Take the tour ×  What exactly is "Approximation Theory"? If I
read the wikipedia-article I doesn't get much clearer. Why are
"pure" mathematicians interested in it? I see a lot of people
that do harmonic analysis also do approximation theory.
share|improve this question add comment  1 Answer  up vote 6
down vote accepted  Approximation theory includes many subject
areas of analysis, but the common idea is how well a target in a
topological space (often a metric space) can be approximated by
the points of a narrower subspace.  Some examples will
illustrate the breadth of this topic. Given a real number x of a
certain kind (e.g. algebraic), what are the rational numbers of
bounded denominator that best approximate x, using the least
absolute value of their difference as the objective?  Given a
real function $f$ on $[0,1]$ of a certain kind (e.g. twice
continuously differentiable), what are the polynomials of
bounded degree that best approximate $f$? There are a variety of
objectives that might be used, such as