Computer algebra and fast algorithms

The utility of modern symbolic computation packages in a course of convolution and discrete Fourier transform (DFT) algorithms is presented. It is shown how Mathematica has been used to help illustrate the number-theoretic, polynomial, and finite-field computations involved. The result is that students are relieved of much of the algebraic drudgery and can concentrate on learning the fundamental aspects of the subject. It has been found that large problems can be successfully solved by students in a way that they find to be both interesting and satisfying. In addition, symbolic verification techniques can be used to prove the correctness of the results that are obtained.<>