Instructor: Sarah Witherspoon
Phone: 845-6178
Email: sjw AT math.tamu.edu
Office and hours: Milner 322, MW 1:15-2:45 and by appointment

Course web address: http://www.math.tamu.edu/~sjw/662/math662.html

Class meetings: TR 11:10-12:25 in Milner 216

Course description
3.0 credits. Problems, methods and recent developments in algebra. May be taken five times for credit as content varies.

Homology refers to various invariants of groups, rings, modules, and spaces by which many of their properties may be expressed. Homological algebra encompasses useful techniques for computing and interpreting homology in algebraic contexts, a fundamental subject underlying many parts of modern algebra, topology, and geometry. In this introductory course, we will discuss the basic terminology and methods of homological algebra which may then be applied in future courses, in research, and to understanding talks and papers in which homology appears.

Specific topics to be covered include: chain complexes, resolutions, Ext and Tor, derived functors, homological dimension, bicomplexes, Kunneth Theorems, and spectral sequences. Further topics may include (co)homology of groups, Lie algebras, and Hopf algebras, and Hochschild (co)homology.