Title:  Introduction to vector bundles and their classifications

Abstract:  We will introduce the definition of a vector bundle and look at a few examples. Next we will look at how to make new vector bundles from old bundles using familiar algebraic operations like direct sum, tensor product, and the pullback. Finally we will discuss classifying isomorphism classes of bundles over a topological space X, and time permitting, we will show these isomorphism classes are in bijection with homotopy classes of maps from X to Grassmanians on R infinity.