### Mathematical Analysis

Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex functions. However, they can also be defined and studied in any space of mathematical objects that has a definition of nearness (a topological space) or, more specifically, distance (a metric space). |