1. Understanding Algebra
Algebra comes from the Arabic "al-jabr" means "meeting", "relationship" or "completion") is a branch of mathematics that can be characterized as a generalization and extension of arithmetic. Algebra is also the name of an abstract algebraic structures, yaitualjabar in a field [1].
Algebra is a branch of mathematics that studies the structure, relation and quantity. To learn about these things in algebra used symbols (usually letters) to represent numbers in general as a means of simplifying and tools to solve the problem. For example, x represents the number of known and y number that we want to know.
2. Origins of Algebra
The origins of algebra can be traced back to ancient Babylon who developed mathematical systems are quite complicated, with this they were able to calculate in a similar way to algebra now. By using this system, they are able to apply formulas and calculate solutions for unknown values for a class of problems that are usually solved by using linear equations, quadratic equations, and indeterminate linear equations. Instead, the Egyptians and most of the nations of India, Greece, and China in melenium first one has not AD, usually still using geometry to solve equations like this, for example, as mentioned in "the Rhind Mathematical Papyrus", "Sulba Sutras", "Eucilid's Elements "and" The Nine Chapters on the Mathematical Art ". The results of the Greeks in Geometry, which is written in the book element, providing a framework to generalize mathematical formula out a special solution of a particular problem in a more general system for stating and solving equations, that frame of mind logic deduction.
As mentioned above the term "algebra" comes from the Arabic word "al-jabr" which comes from the book "Al-Kitab aj-jabr wa al-Muqabala" (which means "The Compendious Book on Calculation by Completion and Balancing") What written by the Persian mathematician Muhammad ibn Musa al-Khwarizmi. The word "Al-Jabr" itself actually means merging (reunion). Greek mathematician at times Hllenisme, Diophantus, traditionally known as the "Father Aljabr", although it is still debated, but the scientist named R Rashed and Angela Armstrong in his work titled The Development of Arabic Mathematics, confirmed that the algebra by Al-Khwarizmi has a difference which is significant compared to the work of Diophantus, which is often cited as the inventor of algebra. In the view of the scientist, Khwarizmi's work is much better compared the work of Diophantus.
Al-Khwarizmi who first introduced algebra in a basic form that can be applied in everyday life. While the concept of algebra Diophantus more likely to use algebra as a tool for the application of number theory.
The sajarawan believe that the work of al-Khwarizmi is the first book in history where the term algebra arise in the context of disciplines. This condition is emphasized in the books, formulations and vocabulary which is technically a new vocabulary.
Science pengetahian algebra itself is actually a revision of the knowledge that has been achieved by the Egyptians and Babylonians. Both of these nations have had the records related to the problem of arithmetic, algebra and geometry at the beginning of 2000 BC. In the book Arithmetica of Diophantus there are a few notes about the quadratic equation. Nevertheless the existing equation has not yet formed a systematic way, but are formed unintentionally through improvements cases arise. Therefore, before the time of al-Khwarizmi's algebra is an object that has not been seriously and systematically studied [2].
3. The figures in Developing Algebra
a. Muhammad ibn Musa al-Khwarizmi, It is the first time that Al-Jabar trigger in his book entitled "Al-Kitab al-jabr wa-l-Muqabala" This book is a work of monumental in the 9th century AD it is a Persian mathematician, born in 194 AH / 780 AD, precisely in Khawarizm, Uzbeikistan.
b. Al-Qalasadi in developing mathematics is extremely invaluable. He is the Muslim mathematician in the 15th century, that without him the world might be the world do not recognize the symbols of arithmetic. As seldom noted, al Qalasadi is a Muslim mathematician credited with introducing the symbols of Algebra. The symbols were first developed in the 14th century by Ibn al-Banna later in the 15th century developed by al-Qalasadi, al-Qalasadi introducing mathematical symbols by using characters from the Arabic alphabet [3].
He wa meaningful use "and" for addition (+), for pngurangan (-), al-Qalasadi using illa mean "less". As for the multiplication (x), he uses fi which means "times". Ala symbol meaning "for" is used to pembegian (/).
c. Nikolai Ivanovich Lobachevsky (December 1, 1792 - February 24, 1856) adalahmatematikawan Russia. He is primarily known as the man who developed the non-Euclidean geometry (independent of the work of János Bolyai) that the announcement on February 23, 1826, as well as the roots of an algebraic equation approximation method known as namaMetode Dandelin-Gräffe
d. Sharaf al-Dīn al-Muzaffar ibn Muhammad ibn al-Muzaffar al-Din Tusi (1135-1213) was a mathematician and astronomer of Islam from Persia. Sharif al-Din teach various topics of mathematics, astronomy and related services, such as numbers, astronomical tables and astrology. Al-Tusi wrote several papers on algebra. He gave a method which was later renamed as Ruffini-Horner method to approach the roots of cubic equations. Although this method has been used previously by the Arab mathematicians to find approximations to the nth root of an integer, al-Tusi is the first to apply these methods to solve the general equation of this type. In Al-Mu'adalat (On Equations), al-Tusi find algebra and numerical solutions of cubic equations and the first to find the derivative of cubic polynomials, an important result in differential calculus
e. Omar Khayyam, a scientist from Persian build Geometry Algebra and geometry find common forms of cubic equations.
f. Seki Kowa scientists from Japan in the 17th century, he floated the determinants.
g. Robert Recorde is the one who introduced the "=" contained in his book entitled "The Whetstone of Witte" in 1557. [4]
4. Classification of Algebra
Algebra can be broadly divided into the following categories:
a. Elementary algebra, which studies the properties of operations on the real number is recorded in symbol as constants and variables, and the rules that establish mathematical expressions and equations involving symbols. (This field also includes material that is usually taught in secondary schools)
Elementary algebra is the most basic form of algebra, which is taught to students who do not have knowledge of anything other than Arithmetic Mathematical Association. Although as in arithmetic, where numbers and arithmetic operations (such as +, -, x,) appears also in algebra, but the numbers here are often simply denoted with a symbol (such as a, x, y,). This is very important because: it allows us to lower the general formula of the rules of arithmetic (such as a + b = b + a for all a and b), and then the first step to a systematic search of the properties of the real number system.
By using the symbol, instead of using direct numbers, allowing us to build a mathematical equation containing an unknown variable (for example "Find the numbers x satisfying the equation 3x + 1 = 10"). It also allows us untukmembuat functional relation of mathematical formulas (for example "If you mnjual x tickets, then you make a profit 3x -10 rupiah, can be written sebagaif (x) = 3x - 10, where f is a function and x is the number where the function f work ") [5]
b. Abstract algebra, sometimes called Modern Algebra, who studied the structural algebra sort of group, ring and field (fields) are defined and taught axiomatic.
c. Linear Algebra, which is studying the specific properties of the Vector Space (including Matrix)
d. Universal algebra, which studies the properties of all the structural together algebra.
[1] http://id.wikipedia.org/wiki/Aljabar
[2] Al-Khwarizmi and his thinking in the field of mathematics, Muhammad Sabirin things: 694-695
[3] www.suaramedia.com
[4] Wahyudin, Antara. "Encyclopedia of Mathematics at the secondary school. Tarity 2003. Samudra Berlian Jakarta hal.104
[5] www.suaramedia.com written by Alexander in March 2009
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