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What is "algebra"

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algebra
Longman Dictionary of Contemporary English
algebra
noun
EXAMPLES FROM CORPUS
▪ Computer graphics is, among other things, just what the mathematician needed: an appropriate mechanism for turning algebra into forms.
▪ Good understanding of most concepts up to and including algebra.
▪ He hoped to be an engineer, and he was taking algebra and trigonometry and falling behind in both.
▪ I shuddered at the memory of numerical computations and algebra.
▪ The relational algebra is a procedural language.
▪ We now look at the relational algebra and the relational calculus in more detail.
The Collaborative International Dictionary
Algebra

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L. mathematica, sing., Gr. ? (sc. ?) science. See Mathematic, and -ics.] That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations. Note: Mathematics embraces three departments, namely:

  1. Arithmetic.

  2. Geometry, including Trigonometry and Conic Sections.

  3. Analysis, in which letters are used, including Algebra, Analytical Geometry, and Calculus. Each of these divisions is divided into pure or abstract, which considers magnitude or quantity abstractly, without relation to matter; and mixed or applied, which treats of magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations.

Algebra

Algebra \Al"ge*bra\, n. [LL. algebra, fr. Ar. al-jebr reduction of parts to a whole, or fractions to whole numbers, fr. jabara to bind together, consolidate; al-jebr w'almuq[=a]balah reduction and comparison (by equations): cf. F. alg[`e]bre, It. & Sp. algebra.]

  1. (Math.) That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.

  2. A treatise on this science.

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Douglas Harper's Etymology Dictionary
algebra

1550s, from Medieval Latin algebra, from Arabic al jabr ("in vulgar pronunciation, al-jebr" [Klein]) "reunion of broken parts," as in computation, used 9c. by Baghdad mathematician Abu Ja'far Muhammad ibn Musa al-Khwarizmi as the title of his famous treatise on equations ("Kitab al-Jabr w'al-Muqabala" "Rules of Reintegration and Reduction"), which also introduced Arabic numerals to the West. The accent shifted 17c. from second syllable to first. The word was used in English 15c.-16c. to mean "bone-setting," probably from Arab medical men in Spain.

Wiktionary
algebra

n. (context uncountable medicine historical rare English) The surgical treatment of a dislocated or fractured bone. Also (context countable English): a dislocation or fracture.

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WordNet
algebra

n. the mathematics of generalized arithmetical operations

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Wikipedia
Algebra (disambiguation)

The word 'algebra' is used for various branches and structures of mathematics. For their overview, see Algebra.

Algebra

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") 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. 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 Middle East, by Persian mathematicians such 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 , the letters E and m are variables, and the letter c is a constant, the speed of light in a vacuum. 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.

Algebra (singer)

Algebra Blessett (born Algebra Felicia Blessett on April 9, 1976) is an American contemporary R&B singer.

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Usage examples of "algebra".

In both cases, the rotations could be treated algebraically, and the traditional way to get a handle on this was to make use of a set of matrices of complex numbers whose relationships mimicked the algebra in question.

The group of the visualizers, who thought in geometrical terms, like the ancient Greeks, and the group of the nonvisualizers who preferred algebra and imageless abstractions.

It treats of partnership in agriculture, the Mezzadria system still prevalent in Tuscany and in other parts of Italy, of the value of money, of the strange properties of certain numbers, and gives the first simple rules of Algebra to serve as stepping-stones to the higher mathematics.

Since she foundered on anything beyond algebra, she relied on her tapas to solve complex problems.

Lucy realizes that this stranger is Mison Reed, whom she used to sit next to in algebra.

I meant the crack facetiously, but I heard him doing the recursive algebra in his head at the other end.

He was a theoretical thaumaturgist who worked with the higher and more esoteric forms of the subjective algebrae, leaving it to others to test his theories in practice.

Little in mathematics beyond the elementary level of calculus of variations, and nothing at all about Banach algebra or Riemannian manifolds.

In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics.

Europe by the great mathematician Leonardo Fibonacci, the Arabic numerals and algebra that revolutionized our way of thought?

These were the kids who, in the midst of earth science, gym, algebra, cafeteria stench would manage to knock out a handwritten thirty-page story or a collection of poems, drop it on his desk at the end of class and split.

The Sankhya philosophy is a regular system of metaphysics, to be studied as one would study algebra.

Using his known or assumed plaintext values, the cryptanalyst sets up equations in which the displacements of the several rotors constitute the unknowns, and then, using higher algebra, solves the equations for them.

Janice gives him no space of secrecy in which blood can gather as it did behind his fly in ninth-grade algebra sitting beside Lotty Bingaman who in raising her hand to show she had the answers showed him wisps of armpit hair and pressed the thin cotton of her blouse tighter against the elastic trusswork of her bra, so its salmon color strained through.

Society was ruled by narrow-minded, profoundly incurious people, predatory businessmen, dull squires, bishops, politicians who could quote Horace but had never heard of algebra.