Algebra is a broad branch of mathematics that uses symbols (often letters like x and y) to represent numbers and express relationships between them. It generalizes arithmetic by dealing with variables and the rules for manipulating these variables in formulas and equations. Algebra is divided into several subfields, including elementary algebra (basic operations and solving equations), linear algebra (vectors and matrices), and abstract algebra (algebraic structures like groups, rings, and fields).
The term 'algebra' comes from the Arabic word 'al-jabr' (meaning 'reunion of broken parts'), from the title of the book 'The Compendious Book on Calculation by Completion and Balancing' written by the Persian mathematician Al-Khwarizmi around 820 CE.
Algebra is the language of modern science and engineering. It is foundational to calculus, statistics, physics, computer science (Boolean algebra, linear algebra in ML), and economics.