Themen der Lehrveranstaltung
Computational Mathematics aims to equip students with the knowledge and skills to derive, analyze, and implement numerical methods for solving systems of linear equations, computing eigenvalues and singular values of matrices, and approximating functions and roots. Students will engage with both exact and finite precision arithmetic to solve mathematical problems and study the underlying theory that supports numerical solutions. Key topics include stability, error analysis, and efficiency in numerical linear algebra and approximation algorithms. The course also introduces Matlab as a software environment for numerical computing, enabling high-performance matrix manipulation, data visualization, and efficient algorithm implementation. Information Security introduces the field of information security, covering both technical and management aspects. Students will learn the foundational principles of security and explore practical strategies for protecting information systems. The course offers a comprehensive view of how to identify vulnerabilities and implement effective safeguards in modern computing environments.

Unterrichtsform
The course includes frontal lectures and lab sessions.

Bildungsziele
Knowledge and Understanding – D1.1 Have a solid knowledge of mathematical, algebra, numerical calculus, and elementary logic that are in support of computer science. – D1.14 Know critical security aspects of information systems, the basic concepts of security and techniques for the development of secure systems. Applying knowledge and understanding – D2.1 Be able to use the tools of mathematics and logic to solve problems. – D2.11 Be able to evaluate the quality of information systems and to identify critical aspects. – D2.17 Ability to analyze and improve data privacy and data security features in the context of complex software infrastructures. – D2.19 Be able to apply your own knowledge in different working contexts. 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. – D4.5 Be able to work in teams for the realization of IT systems. Learning skills – D5.1 Have developed learning capabilities to pursue further studies with a high degree of autonomy. – D5.3 Be able to follow the fast technological evolution and to learn cutting edge IT technologies and innovative aspects of last generation information systems.

Art der Prüfung
Final exam: The exam covers topics from both Computational Mathematics and Information Security, each contributing 50% to the final grade. The Computational Mathematics part consists of a written exam with verification questions, knowledge transfer tasks, and exercises. The Information Security part includes a project, aimed at assessing knowledge application, and an oral exam with verification questions and discussion of the project. A midterm test will be offered at the end of the Computational Mathematics module, covering only its content. Students who score at least 18 out of 30 on the midterm will only need to complete the Information Security part in the final exam.

Bewertungskriterien
The exam is evaluated based on the correctness and clarity of answers, the ability to summarize and critically evaluate concepts, the capacity to connect different topics, problem-solving skills, critical thinking, and the quality of argumentation. To pass the exam, students must achieve a minimum score of 18 out of 30 in each module. Each module contributes 50% to the final grade. For Computational Mathematics, the assessment is based entirely on the written exam. For Information Security, the evaluation is split between a project (30%) and an oral exam (70%). The project assesses the ability to apply knowledge in a practical setting, to summarize concepts, to explain things balancing conciseness and completeness. The oral exam assesses the clarity of answers, the ability to recall principles and methods used of information security and the applied knowledge acquired with the project development.

Pflichtliteratur

 Anne Greenbaum and Tim P. Chartier. Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms. Princeton University Press, Princeton, N.J, illustrated edition, April 2012. ISBN 978-0-691-15122-9.

George Lindfield and John Penny. Numerical Methods: Using MATLAB. Academic Press, Waltham, MA, 3rd edition, July 2012. ISBN 978-0-12-386942-5.

 Dorothy C. Attaway Ph.D. MATLAB: A Practical Introduction to Programming and Problem Solving. Butterworth-Heinemann, Amsterdam Boston, 3rd edition, July 2013. ISBN 978-0-12-405876-7.

Slide materials and scientific articles

Weiterführende Literatur

Kendall Atkinson. An Introduction to Numerical Analysis. Wiley, New York, 2nd edition, January 1991. ISBN 978-0-471-62489-9.

 Cleve B. Moler. Numerical Computing with MATLAB. Society for Industrial and Applied Mathematics, Philadelphia, Pa, January 2004. ISBN 978-0-89871-560-6.

Computer & Internet Security: A Hands-on Approach 3rd Edition (ISBN: 978-17330039-4-0)

Computer Security: A Hands-on Approach, 3rd Edition (ISBN: 978-17330039-5-7)

Internet Security: A Hands-on Approach 3rd Edition (ISBN: 978-17330039-6-4)

Weitere Informationen
Software used: – MATLAB (https://www.mathworks.com/products/matlab.html) – Tools provided during lab sessions