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The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals (that is, with rational coefficients). Galois theory was introduced by Évariste Galois to specify criteria for deciding if an algebraic equation may be solved in terms of ...
In mathematics education, a number sentence is an equation or inequality expressed using numbers and mathematical symbols. The term is used in primary level mathematics teaching in the US, [ 1 ] Canada, UK, [ 2 ] Australia, New Zealand [ 3 ] and South Africa.
In the latter case the LaTeX source is displayed without the tags <math> and </math>. In general, the lead sentence should include the article title, or some variation thereof, in bold along with any alternate names, also in bold. The lead sentence should state that the article is about a topic in mathematics, unless the title already does so.
An algebraic equation is univariate if it involves only one variable. On the other hand, a polynomial equation may involve several variables, in which case it is called multivariate (multiple variables, x, y, z, etc.). For example, + = is a univariate algebraic (polynomial) equation with integer coefficients and
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [43] For example, 3x 2 − 2xy + c is an algebraic expression.
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics.
Rhetorical algebra was first developed by the ancient Babylonians and remained dominant up to the 16th century. In this system, equations are written in full sentences. For example, the rhetorical form of + = is "The thing plus one equals two" or possibly "The thing plus 1 equals 2". [citation needed]
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