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# History of Algebra, Essay Example

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Introduction

This paper explores the history of algebra; it will deeply describe how the algebra started and who were the core founders and facilitators of algebra movement to different parts of the continent. It will indicate how the algebra started and how it has worked in science and mathematics in different countries and its use in the current world. Therefore, algebra is a branch of mathematics which uses symbols mostly than definite numbers for mathematical arithmetic operations. This form of mathematics is divided into three branches; linear algebra, elementary, and modern algebra. The history of algebra can be traced all the way from Egypt and Babylon, from this places people could easily solve equations such as linear (ax=b) and also quadratic equations such as ax+bx=c. People from Babylon could easily solve quadratic equations with the current method taught in schools nowadays. It is argued that the father or founder of algebra was the Alexandrian Greek mathematician known as Diophantus in between 200AD-284AD, which later became the tradition of Egyptians and Babylonians through Diophantus. Also there has been a debate among different people that the al-Khwarizmi the Arabian mathematician who wrote the book of Al-jabr also known as ‘’ the ‘’science of restoration’’ is the founder of the algebra and deserves the title while others have argued that the Diophantus who wrote the book of arithmetica is the father of the algebra (NovZ, 2004).

Algebra has been divided in different groups such as classical algebra which find the unknown number, there is also abstract algebra which involves the study of rings, groups, and fields, and this is also described as the current algebra being used in the schools. The algebra has developed through different stages till the current algebra; the following algebra in relation with countries indicates the algebra history. Egyptian algebra, Babylonian, Greek geometric, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra, and the modern, these regions indicated how the algebra started and the way it has grown to different countries. Therefore, through the following ages, clearly describes the algebra progression to the rest of the world. In consideration of Egyptian Algebra we can be able to determine that, after the algebra was founded it started being practiced by other countries. For instance, the application started with Babylonians and Egyptians. According to Egyptian mathematics, this algebra equation was recorded in Rhind papyrus in between 1650 B.C. and 1850 B.C. Therefore, this method ensures people are able to solve problems relating to linear equation, which was also a method known as method of false position. Therefore, during Egyptian the algebra used no symbols as it was rhetorical, and in case of any problems, they were discussed and solve verbally. In addition, The Babylonian period which ranged between 1800 B.C-1600 B.C., the mathematics applied was more improved than that one which was being applied at the Egypt. In Babylonians people used a system known as sexagesima also known as numeration system which also led to the development of a Kline algebra. This algebra had a common method which could equivalently solve the quadratic equations; they mostly considered one root and that was supposed to be positive. Babylonian also concentrated in the comparable of their systems in the two unknowns in relation to the two equations. Consequently, Greek Geometrical Algebra was during the classical period, in their procedure they did not identify the existence of the numbers which are irrational , they were keen to avoid any problem which later on was produced when demonstrating quantities in the form of geometrical degrees. However, in Greek Geometrical Algebra there was identification of different algebraic with creations comparable to the elucidation of quadratic equations which were to be articulated and be confirmed in geometric structure. Therefore, in Greek geometrical algebra period only a little was done, in relation to the expansion algebra, this led to retardation in the growth of algebra for several years. In this stage only little was done in relation to what Babylonians, had done (Monna, 2003).

In 250 A.D. the Greek mathematician Diophantus also came up with another strategy which was known as syncopated mode of equations inscription. This was the movement organised between him and other fellows known as Archimedes, Ptolemy, Heron, and Apollonius all who were Greeks, they struggled in order to finish the existence of geometrical algebra to something else which was to be independent upon the geometry. Therefore, the accomplishment of rhetorical mode of writing was also left in the use to an rest of other centuries. There was also another period of Hindu algebra, therefore, after the Greeks period the Hindu Algebra became the successors from the Greeks as indicated in the history of mathematics. The Hindus of India gained their civilization at 2000 B.C., and their involvement in mathematic was dated at 800 B.C., Therefore, their involvement in mathematics was motivated by astrologist and astronomy. They were to some extend being affected by the number zero as they mostly considered it should not be included in calculations. In this period Hindu learned a lot that they had not, together with invention of new terms. They really came up with strategies of operating irrational numbers. They also came up with some symbolism which led to identification of the Hindu algebra as symbolic but different from syncopated algebra related to Diophantus. They were also affected by the fact that their quadratic equations had a total of two roots, they also included negative root together with irrational root and could not be used in evaluating quadratics as the recognition of square roots associated with negative numbers as numbers, this led to them being innovative hence advancement through attainment of whole number clarifications. This happed through application of a procedure equivalent to the modern current method. They also concentrated working with the intermediate equation (Martin, 2002).

In addition, Arabic Algebra is another period of history of algebra development which should be considered. During the 7^{th} and 8^{th} centuries Arabs overpowered the Indian dwellers under the leadership of Mohammed, this enabled them to pursue the arts and sciences in the 14^{th} century which enabled them to have greater advancement in science which was made on the western side. Therefore, they took over the symbols which were being used by the Hindus and improved them together with the positional concept ideas. This led to combination of the concept to Hindu-Arabic of numeration together with algorithms; these concepts were all transferred to then European countries in the year 1200. This numerical are up to date being used globally. Therefore, it is this Arabian people who named most of the algebra hence have they have names related to them. For instances, the algebra name come the book’s title which is based in the subject of Hisab al-jabr w’al muqabala which was also translated to ‘’Restoring and Simplification’’ which was printed in 830 by Mohammed ibn-Musa al-Khowarizimi who was a mathematician and a stronomer. However, algebra application with Arabs was wholly rhetorical, that is in evaluation of quadratic equations, they normally recognized two solutions, and they only considered the irrational but discarded negative solutions. Arabs also contributed in evaluation method of cubic equations by the use of geometric process which involved the intersection. Finally the European Algebra came after the 1500, during this time the zero had already been accepted as a number although some of the people were not totally convinced about zero’s state as a number. At this period the negative numbers were recognised but not entirely acknowledged. Therefore, it is during the 19^{th} century people came to accept some of the numbers which they had not entirely acknowledged. There was huge development in technique in the 16^{th} century which led to provision of solution to cubic and quartic equations. These achievements which were known as Boyer and ranged as one of the utmost contribution to the algebra, it was considered great because since the Babylonians were educated on how to solve quadratic equations four millennia ago, there was no other achievement like it. To conclude, British mathematicians in 19^{th} century made the lead the algebra study, they introduced vectors, matrices, transformations, etc. Thus they extended the algebraic study to algebraic forms and structures. Some mathematicians in British such as Peacock initiated the axiomatic thinking in arithmetic and algebra (Bashmakova & Smirnova, 2000)

Conclusion

Finally, algebra in mathematics had a long process of development which happened within different countries with different ethics. The improvement in algebra was facilitated by a number of mathematicians till today. However, the advancement and development has not yet reached the optimal point, as the technology change things will keep changing even in the field of algebra.

References

Bashmakova I., & Smirnova G., (2000). *The Beginnings and Evolution of Algebra*, Dolciani

Mathematical Expositions 23. The Mathematical Association of America, pp. 456-500.

Monna A., (2003). *L’Algebrisation de la mathematique: reflexions historiques.* Mathematisch

Instituut der Rijksuniversiteit Utrecht, Utrecht, pp. 123-156.

Martin A., (2002). *A historical survey of algebraic methods of approximating the roots of*

*numerical higher equations*. Columbia university, New York, pp. 156-176.

NovZ L., (2004). *Origins of modern algebra.* Translation from the Czech: Jaroslav Tauer.

Noordhoff International Publishing, Leiden, pp. 320-340.

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