Mathematics

General objectives: to acquire basic knowledge of classical projective geometry and plane algebraic curves. Specific objectives: Knowledge and understanding: at the end of the module the student will have acquired the basic notions and results relating to classical projective geometry (projectivity, perspectives, cross-ratio, single-line constructions) and to the theory of plane algebraic curves (Bezout's theorem, singularities, inflections and elliptic curves). Applying knowledge and understanding: at the end of the module the student will be able to solve simple problems that require the use of geometric techniques in the study of projective spaces and algebraic curves. Critical and judgment skills: the student will have the basics to analyze the analogies and relationships between the topics covered and topics in the history of mathematics (on the development of projective geometry) and in the use of elliptic curves in cryptography. Communication skills: the student will have the ability to correctly expose the course contents to an audience of people with appropriate mathematical knowledge. Learning skills: the acquired knowledge will allow a study, individual or taught in a PhD course, related to more advanced aspects of algebraic geometry and cryptography.