Physical Sciences and Mathematics Commons^™

Homological Algebra : Tor Functors, Betti Numbers, And Free Resolutions., Ian Philipp

College of Arts & Sciences Senior Honors Theses

The topic of study for this project is homological algebra, a branch of mathematics with applications to a plethora of other branches of mathematics as well as sensor networks, signal processing, uid dynamics, particle physics, etc. The amount of literature written on this topic is vast and there are numerous open problems in homological algebra, but this project has a more modest focus. First, we will explain the fundamental terminology with several examples and later we will proceed to some results concerning certain rings and ideals, and then results about modules generated by zero divisors.