Unit GEOMETRY III
- Course
- Mathematics
- Study-unit Code
- 55256509
- Curriculum
- In all curricula
- Teacher
- Giuliana Fatabbi
- Teachers
-
- Giuliana Fatabbi
- Hours
- 73 ore - Giuliana Fatabbi
- CFU
- 9
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Caratterizzante
- Area
- Formazione teorica
- Academic discipline
- MAT/03
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Projective geometry. Plane algebraic curves.
- Reference texts
- E. Sernesi, Geometria 1, Bollati-Boringhieri, 2000.
M.C. Beltrametti, E. Carletti, G. Monti Bragadin, D. Gallarati, Lezioni di geometria analitica e proiettiva, Bollati-Boringhieri, 2002.
C. G. Gibson, Elementary Geometry of Algebraic Curves, An Undergraduate Introduction, Cambridge University Press,1998.
E. Fortuna, R. Frigerio, R. Pardini, Projective Geometry: Solved Problems and Theory Review, Springer 2016 - Educational objectives
- Basic knowledge of projective geometry and of classical notions og algebraic curves.
Development of capability to face topics in a rigorous way and of capabilty to expose mathematical subject either in ored to teach them or in order to
Exercises and questions should lead inside the definitions and results.
Development of solving-problem ability using the topics faced in the course. - Prerequisites
- Linear algebra. Affine geometry.
- Teaching methods
- face-to-face
- Other information
- As an experiment and with student's agreement, English can be the language either of the entire course or of a part of it. The exam can be attended in English.
- Learning verification modality
- The exam consists of 2 parts: written and oral
Written part: exercises on the topics developed during the course
Oral part: a talk on some topics developed during the course, subjects are chosen by the committee
The written exam lasts 2 hours
The oral exam lasts 30-45 minutes
Upon students' request two partial written exams can be done whose positive result is equivalent to a positive result of any written exam in one of the sessions in the same academic year.
The written test is passed with an evaluation greater than or equal to 15/30.
The students which pass the written test in one of the sessions have to take the oral part in the same session.
The failure in one session implies that the students have to do the written test again in one of the subsequent sessions. - Extended program
- Projective Geometry: projective space. Homogeneous coordinate system and projective frames. Projectivation of the affine plane. Real projective line and plane. Complex projective line. Projectivity. Dual projective space.
Conics and quadrics: classification
Plane algebraic curves: singularities, tangents, intersection numbers.