Algebraic algorithms discovered in the last three decades, coupled with inexpensive high speed computation have created a minor revolution at the research level in algebraic geometry. The new computational methods have found wide application in a number of other fields (including robotics, computer science, and CAD). These ideas are accessible to undergraduates and, in fact, sometimes simpler to grasp than the material in the standard abstract algebra course. This project is creating materials which introduce and explore these methods. The materials can be used as the basis of a number of useful and accessible first algebra courses for students of science, mathematics and engineering.
