An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The branch of mathematics which deals with the properties and relations of numbers using symbols (usually letters of the alphabet) to represent numbers or members of a specified set; the generalization and extension of arithmetic.

Algebra, from M.L., from Ar. al jabr "reunion of broken bones," the first known use in the title of a book by the Persian mathematician and astronomer Abu Ja'far Mohammad ibn Musa al-Khwarizmi (c780-c850), who worked in Baghdad under the patronage of Caliph Al-Mamun. The full title of the tratise was Hisab al-Jabr w'al-Muqabala "Arithmetic of Completion and Balancing." → algorithm.

Jabr, from Ar. al jabr, as above.

Relating to, involving, or according to the laws of algebra.

→ algebra + → -ic.

An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.

→ algebra; → equation.

A function expressed in terms of → polynomials and/or roots of polynomials. In other words, any function y = f(x) which satisfies an equation of the form P₀(x)yⁿ + P₁(x)y^{n - 1} + ... + P_n(x) = 0, where P₀(x), P₁(x), ..., P_n(x) are polynomials in x.

→ algebraic + → function.

A number, → real or → complex, that is a → root of a → non-zero polynomial equation whose → coefficients are all → rational. For example, the root x of the polynomial x² - 2x + 1 = 0 is an algebraic number, because the polynomial is non-zero and the coefficients are rational numbers. The imaginary number i is algebraic, because it is the solution to x² + 1 = 0.

→ algebraic; → number.

An algebra whose multiplication is associative.

→ associative; → algebra.

Any of a number of possible systems of mathematics that deals with → binary digits instead of numbers. In Boolean algebra, a binary value of 1 is interpreted to mean → true and a binary value of 0 means → false. Boolean algebra can equivalently be thought of as a particular type of mathematics that deals with → truth values instead of numbers.

→ Boolean; → algebra. The term Boolean algebra was first suggested by Sheffer in 1913.

A → transcendental function. Examples are: exponential, logarithmic, and trigonometric functions.

→ non-; → algebraic + → function.