Acquire awareness and mastery of the elementary notions of linear algebra in order to introduce the student to the language of vectors and matrices. Applications to linear systems and analytical geometry will have particular importance. Know how to consciously reproduce the main demonstrative phases of theory construction. Knowing how to frame and solve problems and exercises on the diagonalization of matrices, quadratic forms and basic analytical geometry.
Course Prerequisites
Elementary algebra and some basic calculus.
Teaching Methods
Lessons and exercise sessions.
Assessment Methods
The exam consists of a written and an oral exam. The written exam consists of exercises to be carried out on various topics covered in the course. To access the oral exam, the student is required to achieve a minimum score of 15/30 in the written test. The oral part is more theoretical and tests knowledge and understanding of the definitions, statements and proofs of the theorems covered in class. The formulation of the grade will be obtained by considering the overall breadth and depth of learning, as well as the clarity of the presentation and the skills demonstrated in problem solving. The grade will be obtained from the comparison, not necessarily reduced to an arithmetic mean, of the evaluation of the written part and the oral part.
Texts
E. Sernesi: "Geometria 1", Bollati Boringhieri. S. Lang: "Algebra Lineare", Bollati Boringhieri. Lecture notes given by the the professor.
Contents
Linear algebra
Extended summary Geometric vectors. Vector Spaces generators and linear dependence, basis. Linear systems, matrix rank. Determinant, linear problems coordinates and change of coordinates. Operators, eigenvalues and eigenvectors. Diagonalization. Bilinear forms and scalar products. Lines and plane in the space, example of curves and of surfaces.
Course Language
Italian
More information
The students belonging to the categories of the project on innovative teaching will have the possibility to attend office hours also in the late afternoon and to see the notes of the lectures.
