- knowledge of elementary arithmetic operations
- the Euclidean algorithm in various contexts and applications
- elementary linear algebra algorithms (Gaussian elimination)
- some factorisation methods (integers, various polynomial rings)
- LLL algorithm, aim and application
- discrete Fouriertransform
- the ability to implement and apply some of these algorithms
- a feeling for the theoretical and practical complexity of these algorithms
The aim of the lectures will be to provide an introduction into the area of computer algebra. The main focus will be on algebra and algorithms, but there will also be some attention to complexity and implementation issues.
On the one hand this should give some insight into the underlying mathematics, on the other hand also some ability to use computer algebra systems will be acquired. This should lead to an understanding of the theoretical possibilities and the practical limitations of computer algebra.
Among others, topics will be algorithms for efficient integer, rational and modular arithmetic, and computing with polynomials, rational functions and power series, determining the factorization and common factors of integers and of polynomials over finite fields or the integer ring, as well as some techniques from linear algebra and algebraic geometry.