Heinz Lüneburg
Abstract
Five years ago, I discovered the computer for myself. This was certainly no accident, as some people thought not having read carefully enough the books I wrote. I always included one or the other algorithm in them for potential use as a calculation device. Most of these algorithms were very naive I must admit. Anyway, five years ago, I started using the computer. Since I had to learn the art right from the beginning, I began teaching the subject to my students. This seems absurd, but it is the way professors learn. I realized immediately several things. First of all, there existed no book presenting algebra in such a way that one could compute in the end the objects one is dealing with; I say "existed," since the book of Lipson [2] appeared in the meantime. Also, Buchberger, Collins and Loos [1] is a very valuable publication indeed in this context. Secondly, our students - I am speaking of Western Germany and of students of mathematics - do not got enough computing experience. The situation seems improving, but still a lot has to be done in my opinion. Thirdly, applied mathematics or rather applicable mathematics is still considered to be numerical mathematics by many collegues. Of course, one has to integrate numerically differential equations to get a probe near Saturn, but the quality of the pictures we get from there depends heavily on algebra and algebraic computing. Hence algebra has to be taught in a new way. All the beautiful achievements of the last two or three decades in computational algebra should become part of our teaching. For this purpose books must be written. Lipson [2] is a good example for what I mean, but it does not cover enough ground. I am actually writing one planned to have two or three volumes. It will be concerned with the basic algebraic structures including programs ready to use. A preliminary draft of some of them has been published [3]. Unfortunately, this preprint is out of print, but a friend of yours may happen to have got a copy as well as more material about the book to inform you.
- Buchberger, B., G. E. Collins, and R. Loos, Computer Algebra. Computing Supplementum 4. Wien New York: Springer-Verlag 1982.Google Scholar
- Lipson, J. D., Elements of Algebra and Algebraic Computing. Reading, Mass.: Addison-Wesley 1981.Google Scholar
- Lüneburg, H., Programmbeispiele aus Algebra, Zahlentheorie und Kombinatorik. FB Mathematik, Universität Kaiserslautern. Preprint no. 40, 1982.Google Scholar
- Nijenhuis, A. and H. S. Wilf, Combinatorial Algorithms. 2nd ed. New York etc.: Academic Press 1978.Google Scholar
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