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The history of algebra itself is broken into several sub-categories, and has been expanded upon by several hundred of the world's greatest mathematicians. Some of the sub-categories include the Fundamental Theorem of Algebra, abstract linear spaces, as well as quadratic, cubic and quartic equations. Not only can Algebra be divided into sub-categories as subjects, but the groups that studied, or developed them can also categorize them. Egyptian Algebra, Babylonian Algebra, Greek Geometric Algebra, Diophantine Algebra, Hindu Algebra, Arabic Algebra, European Algebra since 1500, and modern Algebra are the most popular categories. All the different theories within Algebra each have been worked millions of times, checked and rechecked for their validity, and many have been proven incorrect. The work of each mathematician has been built upon by their successors, and is still changing presently. (3)
The actual word, "ALGEBRA", comes from the Arabic al-jabr, which means, "the reunion of broken parts". One of the most influential early mathematicians was a man named al-Khwariami. He is known as being so influential because he wrote one of the first Arabic algebras and also introduced the writing down of calculations in place of using an abacus. His collection of works is the basic theory of all equations, and includes examples and proofs for this early form of Algebra. . By the 12th century, a Latin translation of al-Khwarizmi's "Algebra" was created, and that translation is largely responsible for what modern-day Algebra has become. (2)
Another major groups of people to greatly contribute to early Algebra were the Ancient Babylonians. They are the first known people to have solved the quadratic equations much like we solve them today. Similar teaching methods to the present day ones were used during their time, and many of the new ideas are based off of ancient ideas and original problem solving methods. Diophantus of Alexandria first wrote down some of these methods in the 3rd century AD. Diophantus wrote a book called, "Arithmetica", which still gives many good solutions to difficult indeterminate equations.
When these ancient civilizations began writing out their algebraic expressions, they used only occasional abbreviations. However, Islamic mathematicians, by medieval times, already began learning how to talk about high powers of the unknown "x", and started working out polynomials. This included the knowledge of how to multiply, divide, and find square roots. They also knew of the binomial theorem by this time, which was very important. Around the time that these Islamic mathematicians were discovering this material, a Persian man by the name of Omar Khayyam was busy becoming one of the most influential people in the history of Algebra. Khayyam discovered how to express roots of cubic equations by line segments obtained by intersecting conic sections, but he could not find a formula for the roots. (5)
Not too long after that same time period, in the 13th century, an Italian mathem
Quotes talked about in this paper
- Diophantus wrote a book called, "Arithmetica", which still gives many good solutions to difficult indeterminate equations. When these ancient civilizations began writing out their algebraic expressions, they used only occasional abbreviations. However, Islamic mathematicians, by medieval times, already began learning how to talk about high powers of the unknown "x", ...
- He wrote Book III of "La geometrie", ...
Names referenced in this essay
Leonardo Fibonacci, Robert Recorde, Omar Khayyam, William Oughtred, Diophantus, Rene Descartes, Book III, Carl Gauss, Thomas Harriot, John Widman, Rev. John Wallis, John Pell, George Boole, J.H. Rahn, R.T. Gunther,
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Locations mentioned in this paper
Egypt, England, India, Babylon, Europe, Oxford., Alexandria,
Keywords referenced in this paper
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