### Algebra and Numbers

**Algebra**, whose name comes from the Arabic word

*al-jabr*, from the title of a treatise written in the seventh century by the Persian mathematician

*al-Khwarizmi*, is one of many branches of mathematics. It concerns the study of symbolic manipulation laws representing the diverse types of numbers or operations, with the aim of capturing less obvious relations and of developing methods for solving several types of problems. It includes the resolution and study of polynomial equations, as well as the study of properties of abstract structures such as groups, rings and fields. Some of the subareas of this field of Mathematics are:

*Linear Algebra*,

*Abstract Algebra*,

*Homological Algebra*.

**Number Theory**is the area of Mathematics related to the study of the integers — it studies, for example, notions such as primality and factorization, or the resolution of equations with integer solutions, which are called

*Diophantine equations*— although it may include the analysis of other sets of numbers, such as real numbers or certain subrings of complex numbers, among others. Its main subareas are:

*Algebraic Number Theory*,

*Analytic Number Theory*,

*Probabilistic Number Theor*and

*Diophantine Geometry*.

Sub-categories

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