The second chapter contains five papers that describe approaches to core courses in the undergraduate major that excite student interest while delivering solid mathematics courses. In the first paper, Jason Douma of the University of Sioux Falls discusses how an abstract algebra course can be organized around an open-ended research project. The project is not an application of material presented in class but rather serves to motivate and generate the course content. In the same vein, Jill Dietz of St. Olaf's College used a guided discovery approach to generate student input and ideas that eventually lead to a course in module theory as a follow-up to an introductory course in abstract algebra. In both cases, students are expected to be extremely active and, with appropriate guidance, develop the course material on their own. Both papers contain a good deal of supplementary material to support implementation of the respective approaches.

This theme continues in the geometry article by Jeff Connor and Barbara Grover of Ohio University. In this case however, the students are expected to generate axiom systems for both Euclidean and non-Euclidean geometries, using technological supplements when appropriate. Likewise, Samuel Smith of St. Joseph's University works to maximize student participation in developing a topology course that is intended to appeal across the board and not just to students planning to do graduate work. The key in this case is using an initial geometric approach to motivate the axiom structure that characterizes topology.