The Development of Algebra
Ancient algebra has its foundation in Egypt, Babylon, Greek, India and Diophantus. Classical and modern algebra formed the core of algebra. Egyptian algebra is one of the most ancient and depended upon single variables. As such, it was easier to solve verbally and without much problem. Babylonian algebra was more developed as it included solving equations with two unknowns. This meant that Babylonian algebra is the foundation of quadratic equations with linear formations. The Greeks, on the other hand, came up with a more elaborate way of solving equations through geometry. This was simpler as it had a measurable magnitude in terms of numbers. Renowned mathematicians like Pythagoras helped make the solving of these equations simpler by the use of theorems. Thereafter, so many other scientists contributed to the development of algebra through theorems and lemmas that showed the consequences of these important theorems.
Modern forms of algebra fuse the use of unknown variables together with numbers. This has made algebra less abstract than the form it takes in pure mathematics. These can differ from single and quadratic to those with variables having more powers (Case 1) (Behind-the-Scenes View of the Development of Algebra 1). Algebra also involved the multiplication of numbers so that the negative numbers give positive numbers while the positive numbers give positive. On the other hand, the multiplication of positive and negative numbers gives out a negative number. This confirms the fact that a negative and a negative give a positive while a positive and a negative gives a negative. Algebraic equations took the form of quadratic equations that had polynomials with powers. Polynomials represented through graphs that express the magnitude of variables against each other are common. For instance, values of two unknown variables, say x and y, can be drawn.
Modern algebra exhausts the use of numbers in a larger context called a field. A field contains exhaustive numbers ranging from simple to complex numbers. Simple numbers consist of integers and numbers in a real line. Complex numbers, on the other hand, include values that do not use numbers alone. This would imply the use of letters together with numbers to form algebraic numbers and expressions (Warner 1) (Modern Algebra). This makes modern algebra to take a more abstract form in comparison to classical algebra. Modern algebra uses set theory exhaustively setting foundation for the different classes of theories that exist. For instance, group theory, complex analysis and field theory are all sections of algebra that utilize set theory.
In conclusion, algebra is a very important part of mathematics. It forms the foundation for solving several problem sets. They are important in different fields including engineering and other scientific procedures that require mathematical manipulation to arrive at an answer. They are also important in solving equations and giving interpretations in economics and commerce. Stochastic processes require the accurate interpretation from solution of algebraic equations for forecasting the future. This means that algebra finds use in so many fields that are useful for professionals in different fields. Not only are they beneficial in abstract mathematics but also important in philosophy and practical fields like insurance and commerce. For instance, pure mathematics is mainly about abstract algebra while the other practical subjects use the interpretation of algebraic graphs to foresee trends in the future like in system design and analysis. It is therefore prudent to view the development of algebra from simple forms to the use of graphs that could be valuable in other fields for forecasting trends and so many other important issues as crucial for any economy.
Case, J. A Behind-the-Scene View of the Development of Algebra.
2006. SIAM. Web.
Warner, S. Modern Algebra.