B029070 - MATHEMATICS WITH ELEMENTS OF STATISTIC

Italian

Basic arguments of linear algebra and analytic geometry. Algebraic and transcendent functions and their graphs. Differential and integral calculus. Selected examples of differential equations. Arguments of probability calculation and mathematical statistics.

Vinicio Villani e Graziano Gentili, Matematica. Comprendere e interpretare i fenomeni delle scienze della vita, 5/ed con connect, McGraw Hill Education, Milano 2029, ISBN: 9788838615351.
Notes provided by the teachers.
A complete and updated bibliography will be indicated at the beginning of the course.

Study materials produced by the teachers

With regard to the addressed topics, the students must show:
- to have the basic knowledge and the ability to understand mathematical statistical and probabilistic concepts and to know how to use and apply them to solve exercises and to propose simple mathematical models for problematic situations at various levels of complexity related to contexts coming from the natural sciences;
- to know how to organize the knowledge in a hypothetic-deductive way, in particular to be able to organize hierarchically definitions, sufficient conditions, necessary conditions, characterizations, properties and to be able to draw simple conclusions by discussing the hypotheses assumed;
- to know how to construct, analyze and process simple mathematical models suitable for interpreting problematic situations that arise from experimental contexts of the natural sciences.
- to possess communication skills, by using correctly the mathematical statistical and probabilistic language;
- to show good abilities to learn autonomously and personally and to deepen the themes developed in teaching.

Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to understand the arguments developed in the course, as they are normally developed in every pre-academic teaching, which is supposed to be followed with seriousness and commitment.
The followings are indispensable: strong convictions about the importance of scientific-mathematical knowledge in the more general context of the whole culture, a positive attitude towards mathematics and awareness of the importance of mathematical and scientific education for the exercise of conscious and active citizenship.

Lecture-style instruction. As far as possible, students may be required to expose suggestions and remarks on the various topics and to try to solve exercises and to suggest mathematical models for simple problematic contexts.
Through the student reception, it will be possible to discuss and deepen in individual way topics chosen by students and clarify questions posed by the students.

Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis. It is also encouraged the use of comunications via e-mail or the forum included in MOODLE for any question.

Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral examination is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to structure hierarchically the mathematical knowledge learned by enhancing the originality and autonomy of mathematical thought.

Recalls of basic facts from pre-university teaching. Arithmetic. Data representations. Elements of analytical geometry and linear algebra. Algebraic and transcendental functions. Differential calculus. Integral calculation. Differential equations. Elements of discrete and continuous probability. Elements of mathematical statistics.