Homological algebra I 1000-1M02AH

This is an introduction to homological algebra and its applications in algebra , geometry and topology. The first part of the course presents the classical homological algebra methods. If time permits, the last few lectures will be devoted to the more modern approach to homological algebra via the language of derived categories.

1. Elements of category theory (categories, functors, additive and abelian categories )
2. Chain complexes and (co)homology
3. Derived functors of additive functors (with special attention paid to functors on categories of R-modules)
4. Spectral sequences and their applications in algebra, geometry and topology.
5. Derived categories.