#### Date on Master's Thesis/Doctoral Dissertation

3-2013

#### Document Type

Senior Honors Thesis

#### Department

Mathematics

#### Author's Keywords

Homological algebra; Projective dimension; Ideal; Zero divisor; Fibonacci numbers; Tor functor; Betti numbers

#### Abstract

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.

#### Recommended Citation

Philipp, Ian, "Homological algebra : Tor functors, Betti numbers, and free resolutions." (2013). *College of Arts & Sciences Senior Honors Theses.* Paper 20.

Retrieved from http://ir.library.louisville.edu/honors/20