The text is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on, experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires completion of one year of calculus. The course provides a transition to the study of higher, abstract mathematics. The text is written independent of any software. Supplements will be available on the projects' web site.

Preface Introduction 1: Iteration of Linear Functions 2: Cyclic Difference Sets 3: The Euclidean Algorithm 4: Prime Numbers 5: The Coloring of Graphs 6: Randomized Response Surveys 7: Polyhedra 8: The p-adic Numbers 9: Parametric Curve Representation 10: Numerical Integration 11: Sequences and Series 12: Experiments in Periodicity 13: Iteration to Solve Equations 14: Iteration of Quadratic Functions 15: Iterated Linear Maps in the Plane 16: Euclidean Algorithm for Complex Integers Index