In this talk we will provide a basic motivation for the use of multiscale methods in scientific computation. A brief introduction into the discretization of differential equations will lead us into the discipline of scientific computing. Classical computational methods will be shown to not be practical for problems of modern-day interest. We will see that multiscale methods are a natural approach for many scientific and engineering problems and that they lead to optimal solution techniques. The conclusion of this talk will focus on the multigrid method and its extensions to algebraic problems.

NOTE: This talk is intended to be introductory. A basic knowledge of differential equations and linear algebra are the only prerequisites.