08234 - Elements of Mathematics

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.

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

Functions study. Asymptotes, maximum and minimum points, inflection points.

Integrals. Infinitesimal and differential. Indefinite integral. Integral properties. Integration by substitution. Integration for parts. Defined integral. Improper integral.

Elements of Statistics (Teaching unit 2)

Descriptive statistics. One-dimensional variables: Absolute frequencies, relative frequencies, cumulative frequencies. Location measures. Variability measures. Graphical representation of data. Two-dimensional variables: Bivariate frequency distributions. Marginal distributions, conditional distributions. Relationships between two variables: dependence, linear regression, linear correlation.

Inferential statistics. Introduction to the probabilities. Random variables. Probability distributions. The sample design. Confidence intervals. Testing Hypotheses. The linear regression model.

Readings/Bibliography

Mathematics

The files with the lessons teaching material will be stored in AMSCampus.

Elements of Statistics

Mecatti, F. (2015), Statistica di base. Come, quando e perché. (II edizione), Milano, McGraw-Hill

The teaching material, corresponding to the lecture notes, will be available in AMSCampus

Teaching methods

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

Assessment methods

Mathematics

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

For the written test no notebooks, tablets, smartphones or pocket calculators are allowed.

The written exam can include 2 or 3 exercises.

In the case of 2 exercises, the test consists of a function study (max. grade 20) and the calculation of an integral (max. grade 10).

In the case of 3 exercises, the test consists of the calculation of: a function limit (max. grade 10), a derivative (max. grade 10) and an integral (max. grade 10).

The exercises for which only the result is provided without indicating the methodology adopted and the intermediate steps of the calculation will be considered unresolved (grade 0).

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.

Elements of Statistics

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

In the case of "Mathematics with Elements of Statistics", the final grade will be given by the weighted average of the grades of the two exams:

(Mathematical Grade) ∙ 0.75 + (Statistical Grade) ∙ 0.25

Teaching tools

Interactive system of video projection.

Office hours

See the website of Claudio Caprara