Professor John Beachy, Watson 355, 753-6753

Office Hours: 11:00-12:00 MWF (or whenever you can find me)

COURSE: HOMOLOGICAL ALGEBRA (3)
Categories and functors, projective and injective modules, complexes and homology, Ext, Tor, and dimensions. Applications to cohomology of groups and ring theory. PRQ: MATH 521

TEXT: An Introduction to Homological Algebra, by Rotman, Academic Press, 1979

SYLLABUS (by chapter):

1: Introduction (Some history and motivating problems; categories and functors; tensor products)

2. Hom and tensor (Direct sums and products; exact sequences; adjoints; direct and inverse limits)

3: Projectives, injectives, and flats (Modules: free, projective, injective, and flat)

5': Extensions of modules (Notes on n-fold extensions of modules)

6: Homology (Homology functors; derived functors)

7: Ext (The functor Ext and its relation to extensions of modules)

8: Tor (The functor Tor and its relation to torsion in modules)

Unfortunately, it seems to be impossible to also cover several important chapters: Chapter 4: Specific Rings; Chapter 9: Son of Specific Rings; and Chapter 11: Spectral Sequences.

GRADING: Semester grades will be based on 500 points: 100 points for the midterm exam; 200 points for homework and other classwork; and 100 points for the final exam. The final exam is scheduled for Monday, Dec 6, 10:00-11:50 a.m.

TENTATIVE LECTURE SCHEDULE:

Week    Pages     Topic                                 S  M Tu  W Th  F  S
 1       1-22     Categories, tensor products     Aug  22 23 24 25 26 27 28
 2  23-34, 57-62  Sums, products, free modules         29 30 31  1  2  3  4
 3      34-39     Exactness, adjoints             Sep   5  6  7  8  9 10 11
 4      39-49     Direct limits                        12 13 14 15 16 17 18
 5      49-56     Inverse limits                       19 20 21 22 23 24 25
 6      62-75     Projectives and injectives           26 27 28 29 30  1  2
 7      84-94     Flat modules                    Oct   3  4  5  6  7  8  9
 8     166-178    Hom functors                         10 11 12 13 14 15 16
 9     178-193    Derived functors                     17 18 19 20 21 22 23
10      Notes     Extensions of modules                24 25 26 27 28 29 30
11     194-202    Ext                             Nov  31  1  2  3  4  5  6
12     202-211    Ext and extensions                    7  8  9 10 11 12 13
13     211-219    Axioms                               14 15 16 17 18 19 20
14     220-223    Tor                                  21 22 23 24 25 26 27
15     224-227    Tor and torsion                 Dec  28 29 30  1  2  3  4