Algebra
Algebra (from Arabic al-jabr, "reunion of broken parts") is the study of mathematical symbols and the syntax (rules) for manipulating these symbols.
Contents
Role in mathematics
Algebra is both:
- One of the broad parts of mathematics
- A unifying thread running through many different parts of mathematics
Description
Algebra includes everything from 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 Arabic origin of its name suggests, was done in the Near East, by such mathematicians as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).
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 x + 2 = 5 the letter x is unknown, but the law of inverses can be used to discover its value: x=3.
In E=mc^2, the letters E and m are variables, and the letter c is a constant.
Equations and formulas
Algebra gives methods for solving equations and expressing formulas that are much easier (for those who know how to use them) than the older method of writing everything out in words.
Specialized uses of the word algebra
The word algebra is also used in certain specialized ways:
- A special kind of mathematical object in abstract algebra is called an "algebra"
- Linear algebra
- Algebraic topology
Other areas of mathematics
Other broad areas of mathematics include:
See also
External links
- Alebra @ Wikipedia
