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


Course Description

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









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