This course brings fundamental mathematical concepts to life by studying concrete examples of important everyday problems and explaining how they are solved by numerical algorithms. The students will understand the theoretical background of these methods, learn how to implement them, and experience the practical aspects.
We cover some key numerical algorithms for real-world applications, like GPS localization, TrueType fonts, robotic motion, Google’s PageRank, and JPEG compression. After going through some preliminary basics (Newton's root finding method, direct and iterative methods for solving linear systems, polynomial interpolation), we are ready to discuss the algorithms above, which are based on the concepts of least squares, Bézier curves, quadrature, eigenvalues, and the discrete cosine transformation, respectively.
The topics will be presented in the form of lectures and tutorials. Homework assignments with theoretical and practical programming exercises will be handed out, graded, and discussed.
The course grade is determined by the results of the homework assignments (50%) and the written final exam (50%).
- Timothy Sauer. Numerical Analysis. Second Edition. Pearson, 2012 Additional material will be provided through the course homepage.