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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
Pre-modern algebra was developed and used by merchants and surveyors as part of what Jens Høyrup called "subscientific" tradition. Diophantus used this method of algebra in his book, in particular for indeterminate problems, while Al-Khwarizmi wrote one of the first books in Arabic about the general method for solving equations. [37]
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...
e. The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and ...
This use of variables entails use of algebraic notation and an understanding of the general rules of the operations introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers.
Abstract algebra. The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups, rings ...
The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [1][2][3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental ...
The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and was transmitted to the west via Islamic mathematics. [37] [38] A page from al-Khwārizmī's Algebra. Despite their name, Arabic numerals have roots in India.