Course Topics
· Introduction to Computational Modelling, Numerical Error, and Finite-Precision Computation · Numerical Linear Algebra: LU, Cholesky, and QR Factorization · SVD, Data Compression, and Principal Component Analysis · Least Squares, Linear and Nonlinear Regression, and Gauss–Newton Method · Dynamical Models: Numerical ODEs and Parameter Estimation · Eigenvalue Problems and the Google PageRank Model

Teaching format
The course includes frontal lectures and exercises.

Educational objectives
Knowledge and understanding: - D1.1: Have a solid knowledge of mathematical analysis, algebra, numerical calculus, discrete mathematics and elementary notion of logic that are in support of computer science. Applying knowledge and understanging: - D2.1: Be able to use the tools of mathematics and logic to solve problems. Ability to make judgments: - D3.2: Be able to work autonomously according to the own level of knowledge and understanding. Communication skills: - D4.1: Be able to use one of the three languages English, Italian and German, and be able to use technical terms and communication appropriately. Learning skills: - D5.1: Have developed learning capabilities to pursue further studies with a high degree of autonomy.

Assessment
The written exam will include verification questions, transfer-of-knowledge questions, and exercises. The aim is to assess the extent to which students have acquired knowledge and understanding, are able to apply that knowledge, and can demonstrate critical judgment. The same assessment criteria apply to both attending and non-attending students.

Evaluation criteria
The final written exam accounts for 100% of the grade and covers the entire program. Exam questions will be assessed based on correctness, clarity, quality of argumentation, and problem-solving ability. The same evaluation criteria apply to both attending and non-attending students.

Required readings

· M. T. Heath, Scientific Computing: An Introductory Survey, revised 2nd ed., SIAM, 2018.

Supplementary readings

· A. Greenbaum and T. P. Chartier, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms, Princeton University Press, 2012

· J. Shlens, "A Tutorial on Principal Component Analysis," 2014

· D. F. Griffiths and D. J. Higham, Numerical Methods for Ordinary Differential Equations: Initial Value Problems, Springer, 2010

· Lecture slides, selected articles, MATLAB documentation

Further information
If the use of specific software is required, it will be communicated during class by the lecturer.