# A report onCalculus and Mathematical analysis

Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

- Mathematical analysis

In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.

- Calculus

## Discrete mathematics

Study of mathematical structures that can be considered "discrete" rather than "continuous" (analogously to continuous functions).

Study of mathematical structures that can be considered "discrete" rather than "continuous" (analogously to continuous functions).

By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.

Although the main objects of study in discrete mathematics are discrete objects, analytic methods from "continuous" mathematics are often employed as well.

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c.

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c.

Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.

Today's analysis achieves the same result, using limits (see convergent series).

## Smooth infinitesimal analysis

Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.

Smooth infinitesimal analysis is like nonstandard analysis in that (1) it is meant to serve as a foundation for analysis, and (2) the infinitesimal quantities do not have concrete sizes (as opposed to the surreals, in which a typical infinitesimal is 1/ω, where ω is a von Neumann ordinal).