corso|33500

Basic knowledge: elements of set theory, operations between sets, numeric sets, principle of induction, functions, operations, and algebraic structures Vector spaces: geometric vectors and their properties, Vector spaces, Linear independence and bases, Subspaces. Matrices: operations between matrices, the ring of square matrices. Linear systems: solving linear systems, Gauss elimination, homogeneous systems, rank of a matrix. Linear applications: linear applications between vector spaces, kernel and image, injectivity and surjectivity. Determinants: properties and applications of the determinant. Eigenvalues and eigenvectors: definition of eigenvalues, eigenvectors and eigenspaces. Calculation of eigenvalues. Simple endomorphisms and diagonalization. Euclidean vector spaces: Scalar product. Norm and orthogonality. Orthonormal bases. Isometries. Spectral theorem. Analytic geometry in space: Planes and lines in space. Bilinear and quadratic forms: conics and quadrics.

Notions of secondary school mathematics, e.g. numbers (natural, integer, rational, real), operations between numbers, elementary algebraic calculus, sets, elements of Euclidean geometry, and trigonometry.

ALGEBRA LINEARE E GEOMETRIA ANALITICA, Autori: A. Bernardi, A. Gimigliano, casa editrice Città Studi Edizioni

The lectures will be delivered in person and will be made available also on an online platform. During the lessons, all theoretical results will be followed by exercises to encourage the development of the ability to study mathematical problems that can be formalized in linear algebra. Each week homework will be given to verify the level of understanding of the student, and the excercises will be then corrected in the class the week after.

Frequency is not mandatory

The following elements will be considered in the evaluation of the exam : 1. the logic followed by the student in solving the exercises in the written exam 2. the correctness of the procedure adopted for the solution of the exercises 3. the appropriateness of the proposed solution in relation to the skills that the student is expected to have acquired at the end of the course; 4. the acquired knowledge of the theoretical results described during the course, also taking into account the property of language and formalism in describing them. Satisfaction of aspects #1 and #4 is a necessary condition for achieving a grade of 20. Grades above 24 will be awarded to students whose evidence satisfies all four aspects listed above.

GEOMETRIA, Autore: A. Cigliola, Edizioni LaDotta GEOMETRIA, Autore: A. Savo, Hoepli

The lectures will be delivered in person and will be made available also on an online platform. During the lessons, all theoretical results will be followed by exercises to encourage the development of the ability to study mathematical problems that can be formalized in linear algebra. Each week homework will be given to verify the level of understanding of the student, and the excercises will be then corrected in the class the week after.