Mathematics

Knowledge and understanding: at the end of the course the student will have acquired the notions and the results basics related to singular homology, to the study of differentiable varieties and a fair knowledge of Riemann's theory of surfaces. Apply knowledge and understanding: at the end of the course the student will be able to solve even complex problems that require the use of techniques related to de Rham's cohomology, the Hurwitz theorem and the Riemann Roch theorem for compact Riemann surfaces; will be able to determine the kind of a Riemann Surface and the size of the linear systems variety cohomology groups. Critical and judgmental skills: the student will have the bases to analyze the analogies and the relationships between topics that vary between algebraic topology, differential geometry, complex geometry and also algebraic geometry. Communication skills: ability to expose the contents in the oral part of the verification and in the any theoretical questions present in the written test. Learning skills: the knowledge acquired will allow you to devote yourself to more specialized aspects of geometry.