Author

Emily Igo

Date of Award

5-2012

Level of Access

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.

Included in

Mathematics Commons

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