Robinson, ZacharyTeller, Jacek2012-05-202012-05-202012http://hdl.handle.net/10342/3848This thesis offers a clear introduction to p-adic number fields, and the method of Newton polygons to approximate the size of roots of polynomials in the completion of the algebraic closure of p-adic number fields. Ostrowski's theorem is also proved herein. The thesis is intended to serve as an aperitif to further study in the area.  49 p.dissertations, academicMathematicsComputer sciencePhysicsFieldsHensel's lemmaNewton polygonsOstrowski's theoremRootsP-adic numbersNewton diagramsMaster's Thesis