Computer Arithmetic and Numerical Techniques

The course \Computer Arithmetic and Numerical Tech-niques" at the University of Antwerp, is an introductory scientiic computing course for students with a major in computer science or a combined major mathemat-ics/computer science. But it could as well be taught to any exact or applied science student with a reasonable high-school background in mathematics and a fair interest in computers. It is this growing group of science students interested in computer science that we are trying to encourage into scientiic computing. When the idea to set up a special course for computer science students was rst launched in 1993 | it is by the way often hard to get computer science students interested in scientiic computing | many colleagues worldwide reacted very enthusiastically. Unlike engineering students, CS-students are rarely confronted with real-life scientiic computing problems in other courses. Yet we believe that the best approach to a scien-tiic computing course is one where the complete journey is followed from physical problem to computational solution, as described in 1]. The basic steps in this journey are: 1. a motivating problem 2. the identiication of the computational problem behind the given real-life problem 3. the selection of an appropriate numerical technique developed for its solution 4. the actual implementation or use of a numerical routine, be it in Fortran, C, Mathematica, Matlab or the like 5. the evaluation or quality control of the numerical output. The course is structured in such a way that for each topic all of steps (1) through (5) are covered, with special attention to the computer science background of the students. On one hand, special care is taken when choosing motivating examples so that they are not too technical, yet reasonably real-life. On the other hand, all the aspects of step (4) are treated in great detail. Whereas other scientiic computing courses exist, this course is special in that it makes very explicit that one should distinguish between the properties of a mathematical algorithm and the properties of the al-gorithm's implementation in nite precision arithmetic on a computer. Computer science students are interested in computer arithmetic as part of scientiic computing, in the same way they are interested in learning about compilers in order to obtain a full understanding of programming languages. Taking these considerations into account, the course \Com-puter Arithmetic and Numerical Techniques" consists of two parts, one discussing how computations are performed on a binary machine …