Um breve estudo introdutório à teoria dos números algébricos e transcendentes

Abstract

The main objective of this work is to introduce and familiarize the reader with the concept of Algebraic and Transcendent Numbers, showing how these numbers are defined as well as their respective representatives, sometimes little known, but widely used during the undergraduate study. At first, we will recall some fundamental concepts such as Basic Notions of Sets and some definitions of Abstract Algebra and Real Analysis that will serve as a basis for a better understanding and development of this work as a whole. Then, we will study about the body of Complex Numbers, in order to define them in a clear and objective way, studying some of its properties and particularities, especially the Gaussian Integers. Finally, we will introduce the concept of Algebraic and Transcendent Numbers, highlighting some of its main properties and curiosities, still opening space for the reader to seek new and more in-depth knowledge on this subject.