## Learning objectives

The objectives of the course are not limited to the simple acquisition of mathematical tools, but we want to emphasize a deeper critical understanding of the ideas and of the thinking attitude. At the end of the course the student must therefore have acquired basic knowledge and skills in mathematics, starting from the structure of the Euclidean space, up to the differential and integral calculus for functions of one real variable. At the same time he will be able to apply such knowledge in a critical way to various concrete problems, in a solid way, and to handle them easily in relation to other areas of knowledge. In particular, the student must be able to:

be familiar with the basic theories of Linear Algebra and of Geometry and apply them to the manipulation of vectors and matrices in Euclidean space, to the computation of determinants, to the resolution of linear systems and simple exercises of linear geometry in space that in particular concern plans and lines;

be familiar with the structure of sets of real and rational numbers and with basic concepts of integro-differential calculus for functions of one variable (limits, derivatives, definite and indefinite integrals);

be able to qualitatively study problems such as the behavior of a function for certain values of the independent variable; (knowledge and ability to understand)

through the exercises carried out in class on the topics of the program, learn how to apply the abstract knowledge acquired to simple and concrete cases and, only in the second part of the course, be able to connect different concepts in order to solve complex exercises in an independent way;

use the mathematical method to break down complex problems into more easily attackable sub-problems; (ability to apply knowledge and understanding)

evaluate the consistency and correctness of the results obtained and analyze the appropriate resolution strategies for the proposed exercises; (autonomy of judgment)

learn how to use a formally correct language allowing to communicate both the contents of the program and the logical steps used in the resolution of the exercises, showing clarity of exposure and thought. Frontal lectures and direct comparisons with the teacher will ease the acquisition of a specific and appropriate scientific vocabulary; (communication skills)

autonomously deepen their knowledge; starting from the basic tools provided in the course, learn how to appropriately and effectively use additional tools and mathematical concepts. These will be important in the remaining courses of the Degree. (learning ability)