The history of Algebra

The history of algebra began in ancient Egypt and Babylon, where people learn to solve linear (ax = b) and quadratic (ax ^ 2 + bx = c) equation, sertapersamaan indeterminate as x ^ 2 + y ^ 2 = z ^ 2, where some known to be involved. The ancient Babylonians could solve quadratic equations with the same procedure. They also could solve some indeterminate equations.
The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the tradition of Egypt and Babylon, but Diophantus book Arithmetica is in a much higher level and provide solutions surprise many difficult indeterminate equations.Ancient knowledge of the equation solution in turn found a home early in the Islamic world, where it was known as "the science of restoration and balancing." (Arabic for the restoration, al-jabru, is the root of the word algebra). In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arab algebra, a systematic description of the basic theory of equations, with both examples and evidence. At the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of the algebra and solve complex problems such as finding x, y, and z so that x + y + z = 10, x ^ 2 + y ^ 2 = z ^ 2, and xz = y ^ 2.
Ancient civilizations write algebraic expressions using only occasional abbreviations, but by medieval Islamic mathematicians able to talk about arbitrary high powers are unknown x, and worked out basic algebra polynomials (without yet using modern symbolism). This includes the ability to multiply, divide, and find the square root of a polynomial and knowledge-binomial theorem. Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by conic sections, but he could not find a formula for the roots. A Latin translation of Al-Khwarizmi's Algebra appeared in the 12th century. At the beginning of the 13th century, the great Italian mathematician Leonardo Fibonacci achieved close approach to the solution of the cubic equation x ^ 3 + 2 x ^ 2 + cx = d. Because Fibonacci had traveled in the land of Islam, he probably used the Arab approximation method.
At the beginning of the 16th century, Italian mathematician Scipione del Ferro, Niccolo Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation. Cardano's pupil, Ludovico Ferrari, soon find the right solution for the equation of the fourth degree (quartic lihatpersamaan), and as a result, mathematicians for the next few centuries trying to find a formula for the roots of equations of degree five or higher. At the beginning of the 19th century, however, the Norwegian mathematician Niels Abel and French mathematician Evariste Galoismembuktikan that no such formula does not exist.
An important development in algebra in the 16th century was the introduction of a symbol for the unknown and to the power of algebra and operations. As a result of these developments, Book III of géométrie La (1637), written by French philosopher and mathematician Rene Descartes, looks like a modern algebra text. Descartes' most significant contribution to mathematics, however, was the invention of analytic geometry, which reduces the problem solving algebraic geometry for solutions. His geometry text also contains the essence of the course on the theory of equations, including the so-called reign marks to count the number of so-called Descartes (positive) and "wrong" (negative) "correct" the root of an equation. Work continued through the 18th century on the theory of equations, but not published until 1799 is evidence, by the German mathematician Carl Friedrich Gauss, who showed that himpunaniap himpunanidaknya polynomial equation has one root in the complex plane (see Number: Complex Numbers).
At the time of Gauss, algebra had entered the modern phase.Attention shifted from solving polynomial equations to study the structure of the axioms of abstract mathematical systems based on the behavior of mathematical objects, such as complex numbers, which is encountered when learning math equation polinomial.Dua example of such a system algebraic group (see Group) and quaternions, which share properties properties of number systems but also depart from them in important ways.The group began as a system of permutations and combinations of the roots of a polynomial, but they became one of the major unifying concepts of mathematics of the 19th century. Important to study their contribution made by the French mathematician Galois and Augustin Cauchy, British mathematician Arthur Cayley, and the Norwegian mathematician Niels Abel and Sophus Lie. Quaternions invented by British mathematician and astronomer, William Rowan Hamilton, who extended the arithmetic of complex numbers to quaternions as complex number is the form a + bi, quaternions are of the form a + bi + cj + dk.
Soon himpunanelah Hamilton's invention, the German mathematician Hermann Grassmann began investigating vector.Despite the abstract character, the American physicist JW Gibbs recognized in vector algebra for physicists major utility systems, such as Hamilton acknowledges the usefulness quaternions.Widespread influence of the abstract approach that led to George Boole writes Legal Thought (1854), care of the basic algebra of logic. Since then, modern algebra is also called abstract algebra.
Sources:
http://www.algebra.com/algebra/about/history/