Presentations:
Interpolation, Least Squares Approximations, Numerical Integration and Roots of Orthogonal Polynomials
By the time Euler was at the peak of his mathematical powers in the 18th century, the process of constructing polynomials that passed through a given set of points was well-understood. We’ll start with a look at this theory, and see why, when the data is experimental (i.e.), interpolation does not lead to viable models.
Gauss, and later Legendre, independently developed least squares as a tool to "see through" errors in datasets. When applied in the context of more general inner product spaces, however, least squares can serve as a lens to view the development of vast expanses of modern analysis. In this talk, we'll follow a small strand of this history and see how to develop useful tools for numerical integration that turn out to form part of the underlying justification for such modern techniques as the fast Fourier transform.
(More to come, or contact me.)
Links:
MAA Online (www.maa.org) is the principal website of the Mathematical Association of America. In addition to information about the MAA and its programs, this is the place to access Math in the News, regular columns and upcoming events sponsored by the MAA.
The Professional Development page has links to many of the MAA programs my office supports. See also the Special Interest Groups of the MAA (SIGMAAs), Sections, and our pages for students.
The MAA Mathematical Digital Library (MathDL) is a component of the National STEM Digital Library.
Various organizational & policy information is also on the MAA website. Of particular note is the Guidelines for Programs and Departments in Undergraduate Mathematical Sciences.
The MAA participates in the Joint Policy Board for Mathematics (JPBM) and the Conference Board for the Mathematical Sciences (CBMS), where you can find links to other professional organizations in the mathematical sciences.