BRINGING MATHEMATICS EDUCATION INTO THE ALGORITHMIC AGE

We began from the observation that most of our students find algorithms easy and natural and proofs difficult and obscure, and are totally unaware of the close relationship between algorithms and proofs. This observation led to the hypothesis that part of the problem lay in the fact that the students had been born into the algorithmic age, which their mathematics courses had largely yet to enter. This paper explores various ways in which mathematics courses can be made more algorithmic, both in style and in content. Particular attention will be paid to the term non-computable function, which will be seen as oxymoronic. An algorithmic explanation will be developed, particularly for the busy beaver function. We shall also give an algorithmic analysis of Cantor's diagonal method.