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Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Symbolic computation engines usually recognize the majority of special functions.
Statistics, for example, is mathematical in its methods but grew out of bureaucratic and scientific observations, [1] which merged with inverse probability and then grew through applications in some areas of physics, biometrics, and the social sciences to become its own separate, though closely allied, field.
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Algebraic coding theory – aka coding theory, is the study of the properties of codes and their respective fitness for specific applications. Boolean algebra – branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. It is used for describing logical operations.
Differential equations are an important area of mathematical analysis with many applications in science and engineering. Analysis is the branch of mathematics dealing with continuous functions , limits , and related theories, such as differentiation , integration , measure , infinite sequences , series , and analytic functions .
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Most civilisations developed some mathematics, mainly for practical purposes, such as counting (merchants), surveying (delimitation of fields), prosody, astronomy, and astrology. It seems that ancient Greek philosophers were the first to study the nature of mathematics and its relation with the real world.