The course aims to gradually introduce students to formalism, terminology and logic of mathematics tools, which are essential prerequisites for a proper assimilation of many of the economic,statistical and financial content disciplines,  that the student will face in the following. In addition to accustom students the practical use of the tools of algebra and differential calculus, the course aims to educate them in a logically consistent and rigorous approach to the problems, through the logical-deductive method typical of mathematics. The formal discussion of the items will be preceded by a heuristic and intuitive approach, and for many of them will be indicated the possible applications for the description of systems and processes of economic, social and financial. The more theoretical  lessons will be supplemented by exercises in the classroom in order to guide students in independent study and practice.

1. Introductory elements. Elements of logic, elements of set theory. Real numbers, real functions of a real variable, elementary graphs of polynomial functions, fractional, exponential, logarithmic, circular functions.

2. Elements of linear algebra. Algebra of vectors and matrices. Systems of linear equations.

3. Elements of Mathematical Analysis. Notes on numerical sequences and numerical series. Limits of real functions of real variable. Continuity and global theorems for continuous functions. Notion of derivative and derivation rules. Differential calculus theorems, Taylor polynomial. Qualitative study of the graph of functions. Functions of two or more variables. Partial, maximum and minimum free derivatives.

4. Some basic notions for statistics. Statistical Indices such as

CENTRAL TREND (Medium, Median, Fashion, Quantiles, Percentiles)
DISPERSION (Variation range, Average absolute deviation, Variance, Standard deviation, Coefficient of variation)
FORM (Asymmetry coefficient, Kurtosis coefficient)

- Knowledge and understanding: at the end of the course students must have acquired the knowledge and understanding of the topics developed in class. In particular they must know and understand the concept of function in one or more variables and the algebraic part (matrices / vectors). The didactic work methods with which these results will be achieved will consist of: lectures in the classroom and at home and in-depth seminars.

- Applied knowledge and understanding: students must be able to apply the acquired knowledge appropriately and flexibly to analyze, understand and solve both analytical and methodological problems. The didactic work methods with which these results will be achieved will consist of: lectures, analysis and discussions on some topics, exercises and in-depth seminars.

- Making judgments: students must have the ability to link the knowledge acquired during the course into integrated and unitary schemes and to deal with complex problems autonomously and with their own judgment. The didactic work methods with which these results will be achieved will consist of: lectures, analysis and discussions of some problems, in-depth exercises.

- Communication skills: Students must acquire a clear and effective communication skills, thanks to a good command of the vocabulary related to the topics covered during the course. The didactic work methods with which these results will be achieved will consist of: lectures, exercises on the blackboard, presentation of papers.

- Ability to learn: Students must have developed good learning skills, which allow them to deepen the knowledge acquired during the course and to put them into practice by developing models. The didactic work methods with which these results will be achieved will consist of: lectures, classroom and home exercises, group work and in-depth seminars, production of papers.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

The teaching material made available by the teacher can be found, together with other support activities, within the Moodle platform › blended.uniurb.it

Teaching

The course involves the use of different teaching methods:

- frontal lessons;
- Classroom exercises.
- Exercises at home.
- Development of topics proposed by the students
- Educational seminars on particular topics of interest

Attendance

The course does not require attendance

Course books

Titolo Matematica
Autore Guerraggio Angelo
Dati 2004, 432 p.
Editore Mondadori Bruno (collana Campus)

Assessment

The exam consists of a written test articulated on questions that will be half on the part of Mathematical Analysis and half on the part of Algebraic Geometry. If the written test is passed with at least 15/30, the oral exam can be taken.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

The course involves the use of different teaching methods:

- Exercises at home.
- development of topics proposed by the students
- educational seminars on particular topics of interest

Course books

Titolo Matematica
Autore Guerraggio Angelo
Dati 2004, 432 p.
Editore Mondadori Bruno (collana Campus)

Assessment

The exam consists of a written test articulated on questions that will be half on the part of Mathematical Analysis and half on the part of Algebraic Geometry. If the written test is passed with at least 15/30, the oral exam can be taken.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

The student can request to sit the final exam in english.