The course introduces the student to the language, the precision and the accuracy necesary for the study of basic concepts of Linear Algebra and Analytic Geometry: among these, vector space theory, matrix calculus, resolutions of linear systems, linear applications, computation of eigenvalues and eigenvectors, diagonalizations of matrices, lines and planes in the 3-dimensional space, conics in the plane and quadrics in the 3-dimensional space.
The student at the end of the course will be able to: compute the rank of a matrix, solve linear systems, determine the dimension of a vector space and compute a base, study linear applications between vector spaces, compute eigenvectors and eigenvalues of endomorphisms, diagonalize matrices, solve problems of linear geometry with points, lines and planes in the 3-dimensional space, classify and study conics, study conic bundles, classify quadrics in the 3-dimensional space.
The student will face various theoretical aspects of the topics covered, improving logic skills in order to use with precision and accuracy some significant mathematics proof methods. Such proofs are presented in order to catch every detail necessary to reach the target. Moreover, for every topic covered the students are proposed various exercises, to do in the room during the lesson or at home.
Studying Linear Algebra and Geometry and testing their skills through exercises, the student will will learn to communicate with clarity and rigour both, verbally and in writing. The student will learn that using a correct terminology is one of the most important tools in order to communicate correctly in scientific language, not only in mathematics.
Students will be able to use acquired notions, concepts and methods in their further studies.
During the lessons topics and concepts will be proposed in a formal way, together with meaningful examples, applications and exercises. A tutor will carry classroom exercises. The student will be sollicited to carry out exercises autonomously, even during the lessons.
The prooves of the theorem signed with * can be ometted.