65851 - Mathematics and Statistics

Learning outcomes

At the end of the course the student knows the technical mathematical tools and their use, as well as the main methods and basic tools for the quantitative study of collective phenomena. The student is then able to set up and solve problems and to assimilate new concepts from the experience and previous knowledge, to produce and process statistical data independently, developing the ability of interpretation and critical assessment of statistical information.

Course contents

Mathematics (Teaching unit 1)

Elements of set theory.

Definition of set. Operations between sets. Set of real numbers

Functions

Concept of relation. Functions of a variable. Continuous functions.

Theory of limits.

Limits for functions. Asymptotes,

Derivatives.

Definition of incremental ratio. Derivative of a function. Properties of derivatives. Derivative rules.

Basics of Statistics (Teaching unit 2)

Descriptive Statistics.

Types of data, qualitative and quantitative variables, discrete and continuous variables. Data presentation: frequency tables (frequency counts, relative frequencies) and graphical representations (e.g. pie charts, bar charts, histograms, scatter plot, time series, cartograms). Measures of central tendency (mean, median, mode and percentiles). Measures of variability (range, interquartile range, deviation, variance, standard deviation, variation coefficient). Skewness and kurtosis.

Relationships between two variables.

Contingency Tables. Joint frequencies and joint relative frequencies. Conditional and marginal distributions. Relationships between two variables. Chi-squared statistics. Tschuprow’s T.

Elements of Probability.

Introduction to probability. Remarks on the concepts of probability. Definition of simple events and sample space. Operations on events (Venn diagrams). Axioms of probability (Kolmogorov). Rules of the probability (additive, multiplicative). Conditional probability. Bayes’ theorem.

Rates and Rate Standardization.

Crude rates. Specific rates. Standardization of rates (direct and indirect methods).

Readings/Bibliography

Mathematics

The files with the lesson teaching material will be stored on the online platform for teaching support.

Basics of Statistics

G. Cicchitelli. Statistica: Principi e Metodi. Pearson, Milano, 2012.

Teaching materials (accessible through IOL platform), including a self-evaluation test.

Teaching methods

Mathematics

The course will cover the topics of the program through classroom teaching, both for lectures and for exercises.

Basics of Statistics

Lectures. Classroom exercises. Computer exercises (using Excel).

Assessment methods

Mathematics

The exam is done through a final exam with a written test and eventually an oral examination, both with grades expressed in thirtieths.

The written test is passed with a grade between 18 and 30.

The student who fails the written examination must repeat the examination at the next session.

The student who passes the written test can choose to:

- Refuse the grade and take the examination at the next session;

- Accept the grade without the oral examination and in this case the test is passed with a grade corresponding to that of the only written test;

- Try to improve the grade of the written test with an oral examination, in the awareness that, according to the oral examination, the grade of the written test may increase or decrease.

Basics of Statistics

The aim is to evaluate whether students have learnt the basic tools of the subject, including the use of Excel. In particular, students should achieve the following learning outcomes:

-knowledge of the basic tools of Statistics

-use of those tools for data analysis

-interpretation of the findings

Lab exam using Excel: 5-6 exercises to be solved using Excel. Each exercise is composed of different questions, including the interpretation of the findings. Students are allowed to use calculators. Notes and formulary are not permitted.

The evaluation of the exam is expressed as a mark out of 30.

The exam is located in the computer room (exam duration: 1 hour and 30 minutes).

Students must sign up using AlmaEsami. Late registrations are not admitted.

For "Mathematics with Basics of Statistics", the final grade will be given by the weighted average of the grades of the two exams:

(Mathematical Grade) ∙ 0.50 + (Statistical Grade) ∙ 0.50

Teaching tools

Mathematics

PC and video projector.

Basics of Statistics

Whiteboard, PC, video projector, computer lab.

Office hours

See the website of Claudio Caprara

See the website of Stefania Curti