#
Mathematics and Informatics

A.Y. 2020/2021

Learning objectives

The teaching aids to student provides the basic notion of mathematical analisys and descriptive statistics to enable them to develop skills in data processing and modeling. One of the main aims of the course is to develop the ability to analyze the behavior of a real variable function, determining its graph in a system of Cartesian axes through the basic elements of the differential calculation. Another important educational objective pursued by the course is that of acquiring the basic skills in the elaboration of experimental data by introducing the commonly used statistical descriptors.

Expected learning outcomes

The student must know the main notions of mathematical analysis in relation to the study of a real function; in particular the student must know the meaning of domain of a fiction, of continuity of a function in an interval and of derivative of a function in a point. Furthermore the student must demonstrate to know the main statistical descriptors that allow to interpret a series of experimental data. The student must be able to interpret the progress of a function and must be able to describe a series of experimental data on a statistical level. Through the use of acquired notions, he must be able to interpret the tendency of the behavior of variables object of his research.

**Lesson period:** First semester
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

The lessons will be held face to face on Thursdays (every 15 days) from 13.30 to 16.30, starting from October 2020. A team on Microsoft Teams will be set up for teaching for contacts and receptions and for sharing educational material .

**Course syllabus**

Real numbers, coordinates on the straight line and in the plane. Form of a real number.

- Notable products. Equations and inequalities.

- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.

- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.

- Translations and symmetries starting from the graph of elementary functions.

- Concept of limit. Limits of elementary functions. Infinity ladder.

- Continuous functions.

- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.

- Rules of derivation; sum, product, quotient and composition of functions.

- Higher order derivatives.

- Application of derivatives to the study of the graph of a function.

- Discrete random variables.

- Average value, variance, mean square deviation, standard deviation.

- Linear regression (least squares method).

[Program for non-attending students]:

- Real numbers, coordinates on the straight line and in the plane. Form of a real number.

- Notable products. Equations and inequalities.

- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.

- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.

- Translations and symmetries starting from the graph of elementary functions.

- Concept of limit. Limits of elementary functions. Infinity ladder.

- Continuous functions.

- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.

- Rules of derivation; sum, product, quotient and composition of functions.

- Higher order derivatives.

- Application of derivatives to the study of the graph of a function.

- Discrete random variables.

- Average value, variance, mean square deviation, standard deviation.

- Linear regression (least squares method).

- Notable products. Equations and inequalities.

- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.

- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.

- Translations and symmetries starting from the graph of elementary functions.

- Concept of limit. Limits of elementary functions. Infinity ladder.

- Continuous functions.

- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.

- Rules of derivation; sum, product, quotient and composition of functions.

- Higher order derivatives.

- Application of derivatives to the study of the graph of a function.

- Discrete random variables.

- Average value, variance, mean square deviation, standard deviation.

- Linear regression (least squares method).

[Program for non-attending students]:

- Real numbers, coordinates on the straight line and in the plane. Form of a real number.

- Notable products. Equations and inequalities.

- Concept of function and its graph. Domain and codomain. Function properties: injective; surjective; bijective. Inverse function and compound function.

- Graphs of elementary functions, in particular: straight lines, powers, absolute value, parables, exponentials, logarithms and protractor functions.

- Translations and symmetries starting from the graph of elementary functions.

- Concept of limit. Limits of elementary functions. Infinity ladder.

- Continuous functions.

- Notion of derivative in a point and its geometric meaning. Line tangent to the graph of a function at a point.

- Rules of derivation; sum, product, quotient and composition of functions.

- Higher order derivatives.

- Application of derivatives to the study of the graph of a function.

- Discrete random variables.

- Average value, variance, mean square deviation, standard deviation.

- Linear regression (least squares method).

**Prerequisites for admission**

Basics of arithmetic and algebra: literal calculation, first and second degree numerical equations in R; first and second degree inequalities in R.

**Teaching methods**

Frontal lesson in class with multimedia aid

**Teaching Resources**

Any text of Commercial Mathematical Analysis adopted in high school or university level;

lecture notes produced by the teacher and distributed by AD COPIE

Course slides published on the ARIEL website

lecture notes produced by the teacher and distributed by AD COPIE

Course slides published on the ARIEL website

**Assessment methods and Criteria**

written test: five / six exercises to solve concerning the practical aspects covered in class; a question of theory.

Evaluation expressed in thirtieths.

The assessment of basic IT skills is detected through a centralized UNIMI service. The evaluation is expressed in thirtieths.

The final evaluation is given by the arithmetic average of the single positive evaluations obtained.

Evaluation expressed in thirtieths.

The assessment of basic IT skills is detected through a centralized UNIMI service. The evaluation is expressed in thirtieths.

The final evaluation is given by the arithmetic average of the single positive evaluations obtained.

Informatics

INF/01 - INFORMATICS - University credits: 0

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Basic computer skills: 18 hours

Mathematics

INF/01 - INFORMATICS - University credits: 0

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Lessons: 32 hours

Professor:
Musone Massimiliano

Educational website(s)

Professor(s)