1. Linear Space
2. Vector Spaces and Linear Maps
3. Matrices, determinant
4. Eigenvectors, eigenvalues, diagonalization
5. Scalar and Hermitian products, spectral theorem
6. Affine and euclidean geometry of the plane and of the space.
7. Conics and elements of theory of quadrics
A great number of texts provide excellent presentations of the topics summarized in the program. Among the others we recommend:
M. Abate - Chiara de Fabritiis, Geometria con elementi di algebra lineare, McGraw-Hill, Milano 2006.
S. Abeasis, Geometria Analitica del piano e dello spazio, Bologna 2002.
The texts, recommended but not obligatory, besides covering the program, contain useful insights and complements presented with the same formulation and the same language used in the course. A book of exercises that can be useful is:
M. Abate - Chiara de Fabritiis, Esercizi di Geometria, McGraw-Hill, Milano 1999.
For most topics, Notes will be provided by the responsible of the course.
Learning Objectives
Knowledge acquired:
The course provides the fundamental notions of linear Algebra and Analytic Geometry.
Competence acquired:
At the end of the course the student will be able to solve basic problems of linear algebra and analytic geometry of the plane and of the space.
Skills acquired (at the end of the course):
The competences of Linear Algebra and Analytic geometry acquired in the course are those indispensable for learning the basic notions of Physics and to solve the related problems.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...):
300
Hours reserved to private study and other individual formative activities:
Contact hours for: Lectures (hours): 120
The course foresees 9 hours for week between lectures and problem sessions.
Contact hours for: Laboratory (hours):
Contact hours for: Laboratory-field/practice (hours):
The course foresees 9 hours for week between lectures and problem sessions.
Further information
Frequency of lectures, practice and lab:
The course foresees 9 hours for week between lectures and problem sessions. The nature of the material that is introduced in the progress doesn't allow to clearly distinguishing the plan "theoretical" from that of the "applications" that are generally motivations and essential examples for the understanding of the fundamental notions. Thus the didactic demands require often that the roles of the "lectures" and of the "problem sessions" could be exchanged and/or confused. The frequency to the lectures and the problem sessions is therefore equally important.
Office hours:
Teacher: Giorgio Patrizio
e-mail: patrizio@math.unifi.it
Office hours: On Tuesday at 3.30 p.m. (Dip. Di Matematica “U. Dini”, Viale Morgagni 67/A Firenze) and on appointment
Exercises: Carla Parrini
e-mail: parrini@math.unifi.it
Office hours: On Thursday at 12.30 p.m. (Sala Docenti, Blocco Aule, Sesto Fiorentino) and on appointment
Type of Assessment
The examination foresees a written test and an oral exam. Is possible to sustain the oral exam if the written test has a sufficient grade (18/30). Written test and oral exam must be sustained in the same session.
Students who have a grade of at least 20/30 in the written test, upon their request, may be exonerated from the oral exam. In this case the grade for the whole exam will be the grade obtained in the written test with a maximum of 27/30. To obtain a grade above 27/30 it is always necessary to undergo the oral exam.
During the period of the lessons, there will be tests in itinere to exonerate from the written test. There will be two tests, the first one to half course, the second at the end of the lessons. To be exempted from the written test it is necessary to get the average of 18/30 in the two tests, not less than 15/30 in the first one and not less than 18/30 in the second. For the exonerated students the same rules are valid as for those who pass the written test in the first session of examinations.
Course program
Fields and complex numbers. Systems of linear equations. Vector Spaces and linear maps. Matrices, determinant. Eigenvalues and eigenvectors, diagonalization. Scalar and hermitian products, spectral theorem. Affine and metric geometry in the plane and in the space.
Conics, elements of the theory of quadrics.