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Translations of Encyclopedia about Mathematics

 

Analysis

This concept comes from the Greek word meaning enucleation or analysis. In mathematics, it is a very extensive field classified among higher mathematics and which includes such fields as differential and integral calculus, together referred to as infinitesimal calculus and the subfields which developed from it, such as differential and integral equations, differential and integral geometry and variable calculus. The characteristic of these fields is that they work with limiting values. The basis of analyses is arithmetics and algebra.

The foundations of this field of mathematical thought was laid by the Greek Euclides (around 365-300) sometime in the year 340 B.C., in his 13th work of "Stocheia" (Elements), which became the cornerstone of mathematical education for almost 2,000 years. These described elements are actually foundations for introducing the infinitesimal way of thinking. Modern analysis studies primarily real and complex numbers, series, limiting values, functions and their derivatives, and integrals.

This area of mathematics is also often used in school geometry, referring to a certain type of consideration required to resolve geometric problems. Even here we should be thankful to the Greeks in that the philosopher Platon (427-348/347) laid the foundations for the systematic justification of geometric relations.

In analytical geometry, shapes (points, bisectors, plains, objects and other shapes) substitute for numbers, where the relations between these shapes can be explained using equations. In this way, geometry is transformed back into algebra, where the starting point for this transformation is the coordinal system. Analytical geometry is divided into analytical geometric plains and analytical geometric space.

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