The purpose of the 300-level courses is to enable students to expand their view of algebra and geometry to include nonlinear motion and nonlinear functions. The investigation encompasses circular motion and the functions that describe it, ellipses and hyperbolas, exponential and logarithmic functions, dot products and matrices, and geometry on the surface of the Earth. In particular, logarithms are used to straighten nonlinear data; and matrices are used to describe geometric transformations and various patterns of growth. In preparation for 400-level mathematics, two strands are introduced: first, combinatorics and recursion, leading to the binomial theorem; second, approximation behavior, especially instantaneous rates of change and slopes of nonlinear graphs