Finitely Generated Abelian Groups (Roughly Sections 4 & 11) 
Sections 1, 2, & 5 - Simplicial Complexes and Homology Groups
   Example 1   Example 2   Example 3  
Section 3 - Abstract Simplicial Complexes
Section 6 - Surfaces  
Section 7 - Dimension Zero and Reduced Homology
Section 8 - Cones
Section 9 - Relative Homology and Excision
Skip Section 10.
Section 12 
Section 13
Chapter 2: 14-19
Skim Secion 20 on your own.
Section 21 Don't let this happen to you!
Section 22 




Online Course Starts Here ("Holomogy in the Time of COVID-19")

Monday, March 23
Example: Homology Groups of S2 x S3 x S7 x S7. 
Section 26: notes 
Section 26, Braid Lemma and application: notes video (works best in Chrome) webm video format
Read over Sections 27 & 28 on your own.


Wednesday, March 25
Start Chapter 4.
Section 29, Part I: notes video


Friday, March 27.
Section 29, Part II: notes video 
Section 30, Part I:  notes video


Monday, March 30.
Section 30, Part II, Axiom 5: notes  video a  video b 


Wednesday, April 1.
Section 31, Axiom 6, Excision: notes video 1 video 2 video 3 
Note: we skip Sections 32 & 33.


Friday, April 3.
Continue studying the Excision lecture.


Monday, April 6.
Section 34: notes video 1 video 2
Note: We skip Sections 35 & 36; skim Section 37 on your own.


Wednesday, April 8.
The Hurewicz Homomorphism  video 1 video 2


Friday, April 10.
Section 38, CW Complexes. notes video

Monday, April 13.
Section 39, Homology of CW Complexes. 
notes 1 video 1 
notes 2 video 2 
notes 3 [Optional Reading] 
 
Wednesday, April 15. 
Section 40, Projective Spaces. notes video 
            Lens. coming soon (optional)

Friday, April 17. 
Start Chapter 5, Cohomology. 
Section 41: The Hom Functor: notes video 

 
Monday, April 20. 
Section 42: Simplicial Cohomology: notes 1 video 1
                                   notes 2 video 2

Wednesday, April 22.
Section 43: Relative Cohomology (skim)
Sections 44-6: Cohomology Theory (skim)


Friday, April 24.
Section 47:  notes video


Monday, April 27.
Section 48: notes video


Wednesday, April 29.
Section 49: notes video  
            example video 1  video 2  


Friday, May 1.
Section 73: notes video
See also: https://en.wikipedia.org/wiki/Solenoid_(mathematics)
Paper I wrote that uses Cech thoery.

Final Exam Due: Sunday, May 31.



Bonus Lectures!!

Section 50, Tensor Products of Abelian Groups: notes video
Section 10: notes video
Section 51: notes video