Mathematics is the inspiration of many fields of research, resembling commerce, computing, engineering, and science. Mathematics can, broadly speaking, be subdivided into the examine of amount, structure, house, and alter (i.e. arithmetic , algebra , geometry , and evaluation ). Along with these primary considerations, there are also subdivisions devoted to exploring links from the heart of mathematics to other fields: to logic , to set theory ( foundations ), to the empirical mathematics of the varied sciences ( applied mathematics ), and extra not too long ago to the rigorous examine of uncertainty Whereas some areas might sound unrelated, the Langlands program has found connections between areas previously thought unconnected, such as Galois teams , Riemann surfaces and quantity idea.

The rigorous study of actual numbers and capabilities of a real variable is named real analysis , with complex analysis the equal subject for the advanced numbers Purposeful analysis …