The invention of algebra from the ancient world has produced many opportunities for the modern world we live in today. According to the Webster’s Dictionary, “algebra by definition is the part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations.” First and for most, algebra is divided into two different groups, the first group being “classical algebra”, which is solving equations and finding the unknown variable. The second group is “abstract algebra” also called “modern algebra”, which is made up of real numbers, complex numbers, matrices, and vector spaces. In addition, algebra developed through algebraic notation in three different stages: the rhetorical or verbal stage, the syncopated stage, where words are abbreviated, and the stage we are most familiar with, symbolic stage, which are symbols such as minus, division, multiplication sign, parenthesis, brackets, exponents, logarithms, letters for variables, and the list goes on and on. The history of algebra began in Egypt, Babylon, India, and eventually spread throughout the world via the Arabs. The word algebra is an Arabic word al-jabr, meaning the reunion of broken parts. This best describes the method for solving both sides of an equation. Abu Ja’far Muhammad ibn Musa al-Khwarizimi or Father of Algebra is one of the greatest mathematicians ever known as well as the most influential for writing down the first algebraic calculations in place of the abacus; which is a mechanical device that used beads or balls that moved on a rod for calculations. One of al-Khwarizimi’s books, al-Kitab al mukhtasar fi Hisab al jabr w’al muqabala, shows how to solve basic equations and then moves in to the business of practical applications. Al-jabr is about removing negative terms from equations and al-muqabala is balancing the values of an equation across an equal sign. Algebra was incredibly important even from its early stages because it created a...

...Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes ("Letters"). Although not very important to the development of algebra, Archimedes (212BC 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics ("Archimedes").
Although little is known about him, Diophantus (200AD 284AD), an ancient Greek mathematician, studied equations with variables, starting the equations of algebra that we know today. Diophantus is often known as the "father of...

...The History of Algebra
The history of algebra has been around for several decades, this method of mathematics has been used during the beginning of time. The development of algebraic notation progressed through out three stages: the rhetorical stage, the syncopated stage, and the symbolic stage with which we are use to using in our daily usage of algebra. In ancient civilization math was used to help leaders to strategically form how their troops should be lined up for battle and help decide how to attack their enemies. Algebra was used in the many of these civilizations: Egypt, Babylon, Greece, India, Europe, and most parts of the Middle East. In Egypt, the Egyptians used mathematics which included Algebra to solve equivalent to a linear equation. They solved problems without using symbols but rather stated the problems and solved it verbally. Very seldom symbols were used by the Egyptians to solve an algebraic problem; Egyptians interpret algebra as a form of way of communicating how to solve equations, which is called “method of false position.”
In the ancient civilization of the Old Babylonian Period (1800-1600 B.C.) were more advanced than the Egyptians, they used a general procedure equivalent to solving quadratic equations, they mainly dealt with the equivalent of systems of two equations. The Babylonians taught algebra by using...

...HISTORY OF ALGEBRA
M AT H 1
WHAT IS ALGEBRA?
• Denotes various kinds of mathematical
ideas and techniques
• more or less directly associated with
formal manipulation of abstract symbols
and/or with finding the solutions of an
equation.
HISTORICAL OBJECTIVES
1. attempts to deal with problems devoted
to finding the values of one or more
unknown quantities.
2. the evolution of the notion of number
3. the gradual refinement of a symbolic
language
THE SEARCH OF “EQUATION”
• Egyptian Mathematics
Egyptian mathematical texts known to us dated
from about 1650 B.C.
• They attest for the ability to solve problems
equivalent to a linear equation in one unknown
• Later evidence, indicates the ability to solve
problems equivalent to a system of two
equations in two unknown quantities
THE SEARCH OF “EQUATION”
• Babylonian and Egyptian Mathematics
• Throughout this period there is no use of
symbols; problems are stated and solved
verbally, like in the following, typical example:
THE SEARCH OF “EQUATION”
• Method of calculating a quantity,
multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to
this 4. Then 6 results.
Then you divide 1 by 1 1/2. Then 2/3 result.
Then you calculate 2/3 of this 6. Then 4 results.
Behold, it is 4, the quantity that said it.
What has been found by you is correct.
THE SEARCH OF “EQUATION”
• Babylonian Mathematics
• cuneiform texts...

...Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. Seealgebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to...

...History of Classical Algebra
Around grades 8 through 10, most students are learning the basics of Algebra 1 and 2. Where did this subject evolve from and who were the mathematicians who patented it? Was it just one civilization that came up with the concept or many that built on each other? These are all great questions to look at when looking at the evolution of Algebra. The ideas of Algebra were very slow developing, until a few great philosophers made some big discoveries. In order to go back to the first signs of Algebra, we have to go back over 3700 years, to the Babylonian civilization.
Babylonians were particularly proficient algebraists and in the ancient civilizations they could solve quadratic problems (Kleiner, 2007). Records show that in 1600 B.C equations and symbols were not used in these problems, rather they were written out and solved verbally (Corry, 2005). Corry’s (2005) study found that a typical example of a problem made by the Babylonians was,
Method of calculating a quantity, multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to this 4.
Then 6 results. Then you divide 1 by 1 1/2.
Then 2/3 result. Then you calculate 2/3 of this 6.
Then 4 results. Behold, it is 4, the quantity that said it.
What has been found by you is correct.
Most examples or evidence we have of...

...
Algebra
From Wikipedia, the free encyclopedia
"Algebraist" redirects here. For the novel by Iain M. Banks, see The Algebraist.
For beginner's introduction to algebra, see Wikibooks: Algebra.
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The quadratic formula expresses the solution of the degree two equation ax^2 + bx +c=0 in terms of its coefficients a, b, c.
Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the origin of its name suggests, was done in the Near East, by such mathematicians as Omar Khayyam (1050-1123).
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on...

...Various derivations of the word "algebra," which is of Arabian origin, have been given by different writers. The first mention of the word is to be found in the title of a work by Mahommed ben Musa al-Khwarizmi (Hovarezmi), who flourished about the beginning of the 9th century. The full title is ilm al-jebr wa'l-muqabala, which contains the ideas of restitution and comparison, or opposition and comparison, or resolution and equation, jebr being derived from the verb jabara, to reunite, and muqabala, from gabala, to make equal. (The root jabara is also met with in the word algebrista, which means a "bone-setter," and is still in common use in Spain.) The same derivation is given by Lucas Paciolus (Luca Pacioli), who reproduces the phrase in the transliterated form alghebra e almucabala, and ascribes the invention of the art to the Arabians.
Other writers have derived the word from the Arabic particle al (the definite article), and gerber, meaning "man." Since, however, Geber happened to be the name of a celebrated Moorish philosopher who flourished in about the 11th or 12th century, it has been supposed that he was the founder of algebra, which has since perpetuated his name. The evidence of Peter Ramus (1515-1572) on this point is interesting, but he gives no authority for his singular statements. In the preface to his Arithmeticae libri duo et totidem Algebrae (1560) he says: "The name Algebra is Syriac, signifying the art or...

...Paper - I
1. Sources: Archaeological sources:Exploration, excavation, epigraphy, numismatics, monuments Literary sources: Indigenous: Primary and secondary; poetry, scientific literature, literature, literature in regional languages, religious literature. Foreign accounts: Greek, Chinese and Arab writers.
2. Pre-history and Proto-history: Geographical factors; hunting and gathering (paleolithic and mesolithic); Beginning of agriculture (neolithic and chalcolithic).
3. Indus Valley Civilization: Origin, date, extent, characteristics, decline, survival and significance, art and architecture.
4. Megalithic Cultures: Distribution of pastoral and farming cultures outside the Indus, Development of community life, Settlements, Development of agriculture, Crafts, Pottery, and Iron industry.
5. Aryans and Vedic Period: Expansions of Aryans in India. Vedic Period: Religious and philosophic literature; Transformation from Rig Vedic period to the later Vedic period; Political, social and economical life; Significance of the Vedic Age; Evolution of Monarchy and Varna system.
6. Period of Mahajanapadas: Formation of States (Mahajanapada): Republics and monarchies; Rise of urban centres; Trade routes; Economic growth; Introduction of coinage; Spread of Jainism and Buddhism; Rise of Magadha and Nandas. Iranian and Macedonian invasions and their impact.
7. Mauryan Empire: Foundation of the Mauryan Empire, Chandragupta, Kautilya and Arthashastra; Ashoka;...