FIRST PART - MICROECONOMICS
What is economics
Scarcity, choice and economic systems
Demand and supply
Consumer choices
Production and costs
The decision-making process of companies: profit maximization
Perfect competition
Monopoly and imperfect competition
The job market
Economic efficiency and the role of the state

SECOND PART - MACROECONOMICS
Introduction to macroeconomics
Income production and employment
The monetary system, prices and inflation
Economic growth and raising the standard of living
Economic fluctuations
The banking system, the Central Bank and monetary policy
Aggregate demand and aggregate supply

The recommended textbook is:
Lieberman M. and Hall R.E., 2015, Economics. Principles and applications, Maggioli Editore, https://www.maggiolieditore.it/economia-principi-e-applicazioni.html

Attendance at lectures is strongly recommended. A cycle of weekly classes and a personalized tutoring program will also be part of the course.

The classes will be held by Prof. Giovanni Nicola De Vito. The recommended text for the classes is
De Vito G.N., 2022, Political Economy: Tools and Exercises (2nd edition), Maggioli Editore, https://www.maggiolieditore.it/economia-politica.html
Dr. Francesca Marinelli will be responsible for the tutoring meetings

PROGRAM
Logic and set theory
• Logic: 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
• Real functions of a real variable: Definition of a real function of a real variable. Definition of a sequence. 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.
• 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.
Integral calculus
Primitive functions. Indefinite integral. Characterization of the set of primitives (w.p.). Properties of the indefinite integral. Integral of elementary functions. Integration by parts (w.p.). Integration by substitution (w.p.). Definite integral. Properties of the definite integral. Integral function. Integral mean theorem(c.d.). Fundamental theorem of integral calculus (w.p.). Corollary to Torricelli-Barrow's theorem: relationship between the definite integral and the indefinite integral (w.p.). Applications.
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).

Introduction to computer science
Computer architectures
Problems and algorithms
Introduction to programming languages
Programs, source code, compilers and interpreters
Introduction to operating systems
Memories and file management
Information representation
Introduction to Python programming and development environment
Statements, expressions, data types and data conversions in Python
Data structures, functions, modules ans libraries in Python
Introduction to complexity theory
Complexity of programs
Exercises with Python programs

Kenneth A. Lambert. Programmazione in Python. Apogeo. 2° ed. 2018

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

This graduate level course covers the following topics:
An overview of statistics
Data description: scales of measurement, how to describe data graphically for categorical data (pie chart, bar chart) and graphs for quantitative variables (histogram, pie chart)
How to describe data by summary statistics: measures of central tendency, variability and skewness.
How to create a box plot
How probability and probability distributions are involved in statistics
How binomial distributions are involved in statistics
The role that normal distributions play in statistics
Simple random sampling and sampling distribution of sample mean, central limit theorem, normal approximation to the binomial
Differentiation between a population and a sample, how to use a statistic to estimate a population parameter, confidence interval and its interpretation, inferences of population mean and proportion
Confidence interval for population mean, Sample size needed for estimating the population mean with a specified confidence level and specified width of the interval
Hypothesis testing: in terms of how to set up Null and Alternative hypotheses, understanding Type I and Type II errors, performing a statistical test for the population mean
p-value, how to compute it and how to use it
Inferences about μ with σ unknown: the t-distribution and the assumptions required to check in order to use it
How to compare the mean of two populations for independent samples: using pooled variances t-test versus separate variances t-test
How to compare the mean of two populations for paired data
How to compare two population proportions
Using contingency table and the Chi-square test of independence
Understanding concepts related to linear regression models including, least squares method, correlation, inferences about the parameters in the linear regression model

The course the course is taught in Italian so textbooks are in Italian:
- P. Newbold, W. Carlson, B. Thorne, Statistica, Pearson Education, 9° edizione
- Sebastiani M. R. (2015) “Esercitazioni di statistica”. Esculapio Editore, 3° edizione.
For English speaking students a textbook is:
Introductory Statistics for Business and Economics by Thomas H. Wonnacott and Ronald J. Wonnacott
John Wiley & Sons Inc; International 2 Revised ed

LINEAR ALGEBRA.
MULTIVARIABLE CALCULUS
IMPLICIT FUNCTIONS.
QUADRATIC FORMS.
OPTIMIZATION THEORY
CONVEX FUNCTIONS

L. Mastroeni, A. Mazzoccoli, Mathemathics for economic applications, Ed Pearson

Linear algebra.
Eigenvalues, eigenvectors, eigenspace, diagonalization of matrices, eigenvalues of symmetric matrices, properties of eigenvalues.

Sets in R*2 and in R*n.
Metric spaces, regulated spaces. Topology in R*n.

Real functions of several real variables.
Functions defined between Euclidean spaces, graphs, contour lines, continuous functions, concave functions and convex functions.

Differential calculus in several variables.
Partial derivatives, gradient, higher order derivatives, Hessian matrix, Schwartz theorem, Taylor polynomial.

Bilinear and quadratic forms.
Definitions, sign of quadratic forms, principal minors of a matrix, sign of a matrix.

Optimization.
Definitions, first order conditions, second order conditions; optimization for convex functions. Least squares method, regression line.

Implicit functions.
Dini's theorem, geometric interpretation of the theorem, regular points, gradient theorem.

Graphs.
Directed graph, vertices and edges, successor function, undirected graph, incident vertices and edges, outgoing and incoming edges, empty graph, order and dimension of a graph, adjacent vertices, neighborhood, multi-graph, loop, simple graph, degree of a vertex, isolated vertex.
Lemma of handshakes and its corollary. Incoming degree and outgoing degree, graphs with maximum size, complete graphs, weighted graph, weighted incoming degree and weighted outgoing degree.
Mathematical representation of an unweighted graph (directed and not). Adjacency matrix of an undirected graph, sum by rows and by columns, degree vector; adjacency matrix of a directed graph, sum by rows and by columns; adjacency matrix of a multigraph. Mathematical representation of a weighted graph: adjacency matrix. Cucker-Smale model.
Adjacency lists, isomorphism between graphs, permutation matrices, Theorem on isomorphic graphs and permutation matrices, eigenvalues of adjacency matrices, Theorem on isomorphic graphs and eigenvalues. Isomorphism between graphs and vertex degree distribution. Paths on undirected graphs: path, length of a path, simple path, closed path (cycle), simple cycle, acyclic graph. Walks on directed graphs. kth power of the adjacency matrix.
Theorem of the k-th power of the adjacency matrix, subgraph, connected vertices, connected graph, components, maximal connected subgraph, bridge, shortest path, distance between vertices, distance matrix.
Underlying graph, weakly connected graph, strongly connected graph, weight of a path, shortest path for weighted graphs.
Shortest weight path: properties of subpaths of a shortest path. Dijkstra's algorithm for directed and undirected graphs. Definition of centrality, degree centrality, betweenness and closeness.

Recommended:
 Mastroeni - Mazzoccoli. Mathematics for economic applications PEARSON
 Notes and other material downloadable online from the course on the Moodle platform at: https://economia.el.uniroma3.it/

Topics:
What is Economic policy? Microeconomic and macroeconomic market failures. The normative theory of economic policy. Microeconomic policy tools. The anti-monopoly policies. Policies with externalities and public goods. Redistributive policies. Macroeconomic objectives and tools in an open economy. Monetary policy. Fiscal policy. Policies for the balance of payments. Trade policies.
Insights:
Analysis of the economic reports of national and international institutions

Textbook:
Acocella N. Politica economica e strategie aziendali, VII edition, Carocci, 2020.
Other material:
Slides of the lessons, articles, reports and other material will be available on the course's web page.

• The evolution of the analysis of Public Finance
• Public goods
• Taxes: characteristics and classification
• The economic effects of taxes
• The economic analysis of taxes and the theory of incidence
• The main taxes in the Italian tax system

Di Majo A. (2018), Introduzione alla Scienza delle Finanze, Edizioni Pigreco, Roma, capitoli 1, 2, 5, 6, 7 fino a pag. 325.
2) Bosi P., Guerra M.C., I tributi nell'economia italiana, Il Mulino, Bologna, capitoli II, III, IV, V, VI, VII, VIII.

• The evolution of the analysis of Public Finance
• Public goods
• Taxes: characteristics and classification
• The economic effects of taxes
• The economic analysis of taxes and the theory of incidence
• The main taxes in the Italian tax system

1) Introduzione al corso di Scienza delle Finanze, available on line
2) Di Majo A. (2021), Introduzione alla Scienza delle Finanze, Edizioni Pigreco, Roma (chapters 5, 6, 7 until page 325).
3) Bosi P., Guerra M.C. (2022), I tributi nell'economia italiana, Il Mulino, Bologna (Introduzione and chapters III, IV, V, VI, VIII).

Computational complexity
Basic data structures, operations and implementations
Insight into sorting algorithms
Hash tables, trees and graphs
Implementations of algorithms in the Python language
Examples and applications of algorithms implemented in Python language

Kenneth A. Lambert. Programmazione in Python. Apogeo. 2° ed. 2018
(note: it is the same textbook as the first-year course "Fondamenti di Informatica e Programmazione")

Parte I – The textbook economy with "perfect competition": old concepts and new insights
1. Individual decisions Decisioni individuali
• Consumer theory (preferences, utility functions, balance constraint, demand curve, individual welfare).
• Producer theory (technology, cost function, profit maximization, supply function).
• “Big data” and individual decisions: learning about individual characteristics from their choices.
2. "Perfectly competitive" markets: equilibrium, efficiency, equity.
• Single market equilibrium
• General equilibrium, efficiency and equity.
• Information revealed by prices.
Parte II - Choices and transactions under imperfect information
1. Choice under uncertainty. Uncertainty and risk. Lotteries. Expected utility. Attitudes toward. Certainty equivalence and risk premia. Decisions under uncertainty and risk. The importance of risk diversification:
demand of financial assets and insurance. The value of information.
2. Choice under incomplete information: strategic interactions. Game theory. One-stage games. Nash equilibrium. Dynamic games. Backward induction and "sequentially rational" NE. Cooperation and mutual agreements.
Giochi con incertezza.
3. Incomplete information and market power
• Monopoly. Information and firm policies.
• Oligopoly. Models of price competition (Bertrand-Nash). Models of quantitative competition (Cournot-Nash). Collusion. Barriers to entry and monopolistic competition.
Parte III - Choices and "contracts" under information asymmetries.
1. Information asymmetries on the characteristics of the commodities. Adverse selection. Signaling and screening. Price discrimination through menus of contracts.
2. Information asymmetries on actions; moral hazard and contracts.


Part I - Economic decisions
1. Economic decisions with perfect information (recalls). Classical consumer theory (preferences, utility, budget constraint, demand curve, individual welfare). “Big data” and classical consumer theory:
the “revealed preferences”.
2. Economic decisions with imperfect information. 2.1) Decisions with uncertainty. Uncertainty and risk. Lotteries. Preferences and expected utility. Risk aversion. Certainty equivalent and risk premium. Decisions in presence
of uncertainty and risk. Application for financial and insurance activities. 2.2) Decisions with incomplete information: strategic behaviors. Game Theory. Strategies in one-stage (static) and multi-stage games
(dynamic). Balance concepts. Credible cooperation, commitments, agreements and rules. You play with uncertainty.

Part II - The market
1. Perfectly competitive markets, efficiency and fairness.
2. Monopoly. Nature and implications of the monopoly on efficiency and well-being.
3. Oligopoly. Price competition and Bertrand-Nash equilibria; competition on production capacity and Cournot-Nash equilibria. Efficiency considerations. Collusion.
4. The importance of barriers to entry and monopolistic competition.
5. Markets with asymmetric information. Information asymmetry on characteristics. Adverse selection. Contracts and signaling mechanisms (signaling). Contracts and sorting mechanisms (screening). Discrimination of
price based on self-selection. Information asymmetry on actions, unfair behavior (moral hazard) and contractual solutions.

B. Douglas Bernheim, Michael D. Whinston, Microeconomia, Mc Graw Hill, 2022.
Additional material will be distributed through the Moodle platform during classes.

PROGRAM

1. Innovation: stylized facts and key definitions
2. Innovation models, market structure and industrial dynamics
3. Innovation and economic growth
4. Innovative enterprise: knowledge, skills and organization
5. Technological regimes and sectoral innovation systems
6. The diffusion of innovation
7. Geography of innovation
8. Innovation systems
9. Globalization of innovation
10. The economics of knowledge
11. The economics of digital platforms

Essential:
[1] Malerba, F. (2000). Economia dell'innovazione. Carrocci.
[2] Malerba, F., Pianta, M., & Zanfei, A. (2007). Innovazione. Imprese, industrie, economie (pp. 1-305). Carocci.

Recommended for specific topics:
[3] Schilling, M. A., & Izzo, F. (2022). Gestione dell'innovazione. McGraw Hill.
[4] Weil, D. N., D'Amato, M., & Jappelli, T. (2005). Crescita economica: problemi, dati e metodi di analisi. Hoepli.

Additional readings will be suggested during the course on specific topics.

1. Innovation: stylised facts and definitions.
2. Innovation models, market structure and inudstrial dynamics
3. Innovation and economic growth
4. Innovative firms: knowledge, skills and organisation
5. Technological regimes and sectorial patterns of innovation
6. Diffusion of innovations
7. Geography of innovation
8. Systems of innovation
9. Globalisation of innovation
10. Knowledge economics
11. Digital platforms

Essential
[1] Malerba, F. (2000). Economia dell'innovazione. Carrocci.
[2] Malerba, F., Pianta, M., & Zanfei, A. (2007). Innovazione. Imprese, industrie, economie (pp. 1-305). Carocci.

Recommended
[3] Schilling, M. A., & Izzo, F. (2022). Gestione dell'innovazione. McGraw Hill.
[4] Weil, D. N., D'Amato, M., & Jappelli, T. (2005). Crescita economica: problemi, dati e metodi di analisi. Hoepli.

More references on specific topics will be provided during the lectures.

STATISTICS FOR BIG DATA, 2nd year course with the following content:
- data visualization techniques
- Statistical methods and models for the analysis of simple and complex dependency structures. Simple, multiple and logistic regression models. Log-linear model.
- Elements of statistical methods of decision support under uncertainty. Decision tree. Representation by models of decision problems and their optimal solution.
- Multivariate statistical techniques for data dimension reduction (factor analysis, cluster analysis).
- First elements of Bayesian networks.

Foundations of Statistics for Data Scientists - With R and Python (2021) Alan Agresti, Maria Kateri, Taylor and Francis ed.
Teacher will give lecture notes on Bayesian networks and decision support systems.