A three-semester core curriculum for undergraduate computer science is proposed and described. Both functional and imperative programming styles are taught. The curriculum particularly addresses the problem of effectively presenting both abstraction and implementation. Two courses in the first semester emphasize abstraction. The next courses stress implementation as well as analysis. The third semester provides practical experience in programming. This curriculum has innovative aspects with respect to organization, methodology, and content. By integrating programming with mathematics in the first semester, abstractions and implementation become partners rather than competitors. In the later courses, implementation can be emphasized more naturally because of the early mastery of abstraction. The methodology emphasizes active learning via concrete laboratory experiences, and introduces multiple languages within the first year. (Contains 11 references.) (Author/BEW)