1. history of algebra
TRANSCRIPT
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Prepared by:Mr. Christopher N. Satiada
Math IV Teacher
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The history of algebra began inancientEgypt and Babylon,where people learned to solve
linear(ax = b) and quadratic (ax2+ bx = c) equations, as well asindeterminate equations suchas x2 + y2 = z2, whereby several
unknowns are involved.
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The ancient Babylonianssolved arbitrary quadratic
equations by essentially thesame procedures taught
today. They also could solveindeterminate equations.
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The AlexandrianmathematiciansHero andDiophantus continued the
traditions of Egypt andBabylon, but Diophantus' book
Arithmetica is on a muchhigher level and gives many
surprising solutions to difficult
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In the Islamic world, where itwas known as the science ofrestoration and balancing.
(The Arabic word for restoration,
al-jabru, is the root of the word
algebra, and algebra as ascience is an Arabic
contribution.)
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In the 9th century, al-Khwarizmiwrote one of the
first Arabic algebras, asystematic expos of the basic
theory of equations, with bothexamples and proofs.
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By the end of the 9th century theEgyptian Abu Kamil (850-930)stated and proved the basic laws
and identities of algebra andsolved such complicated
problems as finding x, y,and z such that x + y + z = 10,
x2 + y2 = z2, and xz = y2.
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Ancient civilizations wrote out
algebraic expressions, using only
occasional abbreviations, but by
medieval times Islamicmathematicians were able to talk
about arbitrarily high powers of the
unknown x, and work out the basicalgebra of polynomials (without yet
using modern symbolism).
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In the 12
th
century , a Latin translation ofal-Khwarizmi's Algebra, and in the early13th century appeared the writings of the
great Italian mathematicianLeonardoFibonacci (1170-1230), among whoseachievements was a close approximation
to the solution of the cubic equationx3 + 2x2 + cx = d.
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Early in the 16th century, the Italianmathematicians Scipione del Ferro (1465-
1526), Niccol Tartaglia (1500-57), andGerolamo Cardano (1501-76) solved the
general cubic equation in terms of the
constants appearing in the equation.Cardano's pupil, Ludovico Ferrari (1522-65), soon found an exact solution to
equations of the fourth degree, and as a
result, mathematicians for the next several
centuries tried to find a formula for the roots
of equations of degree five, or higher.
Early in the 19th century, however, the
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An important development in algebra in the
16th century was the introduction ofsymbols for the unknown and for algebraicpowers and operations. Thus Book III of the
French philosopherand mathematicianRen Descartes'Lagometrie (1637) looksmuch like a modern algebra text.
Descartes is most significant in mathematics,however, for his discovery of analytic
geometry, which reduces the solution of
geometric problems to the solution of
algebraic ones.
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Until 1799 was the proof published, by the
German mathematician Carl FriedrichGauss, that every polynomial equation has atleast one root.
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Groups began as systems of permutations andcombinations of roots of polynomials, but they
became one of the chief unifying concepts of19th-century mathematics.
Important contributions to their study were
made by the French mathematicians Galoisand Augustin Cauchy, the Britishmathematician Arthur Cayley, and the
Norwegian mathematicians Niels Abel andSophus Lie (1842-99).Quaternions were
the discovery of the British mathematicianWilliam Rowan Hamilton,who extended the
arithmetic of complex numbers to quaternions
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Immediately after Hamilton's discovery, the German
mathematician Hermann Grassmann (1809-77) began
investigating vectors . Despite its abstract character,American physicist J. W. Gibbsrecognized in vector
algebra a system of great utility for physicists, just as
Hamilton had recognized the usefulness of quaternions.
The widespread influence of this abstract approach led tothe publication in 1854 of George Boole's The Laws of
Thought, an algebraic treatment of basic logic. Since that
time, modern algebraalso called abstract algebrahas
continued to develop. Important new results have been
discovered, and the subject has found applications in all
branches of mathematics and in many of the sciences, as
well.