Branch of mathematics that generally deals with calculating the elements of a given set of mathematical objects. The calculation rules used in algebra apply the rules developed in arithmetic to other sets of mathematical objects.

Classical algebra mainly deals with solving equations using clearly stated methods. The focus is also on the theory of real numbers and complex numbers. In modern algebra, the classical properties were generalized so that they could be applied to more recently developed structures such as groups, rings, fields and sets, to name a few.

Algebra provides a set of reasoning methods related to the mathematical objects being considered. Therefore, algebra is made up of a set of objects on which internal and external operations determined by axioms are defined. The list of algebras includes Boolean algebra, the algebra of functions,  the algebra of sets, the algebra of propositions, etc.

Historical note

The term algebra is believed to have first been used in the title of a book written during the Middle Ages (around 825 CE) by a Persian mathematician whose name was Muhammad Ibn Mūsā al-Khuwārizmī and after whom the term algorithm. was named. The book, which presented work based on that of Greek and Egyptian mathematicians, was entitled Al-jabr wa’l-muqqâbalah;  the first words of the title, al-jabr, mean “restoration” or “reunion of broken parts”.

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