Algebra Chapter 0 Pdf 28
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Mathematical analysis deals with functions and their properties. By mathematical analysis, we mean the study of the structure of functions and their properties. This field is called analysis by analytic functions. The functions which are used in analysis are assumed to be real-valued functions. In the theory of functions, it is usually assumed that the functions are defined on an open domain of the real line (or R), or some other completely regular space, and that the range of such functions is the whole real line or some other space, such as the integers, or an algebraically closed field.
By the early 18th century, algebra involved a study of the solutions of equations, employing the methods of Diophantus, al-Khwarizmi, and Brahmagupta, all of whom had lived in India between the 6th and 9th centuries AD. The work of Diophantus and Brahmagupta is preserved, but that of al-Khwarizmi has nearly disappeared. In the second half of the 19th century, algebra became increasingly systematic and abstract.[9] Methods from combinatorics and geometry were also applied to algebraic fields. For instance, the concept of a field was introduced to algebra, and the concept of a field extension from algebra was introduced to abstract algebra. This was a major development in mathematical thought because it showed that a field may be embedded as a subfield of an algebraic structure, such as the real numbers. This was an example of generalization in mathematics, i.e. the development of a mathematical theory which can be applied to a wide variety of objects and situations.
Today, mathematics is a very diverse subject. Unlike the classical Euclidean geometry, some parts of mathematics are related to other subjects, and may involve concepts from physics or number theory. Other parts involve disciplines such as combinatorics, graph theory, number theory, algebra, geometry, calculus, probability theory, and analysis. The purpose of mathematics is to understand concepts, and to use this understanding to solve practical problems.
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