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KnowledgeThe student who successfully completes the course will have the ability to manage projective spaces and homogeneous coordinates, will get a basic knowledge on general topology. Also he/she will be able to calculate the fundamental group of not too much complicate topological spaces, including real and complex projective quadrics. The student will finally get a basic knoledge of holomorfhic functions of one complex variable.
Assessment criteria of knowledgeThe student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology.
- Final oral exam
- Final written exam
- Periodic written tests
Delivery: face to face
- attending lectures
- individual study
- group work
- Task-based learning/problem-based learning/inquiry-based learning
SyllabusA first approach to projective space, including homogeneous coordinates, subspaces, conics and quadrics. Basis of general topology, including comparison of topologies, Hausdorff separation axiom, connectedness and arc connectedness, compactness. A first approach to Algebraic topology; homotopy of maps, contractible space, deformations. The fundamental group. Holomorphic function of one complex variable. Definitions, examples, Cauchy theory, Residue theorem.
BibliographyManetti M. Introduzione alla topologia generale Cartan H. Fonctions analytiques d'une ou plusieures variables complexes (also in English) Personal lectures notes of the teachers on line.
Ultimo aggiornamento 14/11/2016 17:27