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Educational => Mathematics => Topic started by: Mohammad Hassan Murad on May 14, 2013, 06:20:28 PM

Title: Algebra
Post by: Mohammad Hassan Murad on May 14, 2013, 06:20:28 PM

Algebra is a branch of mathematics that uses variables to solve equations. When solving an algebraic problem, at least one variable will be unknown. Using the numbers and expressions that are given, the unknown variable(s) can be determined.

Early Algebra

The history of algebra began in ancient Egypt and Babylon. The Rhind Papyrus, which dates to 1650 B.C.E., provides insight into the types of problems being solved at that time.

Portion of Rhind Papyrus

The Babylonians are credited with solving the first quadratic equation. Clay tablets that date to between 1800 and 1600 B.C.E. have been found that show evidence of a procedure similar to the quadratic equation. The Babylonians were also the first people to solve indeterminate equations, in which more than one variable is unknown. The Greek mathematician Diophantus continued the tradition of the ancient Egyptians and Babylonians into the common era. Diophantus is considered the “father of algebra,” and he eventually furthered the discipline with his book Arithmetica. In the book he gives many solutions to very difficult indeterminate equations. It is important to note that, when solving equations, Diophantus was satisfied with any positive number whether it was a whole number or not. By the ninth century, an Egyptian mathematician, Abu Kamil, had stated and proved the basic laws and identities of algebra. In addition, he had solved many problems that were very complicated for his time.

Medieval Algebra

During medieval times, Islamic mathematicians made great strides in algebra. They were able to discuss high powers of an unknown variable and could work out basic algebraic polynomials. All of this was done without using modern symbolism. In addition, Islamic mathematicians also demonstrated knowledge of the binomial theorem.

Modern Algebra

An important development in algebra was the introduction of symbols for the unknown in the sixteenth century. As a result of the introduction of symbols, Book III of La géometrie by René Descartes strongly resembles a modern algebra text. Descartes’s most significant contribution to algebra was his development of analytical algebra. Analytical algebra reduces the solution of geometric problems to a series of algebraic ones. In 1799, German mathematician Carl Friedrich Gauss was able to prove Descartes’s theory that every polynomial equation has at least one root in the complex plane. Following Gauss’s discovery, the focus of algebra began to shift from polynomial equations to studying the structure of abstract mathematical systems. The study of the quaternion became extensive during this period. The study of algebra went on to become more interdisciplinary as people realized that the fundamental principles could be applied to many different disciplines. Today, algebra continues to be a branch of mathematics that people apply to a wide range of topics.
René Descartes (1596-1650)
Carl Friedrich Gauss (1777-1855)

Current Status of Algebra

Today, algebra is an important day-to-day tool; it is not something that is only used in a math course. Algebra can be applied to all types of real-world situations. For example, algebra can be used to figure out how many right answers a person must get on a test to achieve a certain grade. If it is known what percent each question is worth, and what grade is desired, then the unknown variable is how many right answers one must get to reach the desired grade. Not only is algebra used by people all the time in routine activities, but many professions also use algebra just as often. When companies figure out budgets, algebra is used. When stores order products, they use algebra. These are just two examples, but there are countless others. Just as algebra has progressed in the past, it will continue to do so in the future. As it is applied to more disciplines, it will continue to evolve to better suit peoples’ needs. Although algebra may be something not everyone enjoys, it is one branch of mathematics that is impossible to ignore.
Title: Re: Algebra
Post by: Saba Fatema on May 14, 2013, 06:23:41 PM
Nice post.
Title: Re: Algebra
Post by: msu_math on May 15, 2013, 09:08:32 AM
Now-a-days a group of mathematicians are highly interested in studying algebra using computers. This branch of algebra in known as computational algebra. The central target of computational algebra is developing algorithms for different mathematical and engineering problems that can be executed by using computers. A number of computational algebra systems (CAS) like Matlab, Mathematica, Maxima, Axiom, Reduced etc are already developed by some renowned research groups. These CASes are have been being used for last few years by both mathematicians and engineers.     
Title: Re: Algebra
Post by: omarsharif on October 04, 2015, 02:05:54 PM
What are  the differences between Arithmetic and Algebra ?