Real and Complex Analysis

[msu_math]

Analysis is concerned with the properties of functions. It deals with concepts such as continuity, limits, differentiation and integration, thus providing a rigorous foundation for the calculus of infinitesimals introduced by Newton and Leibniz in the 17th century.

Real analysis studies functions of real numbers, while complex analysis extends the aforementioned concepts to functions of complex numbers. Functional analysis is a branch of analysis that studies infinite-dimensional vector spaces and views functions as points in these spaces.