Mathematics is one of the oldest of all the sciences and as such it has a rich tradition. Today there are three broad areas of study in mathematics: Algebra, Analysis, and Topology. Algebra was created as a type of symbolic language for working with numbers and geometric objects. Analysis deals with questions concerning the infinite and the infinitesimal. Topology, one of the newest areas, was motivated originally by considering alternative constructs to Euclidean geometry but has now incorporated not only geometry but also the fundamental concepts of analysis and algebra. In fact, it is useful in some of our most basic physical theories, including relativistic and cosmological physics. Lying within and in some cases connecting these three broad areas are many specialized areas of study such as Combinatorics, Algebraic Topology and Geometry, Graph Theory, and Categorical Algebra. One such specialized area, Mathematical Modeling, deals with the application of mathematical ideas from all of these fields and subfields to real world problems. Even with all its applications, mathematics is a creative activity unto itself with many aspects being as aesthetically beautiful as the great works of art and music.