Algebra
Algebra is the study of mathematical symbols and the rules for manipulating these symbols. Historically, algebra was emerged from the need to solve equations and understand the properties of numbers. Algebra is a broad field that encompasses various subfields such as elementary algebra, linear algebra, abstract algebra, and universal algebra.
The word algebra is derived from the Arabic word "al-jabr", which means "reunion of broken parts." The term was first used by the Persian mathematician Al-Khwarizmi in his book "Kitab al-Jabr wa al-Muqabala". After that, Omar Khayyam, defined algebra as the science of solving equations.
One of the most influential results of algebra is the development of abstract algebra, which studies algebraic structures in a more general setting. Abstract algebra provides a unified framework for studying various algebraic structures such as groups, rings, fields, and vector spaces. These algebraic structures are essential in many areas of mathematics and science, including number theory, geometry, and physics.
An algebraic structure is a set equipped with one or more operations that satisfy certain properties. The study of algebraic structures and their properties is the central theme of algebra. Some examples of algebraic structures include groups, rings, fields, and vector spaces.