Class Year

2017

Date

12-15-2016

Document Type

Thesis

Distinguished Thesis

Yes

Degree Name

Bachelor of Arts (BA)

Department or Program

Mathematics

First Advisor

Enrique Treviño

Second Advisor

DeJuran Richardson

Third Advisor

Michael M. Kash

Abstract

From our early years of education we learn that polynomials can be factored to find their roots. In 1797 Gauss proved the Fundamental Theo-rem of Algebra, which states that every polynomial every polynomial can be factored into quadratic and linear products. Here we build up the necessary background in advanced complex analysis to prove a variant of the Fundamental Theorem of Algebra, namely that every polynomial has at least one complex root. The proof we show here uses Cauchy’s Integral Formula and Liouville’s Theorem, which we develop and prove. This leads us into the brilliant ideas of conforming complex maps into each other and the limits we can push complex functions to.

Language

English


Included in

Analysis Commons

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