algebra

1. (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.Examples: "Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber."; "Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone."uncountable

2. (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).capitalizedsometimesuncountable

3. (countable, mathematics, algebra) Any of several objects of study in Algebracountableuncountable

4. (countable, mathematics, algebra) Any of several objects of study in AlgebraSynonyms: algebra over a field, algebra over a ringcountableuncountable

5. (countable, set theory, mathematical analysis) 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).Synonyms: field of sets, algebra of setscountable

6. (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.Examples: "Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?"countablefigurativelyuncountable