MATHEMATICAL METHODS IN ENGINEERING (6 CFU)
Corso di Laurea Magistrale in Ingegneria Gestionale |
| IL CORSO SI TIENE IN LINGUA INLGESE |
| Docenti |
| Claudia Landi |
| Frequenza |
| Free |
| Periodo didattico |
| 1 semester |
| Obiettivi Formativi |
| The aim of the course is to offer the basic concepts of graph theory and algebraic topology together with applications to the study of organizational problems, analysis of networks, shape retrieval. |
| Prerequisiti |
| Basic notions of linear algebra |
| Modalità d'esame |
| Grading will be based on an oral exam for part 1, and a written dissertation on selected papers for part 2. |
| Programma del Corso |
Part 1. Graph Theory with Applications:
Graphs and subgraphs. Trees. Connectivity. Euler tours and Hamilton cycles. Matchings. Edge colourings. Independent sets and cliques. Vertex colourings. Planar graphs. Directed graphs. Networks. The cycle space and bond space.
Part 2. Topological analysis of shapes
Simplicial complexes. Homology groups. Matrix reduction. Persistent homology. Reeb graph. |
| Testi di Riferimento |
1. J.A. Bondy and U.S.R. Murty, "Graph theory with applications", North Holland, 1976.
2. H. Edelsbrunner and J.L. Harer, "Computational Topology: An introduction", AMS, 2009 |