Date of Award
5-2012
Level of Access Assigned by Author
Open-Access Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Advisor
Ali Ozluk
Second Committee Member
Andrew Knightly
Third Committee Member
William O. Bray
Abstract
The partition function has long enchanted the minds of great mathematicians, dating from Euler's attempts at calculating the value of this function in the 1700's, to Hardy and Ramanujan's asymptotic approach in the early twentieth century, through to Rademacher's representation as an explicit infinite series mid-century. This thesis will explore the historical attempts at grasping the behavior of this function, with particular attention paid to Euler's Pentagonal Number Theorem and Rademacher's Infinite Sum. We will then explore two reformulations due to Ono et al., with sample calculations from the recent algebraic reformulation, announced January, 2011.
Recommended Citation
Igo, Emily, "On the Algebraic Reformulation of the Partition Function" (2012). Electronic Theses and Dissertations. 1740.
https://digitalcommons.library.umaine.edu/etd/1740