Economia - Marc Lieberman e Robert Hall, Principi e applicazioni, Maggioli Editori, 2015
Economia Politica - Giovanni Nicola De Vito, Strumenti ed esercizi, Maggioli Editori, 2015

PROGRAM
Logic and set theory:
Propositions. Logical operations with propositions. Logical implication. Sets. Operations with sets. Cartesian product. Applications. Injective and surjective applications. One-to-one correspondence. Inverse application.
Numeric numbers and sets: Natural numbers. Integer or relative numbers. Rational numbers. Real numbers and representation on the line. Bounded sets. Upper and lower extreme of sets of rational and real numbers. Intervals and neighborhoods. Accumulation, internal, isolated points. Open sets and closed sets.
Summations and products: Definition of summation. Properties. Special sums. Sum of the first n natural numbers. Arithmetic and geometric progressions and sum of their first n terms. Factorial.
Real functions of a real variable:
Definition of a real function of a real variable. The Euclidean plane and the graph of a function. Injective and surjective functions and graph. Even and odd functions. Increasing and decreasing functions. Concave and convex functions. Bounded functions. Compositin function. Inverse function, monotonicity and invertibility, inverse function graph. Elementary functions. Functions with two laws. Transforming graphs. Domain of a function.
Sequences and numerical series: Definition of a sequence. Converging and divergent sequences. Monotone sequences and regularity theorem (w.p.). Limits of sequnces. Definition of numerical series. NC for convergence (w.p.). Cauchy criterion. Geometric, Mengoli, harmonic and generalized harmonic series.
Limits: Definition of limit. Convergence and divergence. Right limit and left limit. Vertical and horizontal asymptotes. Limit uniqueness theorem (w.p.). Sign permanence theorem in direct and inverse form (w.p.). Comparison theorem. Limit checks. Operations with limits. Indeterminate forms.
Infinitesimals and infinities: Definition of infinitesimal and infinite. Comparing infinitesimals and infinities. Order of infinitesimals and infinities. Propagation of the order. Computing limits with infinitesimals and infinities (w.p.).
Continuity and discontinuity: Definition of continuity. Limits and continuity. Classification of discontinuity points. Continuity of rational functions. Continuity of the inverse. Continuity of composition functions. Theorem of zeros (w.p.). Weierstrass theorem. Darboux's theorem (w.p.).
Differential calculus: Derivative of a function. Geometric interpretation. Derivability and continuity (w.p.) Points of non-derivability. Higher order derivatives. Derivatives of elementary functions. Rules of derivation. Chain rule. Derivative of the inverse function. Differential. First order approximation (w.p.). Taylor and McLaurin polynomial. Approximations of higher order. Stationary points. Local maxima and minima. First order necessary conditions for the existence of local maxima and minima. Fermat's theorem (w.p.). Rolle's theorem (w.p.). Lagrange theorem (w.p.). Lagrange theorem,s corollaries: zero-derivative functions (w.p.). Relations between monotonicity and derivative sign (w.p.). Local concave and convex functions. Relationship between the second order derivative and the concavity (w.p.). Points of inflection. Sufficient second order conditions for the existence of relative maxima and minima (w.p.). Sufficient conditions of order n for the existence of relative maxima and minima or inflections points (w.p.). De L'Hôpital theorem and application to limit calculus.
Graph of a function: Representation of the graph of a function on the Euclidean plane. Oblique asymptotes.
Linear algebra:
Vectors and vector spaces. Geometric representation of vectors. Linear combination of vectors. Linearly dependent and independent vectors. Rank of a set of vectors. Matrices. Operations with matrices. Product rows by columns. Particular matrices. Transposed matrix. Determinant of a matrix of order n. Properties of the determinant. Rank of a matrix. Rank and linear independence of vectors. Systems of linear equations. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems.
(w.p.) = “with proof”

• Notes can be downloaded from the Moodle class on the e-learning platform: https://economia.el.uniroma3.it
• Notes on the Mathematics supplementary course on the platform: https://didatticaonline.uniroma3.it/ (for the access code write to Prof. Guizzi).

General part: the elements of Private Law

1) Private Law and Public Law
2) The sources of Private Law
3) Facts, acts and legal effects
4) The subjects
5) Acts: the contract and its essential discipline. Outline of the concept of obligation.
6) Liability
7) Legal assets and property


Special part: Private Law in the digital era

1) The digital era. Informatics and law
2) Hardware, software and algorithms
3) Networks and Internet
4) From the right to privacy to the right to the protection of personal data
5) The evolution of the concepts of "document" and "subscription"
6) Electronic payments and digital currency
7) E-commerce
8) "Internet of Thing"
9) "Cloud computing" and "edge computing"
10) "Big Data"
11) "Blockchain" and "Smart Contract"
12) Artificial intelligence and robotics
13) "Internet Service Provider"
14) Deterritorialization
15) Destatualization
16) Dematerialization
17) Contract and technique

Ask the Professor for English lectures.

The technological factor and its impact on fundamental freedoms; Sovereignty and power in the digital age; the right of access to the internet and new rights; net neutrality between fundamental rights; electronic communications and disciplines envisaged; freedom and secrecy of communications in the time of the web; freedom of movement in the internet age; freedom of association in the internet; freedom of expression and information on the internet; competition and pluralism; audiovisual content and freedom of expression of thought on the internet; internet and the constitutional re-educational function of punishment; knowledge and education on the Net; right to health and e-health; protection of personal data and employer control; protection of copyright and right to information on the Net; economic freedoms and internet; electronic voting within the framework of digital democracy;

Lecture notes
Rights and freedoms on the internet
Curated by Tommaso Edoardo Frosini, Oreste Pollicino, Ernesto Apa, Marco Bassini
Le Monnier publisher
Last edition

The Statistics course introduces students to the techniques of collecting, organizing, and analysing statistical data. The course also introduces students to the basic concepts of probability calculus and statistical inference for the analysis of statistical data derived from sample surveys.
All topics will also be illustrated using statistical software R through RStudio. The exercises and part of the lectures will be carried out in the computer room or remotely using the statistical software.
For each statistical methodology, a specific application will be illustrated on data sets on which students can practice. Therefore, the student will be taught not only to apply statistical techniques but also to choose the most appropriate technique and to comment on the output for decision-making purposes.
Exploratory Data Analysis
- Statistical characters and measurement scales. Simple distributions. Graphical display of data. Empirical distribution function.
-Position, variability and shape of statistical distributions.
- Double, marginal and conditional statistical distributions. Moments of double distributions, correlation.
Examples of exploratory data analysis using statistical software.
Elements of Probability Calculus
- Conditional probability. Independence. Bayes' rule. Discrete random variables. Probability function, density function, distribution function. Moments of random variables.
- Discrete probability distributions: binomial, Poisson, uniform.
- Continuous probability distributions: uniform, normal, Student's t, χ^2, exponential.
- Linear combinations of random variables, convergence, law of large numbers and central limit theorem.
- Use of statistical software to represent probability distributions and their properties.
Statistical Inference
- Population and sample: finite and infinite populations; random sample from finite and infinite populations; probability distribution of random sample.
- Sample statistics and their distributions.
- Parameter estimation: properties of estimators.
- Confidence intervals for a mean and a proportion.
- Hypothesis testing: elements of statistical tess, tests for means, proportions, and tests for difference in means and proportions.
- Hypothesis testing of independence and conformity.
- Simple linear regression estimation and hypothesis testing on the parameters of the regression line.
- Application of statistical methodologies through analysis of simple datasets using statistical software.

Newbold P. , Carlson W. & Thorne B. (2021) Statistics for Business and Economics, Pearson ed.

Other course material is available on Teams, Moodle and OneDrive.
Solutions to some exercises and exam assignments are also available at the website:
https://corsodistatistica.wixsite.com/website