Graduation Year

Spring 2013

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Chris Towse

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© 2013 Julia J. Ogburn

Abstract

Newton polygons are constructions over the p-adic numbers used to find information about the roots of a polynomial or power series. In this the- sis, we will first investigate the construction of the field Qp on the p-adic numbers. Then, we will use theorems such as Eisenstein’s Irreducibility Criterion, Newton’s Method, Hensel’s Lemma, and Strassman’s Theorem to build and justify Newton polygons.

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