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ALGEBRA REPORT Algebra is a branch of mathematics in which letters are used to represent basic arithmetic relations As in arithmetic the basic operations of algebra are addition subtraction multiplication division and the extraction of roots Arithmetic cannot generalize mathematical relations such as the Pythagorean theorem which states that the sum of the squares of the sides of any right triangle is also a square Arithmetic can only produce specific instances of these relations for example 2 3 4 But algebra can make a purely general statement that fulfills the conditions of the theorem a b c Any number multiplied by itself is termed squared and is indicated by a superscript number 2 Classical algebra which is concerned with solving equations uses symbols instead of numbers and uses arithmetic operations to establish ways of handling symbols Modern algebra has evolved from classical algebra by increasing its attention to the structures within mathematics Mathematicians consider modern algebra to be a set of objects with rules for connecting them Algebra may be described as the language of mathematics HISTORY The history of algebra started in Egypt and Babylon where people learned how to solve linear and quadratic equations They also learned to solve indeterminate equations where several unknowns are involved Babylonians used basically the same procedures that are used today In Alexandrian times Diophantus book Arithmetica led the way in finding difficult solutions to indeterminate equations This early knowledge was embraced by the Islamic world where it was known as the science of restoration and balancing The Arabic word for restoration is al-jabru hence the word algebra In the 9th century the Arab mathematician Al-Khwarizmi wrote one of the first Arabic algebras a systematic expose of the basic theory of equations with both examples and proofs By the end of the 9th century the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities
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