A NEW APPROACH TO TEACHING DISCRETE MATHEMATICS
David Gries, Fred B. Schneider · PRIMUS · 1995
We advocate teaching introductory discrete mathematics by first teaching equational propositional and predicate logic and then using it as tool (and not simply viewing it as an object of study) throughout the study of later topics — e.g., set theory, induction, relations, theory of integers, combinatorics, solving recurrence relations, and modern algebra. The in-depth (6–7 weeks) treatment of logic emphasizes rigorous proofs, strategies for developing proofs, and much practice, so that students develop a skill in formal manipulation. Care is taken to explain all concepts clearly and rigorously. Later topics are dealt with by viewing them as theories — extensions of the predicate calculus. The course should motivate the use of logic as a pervasive tool. It must enlighten, and not stifle and oppress. Our experience shows that this is possible. Anecdotal evidence shows that students come away with less fear of mathematics, proof, and notation, more confidence in their mathematical abilities, an appreciation for rigor, and the urge to try out their new skills in other courses.