The partition function, Euler's pentagonal number theorem, and the proof of the 5k+4 identity : [an honors thesis (HONRS 499)]
The partition function has a long, rich history of being one of the premier number theory concepts. Its uses include being involved in the golden ratio and molecular thermodynamics. The partition function also has some beautiful theory within it, particularly in some of its congruences. In this thesis I would like to focus on one congruence, particularly Ramanuj an's 5k+4 identity. Along the way, I would like to establish some of the underlying concepts in the proof, and give my reasons for taking this subject when there are so many others in the realm of mathematics. The first idea needed is to define a partition function and what it does, how it can be represented, etc. Hopefully this thesis will be beneficial to persons in the future discovering the beauty and grace of a function like the partition function.