# MATHEMATICS AND STATISTICS

**Academic Year 2023/2024**- Teacher:

**Mario PENNISI**

## Expected Learning Outcomes

To acquire adequate knowledge of the main basics and key mathematical tools necessary for understanding of simple mathematical models and the processing and interpretation of experimental data.

## Course Structure

The lessons will be frontal and participated. Exercises are planned.

If the teaching is given in a mixed or remote way, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.

**Information for students with disabilities and/or DSA.**

As a guarantee of equal opportunities and in compliance with current laws, interested students can ask for a personal interview in order to plan any compensatory and/or dispensatory measures, based on their specific needs and on teaching objectives of the discipline. It is also possible to ask the departmental contact of CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or DSAs), in the person of professor Anna De Angelis.

## Required Prerequisites

Knowledge of the fundamental concepts of elementary mathematics.

Good knowledge of the written Italian language; adequate logical-deductive reasoning ability; ability to rework and relate the concepts in one's possession; ability to use the fundamental concepts of elementary mathematics.

## Attendance of Lessons

Strongly recommended

## Detailed Course Content

Propositions and logical propositions. Definitions and primitive entities. Therorems and axiomos. Set and subset. Operations between sets. Cartesian product. Relation between sets. Function. One-to-one function . Inverse function. Composition of functions.

The numerical sets: N, Z, Q, R. logarithms. Equations and inequalities.

Matrix. Determinant.

The Cartesian plane. Distance between two points. midpoint of a segment. Symmetrical of a point with respect to a point. Area of a triangle. Points aligned. Analytical representation of a straight line. Angular coefficient. Parallel lines. Unit circle. Radians. Trigonometric functions and identities. Geometric meaning of the angular coefficien of a line. Perpendicular lines. Symmetrical of a point from a straight. Distance of a point to a line. Parabolas.

Extremes of a numerical set. Intervals. Around. Accumulazion points and internal points. Real function of real variable. Graph of a function. Extremes of a function. Notable functions. Monotone functions. Inverse functions of strogly monotone functions. Graph of an inverse function. Exponential and logarithmic function.

Limit of a function. Number e. Semilogarithmic scales. Continuous function and discontinuous function. Theorems on continuous functions.

Derivative of a function. Differentiability and continuity. Rules of derivation. Derivatives of elementary functions. Theorem of derivation of composite functions. Geometric meaning of the derivative. Maximum and minimum relative. Derivative theorems. Convexity, concavity, inflections. Asymptotes. Gaussian function.

Primitive of a function. Indefinite Integral. Methods of integration. Definite integral. Integral function. Fundamental theorem of calculus. Improper integral. Calculation of areas.

differential equations.

Population, sample, statistical unit, characters. One-dimensional distribution of frequencies. Histogram. Median. Box plots. Arithmetic average. Variance. Standard deviation. joint distribution of two quantitative traits. linear regression.

Event. Random experiment. Frequentist conception of probability. Probability density funtion. Probability distribution. The normal probability distribution.

## Textbook Information

[1] M. Gionfriddo, Istituzioni di matematiche, Culc, Catania.

[2] A. Guerraggio, Matematica per le scienze, Pearson.

[3] V. Villani – G. Gentili, Matematica 5/ed Comprendere e interpretare fenomeni delle scienze della vita, Mc Graw-Hill.

## Course Planning

Subjects | Text References | |
---|---|---|

1 | 1. | Testo 1: cap. 1 - Testo 2: cap. 2 |

2 | *2. | Testo 1: cap. 3 - Testo 2: cap. 2 |

3 | 3. | Testo 1: capp. 4, 5 - Testo 2: cap. 15 |

4 | 4. | Testo 1: cap. 6 |

5 | *5. | Testo 1: cap. 6 |

6 | 6. | Testo 1: cap. 6 |

7 | 7. | Testo 1: cap. 8 |

8 | 8. | Testo 1: cap. 10 |

9 | 9. | Testo 1: cap. 10 |

10 | *10. | Testo 1: cap. 10 - Testo 3: cap. 6 |

11 | 11. | Testo 1: cap. 11 - Testo 2: cap. 5 |

12 | 12. | Testo 1: cap. 11 - Testo 2: cap. 6 |

13 | *13. | Testo 1: cap. 12 - Testo 2: cap. 7 |

14 | *14. | Testo 1: cap. 12 - Testo 2: cap. 7 |

15 | 15. | - Testo 1: cap. 12 Testo 2: cap. 8 |

16 | 16. | Testo 1: cap. 12 - Testo 2: capp. 4, 8 |

17 | 17. | Testo 1: cap. 13 - Testo 2: cap. 9 - Testo 3: cap. 8 |

18 | 18. | Testo 1: cap. 13 - Testo 2: cap. 9 - Testo 3: cap. 8 |

19 | 19. | Testo 1: cap. 13 - Testo 2: cap. 10 - Testo 3: cap. 8 |

20 | *20. | Testo 1: cap. 14 - Testo 3: cap. 9 |

21 | *21. | Testo 2: cap. 17 - Testo 3: cap. 10 |

22 | *22. | Testo 3: cap. 10 |

23 | 23. | Testo 2: cap. 18 - Testo 3: capp. 10, 11 |

## Learning Assessment

### Learning Assessment Procedures

```
The exam consists of an oral test on theory, exercises and applications.
Verification of learning.
```

Voting follows the following scheme:

**Below 18:**

Knowledge and understanding of the topic: Important deficiencies. Significant inaccuracies

Analysis and synthesis skills: Irrelevant. Frequent generalizations. Inability to synthesize

Use of references: Completely inappropriate

`Verification of learning can also be carried out electronically, should conditions require it.`

**18-20**

Knowledge and understanding of the topic: At threshold level. Obvious imperfections

Analysis and synthesis skills: Just sufficient skills

Use of references: As appropriate

**21-23**

Knowledge and understanding of the topic: Routine knowledge Analysis and synthesis skills: Able to correctly analyze and summarize. Argue logically and coherently

Using references: Use standard references

**24-26**

Knowledge and understanding of the topic: Good knowledge

Analysis and synthesis skills: Has good analysis and synthesis skills. The arguments are expressed coherently

Using references: Use standard references

**27-29**

Knowledge and understanding of the topic: More than good knowledge

Analysis and synthesis skills: Has considerable analysis and synthesis skills

Use of references: He explored the topics in depth

**30-30L**

Knowledge and understanding of the topic: Excellent knowledge

Analysis and synthesis skills: Has considerable analysis and synthesis skills.

Using references: Important insights.