Course Descriptions

16:640:560 - Homological Algebra

Daniel Krashen


An introduction to homological algebra, by C. Weibel, Cambridge U. Press


First-year knowledge of groups and modules.


From some perspectives, homological algebra is the study of the failure of modules over rings (and related objects) to behave like vector spaces. Somewhat more precisely, homological algebra collects a number of ideas and tools with origins in topology, such as chain complexes and derived functors, to study categories of modules and other Abelian categories. Homological algebra is fairly ubiquitous, and finds applications in 

module theory over rings

representations of groups and Lie algebras

sheaves on algebraic varieties

algebraic topology

various other subjects

Schedule of Sections: