Mørken K. Numerical Algorithms and Digital Representation

Oslo: University Press, 2008. - 89p.These lecture notes form part of the syllabus for the first-semester course MATINF1100 at the University of Oslo. The topics roughly cover two main areas: Numerical algorithms, and what can be termed digital understanding. Together with a thorough understanding of calculus and programming, this is knowledge that students in the mathematical sciences should gain as early as possible in
their university career. As subjects such as physics, meteorology and statistics, as well as many parts of mathematics, become increasingly dependent on computer calculations, this training is essential.
Our aim is to train students who should not only be able to use a computer for mathematical calculations; they should also have a basic understanding of how the computational methods work. Such understanding is essential both in order to judge the quality of computational results, and in order to develop new computational methods when the need arises.
In these notes we cover the basic numerical algorithms such as interpolation, numerical root finding, differentiation and integration, as well as numerical solution of ordinary differential equations. In the area of digital understanding we discuss digital representation of numbers, text, sound and images. In particular, the basics of lossless compression algorithms with Huffman coding and arithmetic coding is included.