Modern Day Algebra Essay

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Abstract: This paper is a report on the development of algebra throughout time. It’s slow, but nevertheless, unyielding progression brings us to the algebra we know today. However, it was not always based on the abstract, rather, it was born out of necessity. The need to calculate unknown quantities gave rise to algebraic methods and techniques practiced and taught even today. And, even though nowadays, algebra is a rather abstract mathematics, this was not always the case. It was through centuries of work from remarkable individuals with an undying passion and curiosity that algebra slowly but surely evolved.

Introduction

In modern day mathematics, the term algebra denotes the manipulation of abstract symbols, solving equations for unknowns,
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This issue guided much of the progress attained in the 17 and 18th centuries [Allen]. It was during this time period that many noteworthy mathematicians with an unquenchable thirst for mathematical knowledge spent countless amounts of time in the development of modern day algebra. During this time, radicals were still a great issue. It was thought than no solutions by radicals could be accomplished and many expended their efforts in so proving this. However, as often times occurs, through the processes utilized in these efforts, other theories arose. The theory of substitutions, for example, was arrived at by the theory of equations. By the 20th century, algebra was much more than verbal solutions, or illustrated examples. It became the “study of mathematical structures with well-defined operations” [Allen]. This gave rise to the emergence of “groups, fields and rings,” the “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
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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

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