Difference between revisions of "Algebra"
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| − | '''Algebra''' (from Arabic ''al-jabr'', "reunion of broken parts") is one of the broad parts of [[mathematics]]. | + | '''Algebra''' (from Arabic ''al-jabr'', "reunion of broken parts") is one of the broad parts of [[mathematics]]. It is a unifying thread of almost all of mathematics. |
| − | In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols | + | In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols |
| − | As such, it includes everything from | + | As such, it 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. | The more basic parts of algebra are called [[elementary algebra]], the more abstract parts are called [[abstract algebra]] or modern algebra. | ||
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Abstract algebra is a major area in advanced mathematics, studied primarily by professional [[Mathematician|mathematicians]]. | Abstract algebra is a major area in advanced mathematics, studied primarily by professional [[Mathematician|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). | + | 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. | 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. | + | In E=mc^2, the letters E and m are variables, and the letter c is a [[Constant (mathematics)|constant]]. |
| − | Algebra gives methods for solving [[Equation | + | Algebra gives methods for solving [[Equation|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. |
The word algebra is also used in certain specialized ways: | The word algebra is also used in certain specialized ways: | ||
* A special kind of mathematical object in abstract algebra is called an "algebra" | * A special kind of mathematical object in abstract algebra is called an "algebra" | ||
| − | * Linear algebra | + | * [[Linear algebra]] |
| − | * Algebraic topology | + | * [[Algebraic topology]] |
A mathematician who does research in algebra is called an ''algebraist''. | A mathematician who does research in algebra is called an ''algebraist''. | ||
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== Other areas of mathematics == | == Other areas of mathematics == | ||
| − | Other broad areas of mathematics include [[number theory]], [[geometry]], and [[analysis]]. | + | Other broad areas of mathematics include [[number theory]], [[geometry]], and [[mathematical analysis]]. |
== See also == | == See also == | ||
Revision as of 16:46, 28 August 2015
Algebra (from Arabic al-jabr, "reunion of broken parts") is one of the broad parts of mathematics. It is a unifying thread of almost all of mathematics.
In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols
As such, it 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.
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.
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
A mathematician who does research in algebra is called an algebraist.
Other areas of mathematics
Other broad areas of mathematics include number theory, geometry, and mathematical analysis.
See also
External links
- Alebra @ Wikipedia
