Math 205: Topology
Time: MWF, 11:55AM - 12:45PM
Location: Physics 235
Instructor: Paul Bendich
Office Hours: Physics 210, Mondays 3-4, Fridays 1-2
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: 2-1 | HW |
| Sept. 4 | Topological Spaces: Bases | T: 2-2 | HW |
| Sept. 7 | Product Topology, Subspace Topology | T: 2-4 2-5 | HW |
| Sept. 9 | Limit Points, Closure | T: 2-6 | HW |
| Sept. 12 | Continuous Functions I | T: 2-7 | HW |
| Sept. 14 | Continuous Functions II | T: 2-7 | HW |
| Sept. 16 | Metric Spaces I | T: 2-9 | |
| Sept. 19 | Metric Spaces II | T: 2-10 | HW |
| Sept. 21 | Quoitent Topology | T: 2-11 | HW |
| Sept. 23 | Connectedness I | T: 3-1 | HW |
| Sept. 26 | Connectedness II | T: 3-2, 3-3 | HW |
| Sept. 28 | Compactness I | T: 3-5 | HW |
| Sept. 30 | Compactness II | T: 3-6 | HW |
| Oct. 3 | Compactness III | T: 3-7 | 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 | Zig-Zag Lemma | AT: 24 | |
| Nov. 2 | Mayer-Vietoris LES | AT: 25 | |
| Nov. 4 | Homotopy of Paths | T: 8-1 | |
| Nov. 7 | Fundamental Group | T: 8-2 | |
| Nov. 9 | Covering Spaces I | T: 8-3 | |
| Nov. 11 | Covering Spaces II | T: 8-3 | |
| Nov. 14 | Fund. Group of the Circle | T: 8-4 | |
| Nov. 16 | Fund. Group of the Circle | T: 8-4 | |
| Nov. 18 | Fund. Group of n-spheres. | T: 8-5, 8-6 | |
| Nov. 21 | Fund. Group of n-spheres. | T: 8-5, 8-6 | |
| Nov. 28 | Fund. Group of surfaces. | T: 8-7 | |
| Nov. 30 | Review | |
|
| Dec. 2 | Review | |