Mathematics is the science that developed from research of geometric figures and calculation with numbers. It is one of the oldest scientific disciplines, having thousands of years of history.
Algebra is one of the best known mathematical areas. It deals with equations and the properties of calculation operations. This in turn has various sub-divisions, beginning with Elementary Algebra (i.e., "rules of calculation"), through Linear Algebra (equation systems, vector spaces, etc.), up to abstract algebra.
Analysis is concerned with infinitesimal calculation (consisting of differential and integral calculus). It is about, among other things, local changes of functions (derivation or differential quotient of the function) and about calculation of areas by functions (integral).
Geometry investigates shapes in two and three-dimensional space. Important concepts include points, lines, planes, and angles.
Along with Theoretical Mathematics, a bordering discipline is often described as Applied Mathematics, where mathematical methods are used in various specialist areas (e.g., in Financial or Insurance Mathematics).
Apart from this is the subject of Statistics, which together with Probability Theory forms the specialized mathematics of Stochastics. Put simply, this is the analysis and interpretation of data and probabilities.
In Descriptive Statistics, empirical data is prepared meaningfully for interpretation, while in Inductive Statistics conclusions are drawn from a random sample using Probability Theory.
The ever-important Data Science is located at the interface between Statistics/Mathematics and Computer Science.
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