65851 - Mathematics and Statistics

Learning outcomes

At the end of the course the student acquires both a good knowledge of mathematical technical tools and their use and of the main basic methods and tools for the quantitative study of collective phenomena. He is therefore able to set up and solve problems and to assimilate new concepts from previous experience and knowledge. Furthermore, he/she is able to autonomously produce and process statistical data by developing the ability to interpret and critically evaluate information of a statistical nature.

Course contents

Mathematics (60 hours).
Sets; natural, rational and real numbers; geometric representation of numbers; carriers; operations with carriers; dot product; geometry; linear equations and inequalities; matrices and transformations; matrix operations; determinants; linear, quadratic, exponential, polynomial, power, rational, absolute value functions; graph of a function; increasing and decreasing functions; maxima and minima of a function; real functions of several variables; linear laws; quadratic laws; exponential functions; logarithmic functions; logarithmic scale; asymptotic behavior; continuity of a function; limits; successions and laws of recurrence; average and instantaneous rate of change; derivation; calculus with derivatives; differential calculus; models of evolution in continuous time; integral.

Statistics (20 hours).
Statistical data: Concepts of statistical unit, collective, quantitative and qualitative characters, absolute, relative and cumulative frequencies, examples of graphical representations. Centrality indices: arithmetic and geometric mean, position averages, loss functions. Variability indices: range, variance, standard deviation. Elements of bivariate descriptive statistics: double distributions of frequencies, joint and marginal frequencies, analysis of the association between two characters. Elements of probability: models for uncertainty, theoretical distributions of frequencies, Bernulli, binomial, uniform, normal, chi-square, central limit theorem. Elements of inferential statistics: confidence intervals, statistical tests, chi-square test.

Readings/Bibliography

Matematica per le Scienze, Marco Bramanti, Fulvia Confortola, Sandro Salsa.

 

Matematica per le scienze della Vita. Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei. Casa Editrice Ambrosiana.

Teaching methods

Teaching and exercises hours during the course.

Assessment methods

Written examen (one exam for both)

Necessary conditions in order to have the exam:

• at least 14 points in the Mathematics part
• at least 4 points in the Probabilistic and Statistical part

Teaching tools

Slides and lecture notes of the teacher. 

Exercises with teacher.

Office hours

See the website of Cristina Di Girolami

See the website of Stefano Pagliarani