Arithmetic vs. Algebra

Arithmeticnoun

The mathematics of numbers (integers, rational numbers, real numbers, or complex numbers) under the operations of addition, subtraction, multiplication, and division.

Arithmeticadjective

(mathematics) Of, relating to, or using arithmetic; arithmetical.

Arithmeticadjective

(arithmetic) Of a progression, mean, etc, computed solely using addition.

Arithmeticnoun

The science of numbers; the art of computation by figures.

Arithmeticnoun

A book containing the principles of this science.

Arithmeticnoun

the branch of pure mathematics dealing with the theory of numerical calculations

Arithmeticadjective

relating to or involving arithmetic;

Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, 'number' and τική [τέχνη], tiké [téchne], 'art' or 'craft') is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation and extraction of roots. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis.

Algebranoun

A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

Algebranoun

The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.

Algebranoun

The study of algebraic structures.

Algebranoun

A universal algebra.

Algebranoun

An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.

Algebranoun

A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).

Algebranoun

One of several other types of mathematical structure.

Algebranoun

(figurative) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.

Algebranoun

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.

Algebranoun

A treatise on this science.

Algebranoun

the mathematics of generalized arithmetical operations

Algebra

Algebra (from Arabic: الجبر‎, romanized: al-jabr, lit. 'reunion of broken parts, bonesetting') is one of the broad areas 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.