Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Pure and Applied Applications of Numerical Algebraic Geometry by Chris PETERSON, Colorado State University Abstract: The goal of this talk is to give a (biased) viewpoint of Numerical Algebraic Geometry and to illustrate why both pure and applied mathematicians should be interested in this area. Four examples that will be described are: Secant Varieties, the Twisted Cubic, Jordan Canonical Form, and Computer Vision.