Study-unit NUMERICAL MODELS

Course name	Mathematics
Study-unit Code	55A00097
Curriculum	Matematica per la crittografia
Lecturer	Bruno Iannazzo
Lecturers	Bruno Iannazzo
Hours	47 ore - Bruno Iannazzo
CFU	6
Course Regulation	Coorte 2023
Supplied	2024/25
Learning activities	Affine/integrativa
Area	Attività formative affini o integrative
Sector	MAT/08
Type of study-unit	Opzionale (Optional)
Type of learning activities	Attività formativa monodisciplinare
Language of instruction	Italian or English (only if all students agree).
Contents	Selected topics in Numerical Linear Algebra for Numerical Modeling
Reference texts	Horn, Johnson, Matrix Analysis. Material provided by the teacher. During the course text based on the topics chosen by the students will be indicated.
Educational objectives	The course aims at presenting advanced topics of numerical analysis and applications to mathematical modeling. The mathematical models will be studied in detail. The student will be aware of advanced methodologies in numerical analysis, and will use some scientific research techniques. The student will be able to appreciate the richness of mathematical modeling with the application of linear algebra techniques to problems in very different contexts (differential equations, applied probability, social network analysis).
Prerequisites	Linear algebra, Multivariate analysis, Numerical Analysis (it may be useful an elementary knowledge of Functional Analysis and Differential Geometry).
Teaching methods	Face-to-face lectures and laboratory with Matlab/Octave.
Learning verification modality	Oral exam of about one hour. (Optional mid-term exam on a presentation.)
Extended program	Matrix analysis. Positivity: Perron and Frobenius theory. Localization of eigenvalues. Krylov subspace method. Tensor analysis. There will be applications to mathematical models: Markov chains, differential equations, complex networks.
Obiettivi Agenda 2030 per lo sviluppo sostenibile