SM/0160 - STATISTICAL AND MATHEMATICAL LABORATORY
Academic Year 2022/2023
Free text for the University
MARIA PAOLA PIU (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/64] MATHEMATICS||[64/00 - Ord. 2017] PERCORSO COMUNE||3||36|
The student will learn the principal functions of the Matlab software that will allow him to handle mathematical objects such as vectors and matrices. The student will also learn how to build graphs in 2 and 3 dimensions.
The student will be able to perform a descriptive statistical analysis of real data using the statistical software R. At the same time he will have acquired a good knowledge of the basic resources of the software R.
Furthermore, will be introduced the symbolic calculation with Mathematica which will allow to the student to solve simple problems of linear algebra and analytical geometry.
Mathematical Analysis 1, Algebra 1, Geometry 1
The course includes 3 modules of 1 CFU:
1. Introduction to the scientific Matlab environment. Constants and variables. Real and complex arithmetic. Use of the library functions. Manipulation of vectors and matrices. Construction of graphics in 2 and 3 dimensions. Programming through scripts and functions. Basic programming with Matlab.
2. Introduction to the statistical environment R. Main features and interactive use of the environment. The help function: learn to use the functions implemented in the software by reading the available documentation. Data manipulations using the main objects of R: construction of numerical vectors, of character and logic type, construction of matrices, management of missing data, generation of subsets of matrices and vectors, arithmetic calculation exploiting the functionality of the software. Data entry and creation of a dataset. Lists on R. Saving data externally, importing data and coding variables. Univariate descriptive statistics: position indexes, variability indices, form of the distribution of a variable, frequency tables. Bivariate descriptive statistics: double-entry frequency tables, correlation measures, relationship between a categorical variable and a numerical one, relationship between two categorical variables, introduction to linear regression. Elementary graphic tools: bar charts, pie charts, histograms, boxplots, scatterplots, bivariate bar charts. Basic programming elements: construction of a function, use of cycles and conditional functions.
3. Basics of symbolic tool:
Simplifications of algebraic expressions; solution of equations and linear systems; calculation of limits and derivatives; calculation of integrals.
Linear algebra: vector and matrix calculus. Determinant, inverse, eigenvalues and eigenvectors. Linear systems resolution.
Exercises in laboratory supported by some theoretical explanation and recall on the blackboard and/or slides.
Furthermore, the exercises can be carried out by means of remote interaction forms with the available IT supports.
Verification of learning
In the final exam we aim to verify that the student has acquired a good level of competence in the use of basic functions of the 3 software Matlab, R and Mathematica.
The final exam consists in solving 3 separate laboratory tests, one relating to the Matlab module, one to the R and one to the Mathematica module, using the 3 softwares.
The 3 tests are evaluated separately, the minimum grade in each of the two is 18/30. The final grade is calculated as the arithmetic mean of the grades in the individual tests.
Compatibly with the University indications on how to carry out the exams according to the evolution of the COVID-19 emergency, the exams could be held in the presence or online with a written test at a distance using computer aids (moodle, Teams) .
Manuals of Matlab, R and Mathematica made available by the teachers on their reference web sites.
Other material: slides from the lessons held in the classroom.
Our University provides support for students with specific learning disability (SLD). Those interested can find more informations at this link: http://corsi.unica.it/matematica/info-dsa/.