Module page
Geometry I
| academic year: | 2013/2014 |
| instructor: | Kieran O'Grady |
| degree course: | Mathematics - DM 270/04 (triennale) |
| type of training activity: | di base |
| credits: | 9 (72 class hours) |
| scientific sector: | MAT/03 Geometria |
| teaching language: | italiano |
| program: | I-Z |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject: Projective spaces. Duality. Quadric hypersurfaces: polarity, classification modulo projectivities. Hypersurfaces. Resultant of two polynomials. Bezout's Theorem for plane curves. Topological and metric spaces, continuos maps. Separation axiom and countability axioms. Subspaces, products, connectedness, compactness. Quotient topology. Topological manifolds. Topological proof of the Fundamental Theorem of Algebra.
Suggested reading: E. Sernesi: Geometria 1, Bollati Boringhieri. M. Manetti: Topologia, Springer.
Type of course: standard
Knowledge and understanding: Successful students will have a basic knowledge of main topics in Projective Geometry (coordinates in projective spaces, elementary theory of conics and quadrics) and of general topology.
Skills and attributes: Successful students will be able to solve elementary problems concerning the above aspects of Projective Geometry and general topology.
Personal study: the percentage of personal study required by this course is the 65% of the total.