abstract algebra
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Abstract algebra is a branch of mathematics that studies algebraic structures—like groups, rings, and fields—and how they relate to one another. It matters because it provides a unified framework for understanding patterns and operations that appear across many areas of mathematics and science, making it foundational for advanced mathematics and practical applications in cryptography and computer science.
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Article
The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in pedagogy.