Teaching code

4S02690

Credits

11

Coordinator

Maurizio Tavelli

Language

Italian

Location

VERONA

Scientific Disciplinary Sector (SSD)

MAT/08 - NUMERICAL ANALYSIS

Courses Single

Not Authorized

Moodle Seminars 0

The teaching is organized as follows:

Learning objectives

The course constitutes an essential mathematical cultural background that every student who attends a scientific course of study should possess. The purpose of the module is twofold. On the one hand, it aims to provide the students with the main guidelines for a rigorous analysis of problems and for a logical search of their solutions. On the other hand, it aims to provide tools to mathematically address even extremely concrete problems. For this purpose, some examples of physical and biological problems will be addressed and resolved. The course also provides natural prerequisites for subsequent Physics, Physical Chemistry, Genetics, and Electronics courses. In addition, the course aims to provide students with the basic statistical knowledge for planning experiments, collecting and analysing data, interpreting and presenting results, and, therefore the cultural elements that allow them to analyse and understand the functioning of biological systems and, at the same time, acquire real professional expertise. Students are encouraged to use theoretical notions of mathematics and statistics to solve problems commonly faced in laboratory practice.

Prerequisites and basic notions

None

Program

Part 1 (mathematics):
- Introduction to the course
- Set theory
- Functions
- Linear algebra and linear systems
- Trigonometry
- Sequences
- Limits, continuity and derivatives
- Integrals and complex numbers
- Elements of multivariate calculus and ordinary differential equations

Part 2 (statistics)
1-Descriptive statistics:
- Measurement scales
- Frequency distributions and bivariate distributions (contingency tables)
- Position, dispersion and shape indices
2-Probability
- Principles of probability calculation
- Discrete and continuous random variables
- Notable classes of random variables
- Expected value, variance and correlation index.
3-Statistical inference
- Sample statistics and central limit theorem
- Propagation of errors
- Estimating with confidence
- Tests of significance and main statistical tests
- Linear regression

Bibliography

Didactic methods

Frontal lectures and exercises.

Learning assessment procedures

The test will be carried out through a written test that requires answering theoretical questions and solving exercises. The test is divided into two parts, one for mathematics and one for statistics.

Evaluation criteria

At the end of the course, the student must demonstrate that he/she has understood and is able to apply the fundamental concepts of mathematical logic, set theory, real functions, differentiability and integration. He/she must be able to solve differential equations and apply concepts of linear algebra, vector calculus and geometry of space. Finally, he/she must demonstrate that he/she knows and is able to use the main statistical tests for the analysis and interpretation of data, know how to use probability calculus and know the main discrete and continuous distributions. He/she must also know how to correctly represent the results obtained and analyze the data from the perspective of descriptive statistics.

Criteria for the composition of the final grade

Grade out of thirty, the average of the two parts will be considered (50% for mathematics and 50% for statistics)

Exam language

Italiano