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Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and ...
Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the ...
Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown below. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and ...
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
List: An abstract data type that represents a sequence of values, where the same value may occur more than once. Data order maintenance, implementation of stacks, queues, etc. Stack: A collection that supports a last-in, first-out access pattern. Function calls/recursive calls, undo mechanisms in applications. Queue
Categorization is a type of cognition involving conceptual differentiation between characteristics of conscious experience, such as objects, events, or ideas.It involves the abstraction and differentiation of aspects of experience by sorting and distinguishing between groupings, through classification or typification [1] [2] on the basis of traits, features, similarities or other criteria that ...
A representation of the concept of a tree. The four upper images of trees can be roughly quantified into an overall generalization of the idea of a tree, pictured in the lower image. A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. [1]
It is used as an expressive way to depict an idea. The symbol generally conveys an emotional response far beyond what the word, idea, or image itself dictates. Example: A heart standing for love. (One might say "It broke my heart" rather than "I was really upset") Example: A sunrise portraying new hope. ("All their fears melted in the face of ...