13644 - MATEMATICA E STATISTICA

Learning outcomes

At the end of the course, the student will master the basics of math, which is needed to proceed with the following courses in Natural Sciences. Namely, the student will be able to: - understand and use function charts of mathematical models; - know the basics of differential and integral calculus, as well as linear algebra, for simplest applications; - use a simple mathematical software to solve equations, draw charts, compute derivatives, integrals, and matrices. Moreover, the student will know the basics of statistics: namley, the student will be able to: - understand the concept of statistical significance; - use simple statistical analysis methods for field and lab applications.

Course contents

APPLIED STATISTICS

Introduction to the course; introduction to descriptive statistics; starting test; means, median, and mode; quantiles.

Dipsersion indices; data distributions; the normal distribution; the standard normal curve and the test Z.

Normality tests (quantiles and Q-Q plot; Shapiro and Wilk’s test).

Introduction to inferential statistics; one-sample Student’s t-test.

Two-sample t-test (paired/unpaired samples); nonparametric tests: Wilcoxon’s and Mann-Whitney tests.

Qualitative variables: chi squared test.

Linear regression and correlation: Pearson’s method, r and R squared; significance of a correlation.

Analysis of variance; one-way and two-way ANOVA; Tukey’s post-hoc test.

Lab class: introduction to R; create an input file; call and explore data; normality and t tests with R; chi squared, regression and ANOVA with R.

Readings/Bibliography

No specific textbook is requested for the present course. Every high school textbook is suitable for following and scaffolding the course.

Teaching methods

The course will be developed through frontal lessons and a lab class for the module of Applied Statistics.

Assessment methods

The exam aims to evaluate learning goals as described above. The module of General Mathematics involves a written test, followed by an oral integration, on a volunteer basis; the module of Applied Statistics involves a written test; the module of Informatics involves an online test.

The final grade will be the weighted mean of the three grades, using CFUs as weights (8, 2, and 2 for General Mathematics, Applied Statistics, and Informatics, respectively).

Teaching tools

.ppt presentations

Office hours

See the website of Federico Plazzi