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A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
Algebraic notation describes the rules and conventions for writing mathematical expressions, as well as the terminology used for talking about parts of expressions. For example, the expression + has the following components: Algebraic expression notation: 1 – power (exponent) 2 – coefficient 3 – term
Sometimes boxes or shapes are used to indicate unknown values. As such, number sentences are used to introduce students to notions of structure and elementary algebra prior to a more formal treatment of these concepts. A number sentence without unknowns is equivalent to a logical proposition expressed using the notation of arithmetic.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Cubic equation – an algebraic equation with a degree of three; Quartic equation – an algebraic equation with a degree of four; Quintic equation – an algebraic equation with a degree of five; Polynomial – an algebraic expression consisting of variables and coefficients; Inequalities – a comparison between values
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 ...
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