We will be using Chuck Weibel's book 
"Introduction to homological algebra". The syllabus will develop as we go 
along.

<br><br> <b>Lecture 1. Sep. 4, 1.1
</b>
Complexes of R-modules. Exercises: 1.1.1, 1.1.2, 1.1.4, 1.1.5

<br><br>
<b>Lecture 2. Sep. 8, 1.2
</b>
Abelian categories. Operations on chain complexes. 
Exercises: 1.2.1, 1.2.2, 1.2.5, 1.2.6, 1.2.8

<br><br>
<b>Lecture 3. Sep. 11, 1.3. 
</b> 
Long exact sequences. 
Exercises: Prove the Snake Lemma, 1.3.3, 1.3.4, 1.3.5. 

<br><br>
<b>Lecture 4. Sep. 15. 
</b>
Solving exercises from the book.


<br><br>
<b>Lecture 5. Sep. 18, 1.4.
</b>
Chain homotopies. 
Exercises: 1.4.2, 1.4.4, 1.4.5


<br><br><b>
Lecture 6. Sep. 22, 2.1.
</b>
Delta functors.

<br><br><b>
Lecture 7. Sep. 25, 2.2
</b>
Projective resolutions.
Exercises: 2.2.1, 2.2.2

<br><br><b>
Lecture 8. Sep. 29, 2.2-continued, 2.3
</b>
Exercises: 2.2.4, 2.3.1, 2.3.2

<br><br><b>
Lecture 9. Oct. 2, 2.3-continued, 2.4
</b>

<br><br><b>
Lecture 10. Oct. 6, 2.4-continued
</b>

<br><br><b>
Lecture 11. Oct. 9, 2.4-continued, 2.5
</b>

<br><br><b>
Lecture 12. Oct. 13, 2.7
</b>

<br><br><b>
Lecture 13. Oct. 16, 2.7-continued, 3.1
</b>

<br><br><b>
Lecture 14. Oct. 20, Hilbert Syzygy Theorem
</b>

<br><br><b>
Lecture 15. Oct. 23, Hilbert Syzygy Theorem-continued, 3.4
</b>

<br><br><b>
Lecture 16. Oct. 27, 3.4-continued
</b>

<br><br><b>
Lecture 17. Oct. 30, 3.6
</b>

<br><br><b>
Lecture 18. Nov. 3, Spectral sequences of filtered complexes (from G-H book)
</b>

<br><br><b>
Lecture 19. Nov. 6, 5.1, 5.2
</b>

<br><br><b>
Lecture 20. Nov. 10, 5.2-continued
</b>

<br><br><b>
Lecture 21. Nov. 13, 5.5
</b>

<br><br><b>
Lecture 22. Nov. 17, 5.6
</b>

<br><br><b>
Lecture 23. Nov. 20, 5.7
</b>

<br><br><b>
Lecture 24. Nov. 24, 5.8
</b>

<br><br><b>
Lecture 25. Nov. 25 (Tuesday!), 10.1
</b>

<br><br><b>
Lecture 26. Dec. 1, 10.2
</b>

<br><br><b>
Lecture 27. Dec. 5, 10.3
</b>

<br><br><b>
Lecture 28. Dec. 8, 10.4
</b>