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Algebra (from Arabic ''"al-jabr"'' meaning "reunion of broken parts"〔(【引用サイトリンク】work=Online Etymology Dictionary )〕) 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;〔I. N. Herstein, ''Topics in Algebra'', "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964〕 it is a unifying thread of almost all of mathematics.〔I. N. Herstein, ''Topics in Algebra'', "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964〕 As such, 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. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Near East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).〔Omar Khayyám〕〔(【引用サイトリンク】title=Omar Khayyam )〕 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 the law of inverses can be used to discover its value: . In , the letters and are variables, and the letter 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", 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. == Etymology == The word ''algebra'' comes from the Arabic language ( ' "restoration") from the title of the book ''Ilm al-jabr wa'l-muḳābala'' by al-Khwarizmi. The word entered the English language during Late Middle English from either Spanish, Italian, or Medieval Latin. Algebra originally referred to a surgical procedure, and still is used in that sense in Spanish, while the mathematical meaning was a later development.〔(【引用サイトリンク】url=http://www.oxforddictionaries.com/us/definition/english/algebra )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Algebra」の詳細全文を読む スポンサード リンク
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