct. 19  Homology of a Cone  AT: 8  
Oct. 21  Relative Homology  AT: 9  
Oct. 24  Singular Homology  AT: 29  
Oct. 26  Functoriality  AT: 29, 12  
Oct. 28  LES of a Pair  AT: 23  
Oct. 31  ZigZag Lemma  AT: 24  
Nov. 2  MayerVietoris LES  AT: 25  
Nov. 4  Homotopy of Paths  T: 81  
Nov. 7  Fundamental Group  T: 82  
Nov. 9  Covering Spaces I  T: 83  
Nov. 11  Covering Spaces II  T: 83  
Nov. 14  Fund. Group of the Circle  T: 84  
Nov. 16  Fund. Group of the Circle  T: 84  
Nov. 18  Fund. Group of nspheres.  T: 85, 86  
Nov. 21  Fund. Group of nspheres.  T: 85, 86  
Nov. 28  Fund. Group of surfaces.  T: 87  
Nov. 30  Review  

Dec. 2  Review  