Unit GEOMETRY III
- Course
- Mathematics
- Study-unit Code
- 55256509
- Curriculum
- In all curricula
- Teacher
- Daniele Bartoli
- Teachers
-
- Daniele Bartoli
- Hours
- 73 ore - Daniele Bartoli
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- 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
- For further information, please contact the teacher
daniele.bartoli@unipg.it - Learning verification modality
- The test consists of three parts
-TEST concerning definitions and statements (30. minutes)
- WRITTEN TEST concerning the resolution of exercises (at least 2,5 hours)
- ORAL EXAM on theoretical notions (at least 30 minutes)
The test is aimed at verifying the student's basic knowledge.
The written test is aimed at verifying the ability to solve exercises.
The oral exam is aimed at verifying the understanding of the topics covered e
of the student's communication skills.
The three tests must be done in the same appeal. Passing the TEST is necessary for the continuation of the exams.
For information on support services for students with disabilities and / or SLD visit http://www.unipg.it/disabilita-e-dsa - 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.
Bezout's Theorem.
Plane algebraic curves: singularities, tangents, intersection numbers.