algèbre

Algebra is a branch of mathematics concerned with symbols and the rules for manipulating those symbols. It is a generalization of arithmetic in which unknowns are represented by letters or other symbols. Algebra can be divided into several main areas. Elementary algebra, which deals with basic operations, variables, and solving linear equations, is the foundation for more advanced topics. Abstract algebra, also known as modern algebra, explores algebraic structures such as groups, rings, and fields. These structures are sets equipped with operations that satisfy certain axioms. Linear algebra is a field that studies vector spaces, linear mappings, and systems of linear equations. It is crucial in many areas of science and engineering. Commutative algebra focuses on commutative rings and their ideals.

The word "algebra" comes from the Arabic word "al-jabr," which means "reunion of broken parts." This term was first used in the title of the book "Al-jabr wa al-muqabala" by the Persian mathematician Muḥammad ibn Musa al-Khwarizmi, written around 820 AD. This book presented systematic methods for solving linear and quadratic equations. Over centuries, algebra evolved from a tool for solving specific problems to a rich and abstract field of study with wide-ranging applications in mathematics, science, technology, and economics. It provides a powerful framework for understanding relationships, modeling complex systems, and solving problems that cannot be addressed by arithmetic alone.