Complex Analysis
The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions, which are commonly represented as two-dimensional graphs, complex functions have four-dimensional graphs and may usefully be illustrated by color coding a three-dimensional graph to suggest four dimensions, or by animating the complex function's dynamic transformation of the complex plane.
Read more about this topic: Complex Number
Famous quotes containing the words complex and/or analysis:
“In the case of all other sciences, arts, skills, and crafts, everyone is convinced that a complex and laborious programme of learning and practice is necessary for competence. Yet when it comes to philosophy, there seems to be a currently prevailing prejudice to the effect that, although not everyone who has eyes and fingers, and is given leather and last, is at once in a position to make shoes, everyone nevertheless immediately understands how to philosophize.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Whatever else American thinkers do, they psychologize, often brilliantly. The trouble is that psychology only takes us so far. The new interest in families has its merits, but it will have done us all a disservice if it turns us away from public issues to private matters. A vision of things that has no room for the inner life is bankrupt, but a psychology without social analysis or politics is both powerless and very lonely.”
—Joseph Featherstone (20th century)