Modern Day Algebra Essay
“basic units” of algebra [Allen]. These concepts undoubtedly, integrated and related many areas of mathematics, amongst these, topology, theory and analysis [Allen].
The Fundamental Theorem of Algebra
As the study of algebra became more expansive and necessary, it became of extreme importance to many other disciplines as well. And as remarkable mathematicians made new discoveries, algebra developed and progressed as a mathematical science. Prodigious individuals such as Descartes and Fermat were founders in the creation and development of analytical geometry, including theory on polynomials.
Polynomial theory, thanks to Descartes, then became a topic of great interest. Therefore, algebra came to be identified with the “theory of polynomials” [Corry]. And so, the need to solve equations of a higher order than four, gave rise to the Fundamental Theorem of Algebra. The theorem states: “Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers” [FTA]. Many mathematicians, such as, Leibniz, Euler, Laplace and D’Alembert attempted to prove this to no avail. It was not until 1799 that Gauss, Fig 1, provided the first complete proof to this theorem in his doctoral dissertation [FTA]. Gausses’ efforts led to the complex numbers of the form a + bi, which in turn led to fields and later to rings [Allen].
Figure 1, Carl Friedrich Gauss 
Algebra, as it is known today, encompasses a wide range of mathematics. In essence, it…