Abstract algebra
From Wikipedia, the free encyclopedia
Abstract algebra is a part of math which studies algebraic structures. These include:
It is normal to build a theory on one kind of structure, like group theory or category theory.
The purpose of each theory is to organize in a simple-to-complex model the precise definition of a concept, examples, its substructures, the relations between them: morphisms and its applications, inside the own theory as well outside.
During history, different fields of mathematics have used algebras. Algebras are about finding or specifying rules on how to calculate with certain mathematical formulas and expressions. Another algebra (which is not abstract) is elementary algebra, for example.
[change] Examples
- Solving equations with many variables. This leads to matrices, determinants and linear algebra
- Finding formulas for polynomial equations. This led to the discovery of groups, as an expression of symmetry.
- Quadratic and higher-degree equations and Diophantine equations - espectially when Fermat's last theorem was proved led to the definition of rings, and ideals.
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