Mathematics and Algorithms for Computer Algebra

This course will be mainly mathematics, some computer science and a little computing. Little or no essential use will be made of actual computer languages, although I may occasionally use Pascal, C, Lisp or REDUCE for concrete examples. The aim of the course is to provide an entry into the current research literature, but not to present the most recent research results. The first half of the course (taught by me) will deal with basic mathematics and algorithms for computer algebra, primarily at the level of arithmetic and elementary abstract algebra, including an introduction to GCDs and the solution of univariate polynomial equations. This leads into the second half of the course (taught by Dr Jim Skea) on the more advanced problems of polynomial factorization, indefinite integration, multivariate polynomial equations, etc. The first week provides an introduction to the computing aspects of computer algebra, and contains almost no mathematics. It is intended to show how the later theory can be implemented for practical computation. The second week provides a rapid but superficial survey of the abstract algebra that is most important for computer algebra. The next five weeks will build on this abstract basis to do some more concrete mathematics in more details, referring back to the basis established in the first two weeks as necessary. At the end of each set of notes will be exercises, one (or more) of which will be assessed.