# Mathematics 560:

Homological Algebra

### Rutgers University, Spring 2010

### Anders Buch (asbuch at math dot rutgers period edu)

### Tentative Syllabus:

This will be an introduction to the subject of Homological Algebra.
Homological Algebra is a tool used in many branches of mathematics,
especially in Algebra, Topology and Algebraic Geometry.

The first part of the course will cover Chain Complexes, Projective and
Injective Modules, Derived Functors, Ext and Tor. In addition,
some basic notions of Category Theory will be presented: adjoint functors,
abelian categories, natural transformations, limits and colimits.

The second part of the course will study Spectral Sequences,
and apply this to several topics such as Homology of Groups and
Lie Algebras. Which topics we cover will be determined by the
interests of the students in the class.

Notes from class

### Textbook:

An introduction to homological algebra, by C. Weibel,
Cambridge University Press, paperback edition (1995)

### Course web site:

`http://sites.math.rutgers.edu/~asbuch/homalg_s10/`