History of Algebra

History of Algebra

 Algebra (Algebra) is a branch of mathematics that studies structure, relationships and quantity.  To learn these things in algebra, symbols (usually letters) are used to represent numbers in general as a means of simplification and as a tool to solve problems.  For example, x represents the number that is known and the number y that you want to know.  So if Andi has x books and then Budi has 3 more books than Andi, then in algebra, Budi's book can be written as y = x + 3. By using algebra, you can investigate the pattern of general number rules.  Algebra can be assumed by looking at things from above, so we can find general patterns.

 

 Algebra has been used by mathematicians for several thousand years.  History records the use of algebra by the Mesopotamians in 3,500 years ago.  The name Algebra is derived from a book written in 830 by Persian mathematician Muhammad ibn Musa al-Kwarizmi with the title 'Al-Kitab al-Jabr wa-l-Muqabala' (which means "The Compendious Book on Completion and Balancing"),  which applies symbolic operations to find solutions systematically to linear and quadratic equations.  One of his students, Omar Khayyam translated Al-Khwarizmi's work into European languages.  A few centuries ago, English scientist and mathematician, Isaac Newton (1642-17 27) showed that the behavior of something in nature could be explained by mathematical rules or formulas involving algebra, known as Newton's Gravitational Formula.

 Algebra together with Geometry, Analysis and Number Theory are the main branches in Mathematics.  Elementary algebra is part of curriculums in secondary schools and provides a foundation for basic ideas for Ajabar as a whole, including the properties of addition and multiplication of numbers, variable concepts, polynomial definitions, factorization and determining rank roots.

 Now the term Algebra has a broader meaning than Elementary Algebra, which includes Abstract Ajabar, Linear Algebra and so on.  As explained above in algebra, we do not work directly with numbers but rather work using symbols, variables and set elements.  For example Addition and Multiplication is seen as a general operation and this definition leads to number structures such as Groups, Ring and Fields.

 The Origin of Algebra

 The origins of Algebra can be traced to the ancient Babylonians who developed a fairly complex arithmetic system, with this they were able to calculate in a manner similar to algebra today.  By using this system, they are able to apply formulas and calculate solutions for unknown values ​​for class problems that are usually solved using Linear Equations, Quadratic Equations and Indeterminate Linear Equations.  On the contrary, the Egyptians, and most Indians, Greeks, and Chinese in the first millennium BC, usually still use geometric methods to solve equations like this, for example as mentioned in 'the Rhind Mathematical Papyrus',' Sulba Sutras', 'Euclid's  Elements', and 'The Nine Chapters on the Mathematical Art'.  The work of the Greeks in Geometry, written in the book of Elements, provides a framework for thinking to generalize mathematical formulas outside the specific solution of a particular problem into a more general system for expressing and solving equations, namely the logic framework of Deduction logic.

 As mentioned above the term 'Algebra' comes from the Arabic word "al-jabr" which comes from the book 'Al-Kitab al-Jabr wa-l-Muqabala' (which means "The Compendious Book on Calculation by Completion and Balancing")  , written by Persian mathematician Muhammad ibn Musa al-Kwarizmi.  The word 'Al-Jabr' itself actually means reunion.  The Greek mathematician in the Hellenism era, Diophantus, was traditionally known as the 'Father of Algebra', although it is still being debated who is actually entitled to that title Al-Khwarizmi or Diophantus ?.  Those who support Al-Khwarizmi point to the fact that the results of his work on the principle of reduction are still in use today and he also provides a detailed explanation of solving quadratic equations.  Whereas those who support Diophantus show that Algebra found in Al-Jabr is still very elementary compared to Algebra found in 'Arithmetica', by Diophantus.  Another Persian mathematician, Omar Khayyam, built Algebra Geometry and discovered the general geometry of cubic equations.  Indian mathematician Mahavira and Bhaskara, as well as Chinese mathematician Zhu Shijie, succeeded in solving various kinds of cubic, quartic, quintic and other high-level polynomial equations.

 Another important event was the further development of algebra, occurring in the middle of the 16th century.  The idea of ​​determinants developed by the Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, with the aim of solving the Linear Equation System simultaneously using Matrices.  Gabriel Cramer also contributed his work on Matrices and Determinants in the 18th century.  Abstract algebra was developed in the 19th century, initially focusing on Galois theory and on the problem of constructibility

 The stages of the development of symbolic algebra are as follows:

 - Rhetorical algebra, which was developed by the Babylonians and still dominated until the 16th century;

 - Geometrically constructed algebra, developed by Indian Vedic Mathematicians and Ancient Greeks;

 - Syncopated algebra, developed by Diophantus and in 'The Bakhshali Manuscript';  and

 - Symbolic algebra (Symbolic algebra), the culmination of which is Leibniz's work.

 Classification of Algebra

 Algebra can be broadly divided into the following categories:

 1. Elementary Algebra, which studies the properties of operations on real numbers recorded in symbols as constants and variables, and Rules that construct Mathematical expressions and equations involving symbols. (This field also includes material that is usually taught in secondary schools, namely '  Intermediate Algebra 'and' college algebra ');

 2. Abstract Algebra, sometimes called Modern Algebra, which studies Algebraic Structures such as Groups, Ring and Fields (fields) that are defined and taught axiomatically;

 3. Linear Algebra, which studies the special properties of the Vector Room (including Matrices);

 4. Universal algebra, which studies the shared properties of all algebraic structures.

 In further algebra studies, axiomatic algebraic systems such as Groups, Ring, Medan and Algebra on a Medan (algebras over a field) are studied together with the study of Natural Geometry Structures that are compatible with these Algebraic Structures in the field of Topology.

 Elementary Algebra

 Elementary Algebra is the most basic form of Algebra, which is taught to students who do not have any knowledge of Mathematics other than Basic Arithmetic.  Although as in Arithmetic, where arithmetic numbers and operations (such as +, -, ×, ÷) also appear in Algebra, but numbers are often denoted only by symbols (like a, x, y).  This is very important because: It allows us to derive general formulas from Arithmetic rules (such as a + b = b + a for all a and b), and then it is the first step for a systematic search for the properties of real number systems.

 Using symbols, instead of using numbers directly, allows us to construct mathematical equations that contain unknown variables (for example "Look for x numbers that satisfy the equation 3x + 1 = 10"). This also allows us to make relations  functional mathematical formulas (for example "If you sell x tickets, and then you get a profit of 3x - 10 rupiah, it can be written as f (x) = 3x - 10, where f is a function, and x is a number where the function  f works. ").