Algebra (from Arabic: Ø§Ù„Ø¬Ø¨Ø±â€Ž al-jabr, meaning reunion of broken parts and bonesetting) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. 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 generally considered to be 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. 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 many values. For example, in the letter is unknown, but applying additive inverses can reveal its value: . In E = mc2, the letters and are variables, and the letter is a constant, the speed of light in a vacuum. Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words. The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an algebra, and the word is used, for example, in the phrases linear algebra and algebraic topology. A mathematician who does research in algebra is called an algebraist.
El álgebra (del árabe: الجبر al-ŷabr ‘reintegración, recomposición’) es la rama de la matemática que estudia la combinación de elementos de estructuras abstractas acorde a ciertas reglas. Originalmente esos elementos podían ser interpretados como números o cantidades, por lo que el álgebra en cierto modo originalmente fue una generalización y extensión de la aritmética. En el álgebra moderna existen áreas del álgebra que en modo alguno pueden considerarse extensiones de la aritmética (álgebra abstracta, álgebra homológica, álgebra exterior, etc.).