Evolution of the global economy in the nineteenth and twentieth centuries:
– The factors which determined economic development in the nineteenth century
– The gold standard and growth in international trade
– The consequences of the First World War and of subsequent peace treaties
– The Great Depression (1929-1933)
– The global economy between the two world wars
– The difficult post-Second World War reconstruction period
– The Marshall Plan and the new economic world order
– Processes of economic cooperation and integration
– The end of the golden age
– From the European Monetary System to the Treaty of Maastricht
The Italian economy and the international context from the post-Second World War period to the 1980s:
– From reconstruction to the economic ‘boom’
– Southern Italy and emergency intervention
– Industrial disputes (1963-1973)
– The international context of the 1970s and 80s and the reconstruction process of the Italian economy
– Transformations in the international monetary system
– The difficult construction of monetary cooperation in Europe

R. CAMERON – L. NEAL A Concise Economic History of the World: From Paleolithic Times to the Present, Oxford University Press, 2003
V. ZAMAGNI, The Economic History of Italy 1860-1990, Clarendon Press, 1991

Evolution of the global economy in the nineteenth and twentieth centuries:
– The factors which determined economic development in the nineteenth century
– The gold standard and growth in international trade
– The consequences of the First World War and of subsequent peace treaties
– The Great Depression (1929-1933)
– The global economy between the two world wars
– The difficult post-Second World War reconstruction period
– The Marshall Plan and the new economic world order
– Processes of economic cooperation and integration
– The end of the golden age
– From the European Monetary System to the Treaty of Maastricht
The Italian economy and the international context from the post-Second World War period to the 1980s:
– From reconstruction to the economic ‘boom’
– Southern Italy and emergency intervention
– Industrial disputes (1963-1973)
– The international context of the 1970s and 80s and the reconstruction process of the Italian economy
– Transformations in the international monetary system
– The difficult construction of monetary cooperation in Europe

R. CAMERON – L. NEAL A Concise Economic History of the World: From Paleolithic Times to the Present, Oxford University Press, 2003
V. ZAMAGNI, The Economic History of Italy 1860-1990, Clarendon Press, 1991

Main official statistical surveys: data production and interpretation. In particular: Consumer prices, Industrial production, Labour force, Household consumptions, Income and living conditions, Household Income and Wealth, National accounts. Main statistical indicators for economic phenomena: (simple and complex) index numbers, measures of concentration.
Calendar adjusted and seasonal adjusted time series. Chain-linked values. The use of moving averages to reconstruct the trend.
Introduction to econometrics. Single and multiple Linear Regression: ordinary least squares, goodness of fit, homoscedasticity and heteroscedasticity, nonlinear regression functions. An introduction to the use of R for statistical analysis.

Class notes. Press releases (Istat - Banca d'Italia).
Stock J.H. and Watson M.W., Introduction to Econometrics, Update, Global edition, 3rd Edition, 2014, Pearson.

The course consists of two teaching modules.
The first module concerns the general part and trade union law (Introduction to the study of labor law). The boundaries and the meaning of labor law. Historical evolution and current trends. Sources. Constitutional principles. European sources and international aspects of Trade union law. Trade union freedom and Trade Union Organization. Union rights and their protection with particular reference to art. 28 of the Workers’ Statute. The collective agreement: the structure of collective bargaining, the negotiability and effectiveness of the collective agreements at different levels, the relationship between law and collective agreement. The strike and other forms of union struggle; the strike in essential public services.
The second module concerns the employment relationship: the employment contracts (subordinate, autonomous, coordinated). The flexible contractual forms. The forms of indirect acquisition of work. The subordinate employment contract: the subjective and objective requirements. The obligations of the employer: collaboration, diligence, obedience, loyalty. The powers of the employer. The protection of the person, of dignity and freedom of workers. The prohibitions of discrimination. Worker’s rights: pay, holidays, rest, leave, right to health and safety. The content of the work performance: the tasks, the working hours. The end of the employment relationship: individual dismissals. The enterprise crisis and excess staff: earning redundancy fund, solidarity contracts, transfer of the undertaking, collective dismissals. The protection of the employer’s rights; waivers and transactions; limitation. The employment services and the worker’s protection on the labor market.

- G. Santoro Passarelli - Diritto dei lavori e dell'occupazione - Giappichelli- Latest edition

1. L'AMMINISTRAZIONE E IL SUO DIRITTO - ORDINAMENTO GIURIDICO E AMMINISTRAZIONE: LA DISCIPLINA COSTITUZIONALE.
2. L'ORGANIZZAZIONE AMMINISTRATIVA: PROFILI GENERALI - L'ORGANIZZAZIONE DEGLI ENTI PUBBLICI - LE AUTORITÀ AMMINISTRATIVE INDIPENDENTI.
3. L’EVOLUZIONE DELLO STATO A PUBBLICA AMMINISTRAZIONE - STATO LIBERALE E STATO SOCIALE - DIMENSIONAMENTO DELLO STATO SOCIALE E DIRITTO COMUNITARIO - PRIVATIZZAZIONE DEGLI ENTI PUBBLICI ECONOMICI.
4. IL RAPPORTO DI LAVORO CON LA PUBBLICA AMMINISTRAZIONE – LA PRIVATIZZAZIONE – LA DIRIGENZA PUBBLICA.
5. LE SITUAZIONI GIURIDICHE SOGGETTIVE NEI CONFRONTI DELLA PUBBLICA AMMINISTRAZIONE E LE RELATIVE VICENDE - IL PROCEDIMENTO AMMINISTRATIVO - IL PROVVEDIMENTO: VALIDITÀ ED EFFICACIA.
6. OBBLIGAZIONI, CONTRATTI E RESPONSABILITÀ DELLA PUBBLICA AMMINISTRAZIONE.
7. LA TUTELA GIURISDIZIONALE NEI CONFRONTI DELLA PUBBLICA AMMINISTRAZIONE.

PER LA PREPARAZIONE ALL’ESAME SI CONSIGLIA IL SEGUENTE PROGRAMMA:

STUDENTI NON FREQUENTANTI.

- V. CERULLI IRELLI, LINEAMENTI DI DIRITTO AMMINISTRATIVO, TORINO, GIAPPICHELLI, 2011, DA PAG. 1 A PAG. 542.
OPPURE
- G. CORSO, MANUALE DI DIRITTO AMMINISTRATIVO, TORINO, GIAPPICHELLI, 2008 DA PAG. 1 A PAG. 516.
OPPURE
- E. CASETTA, COMPENDIO DI DIRITTO AMMINISTRATIVO, MILANO, GIUFFRÈ, 2010, CAPITOLI DA I A IX, CAP. X, SEZ.I.
OPPURE
- D. SORACE, DIRITTO DELLE PUBBLICHE AMMINISTRAZIONI, BOLOGNA, MULINO, 2010, IN CORSO DI PUBBLICAZIONE.
OPPURE
- MAZZAROLLI, PERICU, ALB. ROMANO, ROVERSI MONACO, SCOCA (A CURA DI), DIRITTO AMMINISTRATIVO, VOL. I, BOLOGNA, MONDUZZI, 2005.

SI CONSIGLIA ALTRESÌ LA LETTURA DI:
P. LAZZARA, GLI ATTI E I PROVVEDIMENTI, IN MANUALE DI DIRITTO PUBBLICO, A CURA DI F. FRACCHIA, NAPOLI, EDITORIALE SCIENTIFICA, 2010, PAGG. 225 – 237.

STUDENTI FREQUENTANTI.

- V. CERULLI IRELLI, LINEAMENTI DI DIRITTO AMMINISTRATIVO, TORINO, GIAPPICHELLI, 2011, DA PAG. 233 A PAG. 542.
OPPURE,
- G. CORSO, MANUALE DI DIRITTO AMMINISTRATIVO, TORINO, GIAPPICHELLI, 2010, DA PAG. 167 A PAG. 444.

GLI STUDENTI FREQUENTANTI POTRANNO SVOLGERE APPROFONDIMENTI SU ARGOMENTI DA CONCORDARE CON IL DOCENTE. I RELATIVI RISULTATI SARANNO DISCUSSI IN FORMA SEMINARIALE.
DURANTE IL CORSO SARANNO ORGANIZZATI INCONTRI DI APPROFONDIMENTO E DI AGGIORNAMENTO SU TEMI DI ATTUALITÀ.

LO STUDIO DEVE ESSERE SVOLTO UTILIZZANDO LE FONTI PIÙ IMPORTANTI DEL DIRITTO AMMINISTRATIVO. SI SEGNALANO IN PARTICOLARE: L. 23 AGOSTO 1988, N. 400 (ART. 17) (IN TEMA DI REGOLAMENTI DEL GOVERNO); L. 7 AGOSTO 1990, N. 241 (IN TEMA DI PROCEDIMENTO AMMINISTRATIVO E ACCESSO AI DOCUMENTI), AGGIORNATA CON LE L. 15/2005, 80/2005 E 69/2009; D.LGS. 30 LUGLIO 1999, N. 300 (IN TEMA DI AMMINISTRAZIONE DELLO STATO E MINISTERI); D.LGS. 30 MARZO 2001, N. 165 (IN TEMA DI ORGANIZZAZIONE DELLE AMMINISTRAZIONI PUBBLICHE), NONCHÉ LE L 20 MARZO 1865, N. 2248 (ALL. E), R.D. 26 GIUGNO 1924, N. 1054, L. 6 DICEMBRE 1971, N. 1034, D.LGS. 31 MARZO 1998, N. 80 E L. 21 LUGLIO 2000, N. 205 E SUCC. MOD. (IN TEMA DI GIUSTIZIA AMMINISTRATIVA). E’ INDISPENSABILE LA CONOSCENZA DELLA COSTITUZIONE DELLA REPUBBLICA ITALIANA COME MODIFICATA CON L. COST. 18 OTTOBRE 2001, N. 3 (DI RIFORMA DEL TITOLO V DELLA PARTE SECONDA).

PER IL REPERIMENTO DELLE FONTI NORMATIVE SI PUÒ CONSULTARE LA GAZZETTA UFFICIALE, NONCHÉ, SOLTANTO PER GLI ATTI LEGISLATIVI ENTRATI IN VIGORE A PARTIRE DALLA XIII LEGISLATURA (1996), IL SITO INTERNET DEL PARLAMENTO O ALTRI SITI PRESENTI NELLA RETE. N.B.: IN QUESTO MODO SI ACCEDE AL TESTO ORIGINARIO DELLE FONTI NON AGGIORNATO CON LE MODIFICHE SUCCESSIVE.

PER DISPORRE DEL TESTO AGGIORNATO PUÒ ESSERE UTILE L'IMPIEGO DI UN "CODICE AMMINISTRATIVO" (ESISTONO IN COMMERCIO VARIE RACCOLTE), CON L'AVVERTENZA DI UTILIZZARE UN'EDIZIONE RECENTE. IN PARTICOLARE SI PUÒ FAR RIFERIMENTO A M. CAMMELLI, G. SCIULLO, CODICE BREVE DELLE AMMINISTRAZIONI PUBBLICHE ,ZANICHELLI, BOLOGNA, ULTIMA EDIZIONE DISPONIBILE OPPURE A F.A. ROVERSI MONACO, L. VANDELLI, CODICE BREVE DI DIRITTO AMMINISTRATIVO , MAGGIOLI, RIMINI, ULTIMA EDIZIONE DISPONIBILE.

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identity. Types of firms.
2) The firm in its broader economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and company profitability.
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting logic: Rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2009
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2012

Alternatively:

David Boddy, Management: an Introduction, Financial Times Prentice Hall, 2011
Leslie K. Breitner and Robert N. Anthony, Essentials of Accounting, Pearson, 2013

Program
1) Organisations and entities.
General characters: Aims of organisations. "Legal entity" and "economic entity." Various types of organisations
2) Broader characters of an Organisation.
Private and public companies. Equilibrium conditions. Possible ways to remunerate resources used by the organisation. The business risk. Income and profit.
3) Funding
The need for capital and its determination. Corporate finance, "equity" and "debt capital"; corporate self-financing; the dynamic relationship between "equity" and "debt capital". A corporate' s financial structure.
4) Accounting as a tool for information
Logical moments. The nature of facts under investigation. Methods.
5) The accounting recognition
Theory of the double-entry accounting. Systematic and comprehensive recording of financial transactions pertaining to a business.

Part I: The Economy of the Company: Business Economics and Accounting. The study of the conditions of existence of the corporate body; the personal component and the operating means of the company. Object of the company. Corporate subjects: "legal entities" and "economic subject". Organization. The organizational structures. Various types of company. The institution of the company, its location, its size.
The supply company: general characteristics and management schemes. Production companies for the exchange of goods and services: companies. The aims of the company. The economic balance as a fundamental condition of the life of the company. Economic balance and economy. The possible ways of remunerating the productive factors used by the company. The business risk and the subjects on which it weighs. Business efficiency. The process of forming the company's income. The capital requirement and its determination. Company financing: equity and credit capital in their various forms; corporate self-financing; the choice of convenient forms of financing; the dynamic relationship between equity and credit capital. The financial structure of the company.
The process of dimensional growth of companies: the main characteristics, nature, structure, internal exchange and production operations in groups of companies.
Part II: Accounting elements: Double-entry theory and method. The double-entry method applied to the income system in production companies. The accounting records of the incorporation operations and of the main operations. The accounts for closing and reopening the accounts.

Zanda, Fondamenti di Economia Aziendale, Giappichelli, ultima edizione
oppure
Zanda, Lineamenti di Economia Aziendale, Kappa, ultima edizione

L. MUSERRA, T.ONESTI, Esercitazioni di economia aziendale, Giappichelli, 2013 (ebook, available on the website giappichelli.it).
Please refer to the onestieconomiaaziendale.wordpress.com course page for course material.

GENERAL CHARACTERISTICS OF CORPORATE ORGANISATIONS
1) The firm as an economic entity: General characteristics of the firm. Corporate entities: legal and economic identity. Types of firms.
2) The firm in its broader economic perspective: The enterprise as an individual economic undertaking: private enterprises and state-owned enterprises. The company’s purpose. Financial and economic stability as a prerequisite of a company’s existence. Economic stability and different types of economic operability. Payment for operating and production inputs used by enterprises. Corporate risk and who bears it. Income and company profitability.
3) The organizational structure as part of the decision-making process; management control in modern corporations: Evolution of the corporate organizational models shaping the decision-making structure. Control exercised in corporations by different stakeholders. The planning and control function in modern corporations.
4) Corporate funding: Capital requirements, and how much is needed. Corporate funding: equity and debt capital in their various forms. Funding through cash generation. Capital structure of the company; choice of cost-efficient financing options; the dynamic relationship between equity and debt capital. Short-term capital and long-term financing.
MONITORING AND MEASUREMENT OF COMPANY PERFORMANCE
1) The accounting logic: Rationale. Nature of data to be examined. Methodologies. The corporate record-keeping system in a broad sense.
2) Accounting practice: The theory of double entry bookkeeping. Double entry bookkeeping applied to manufacturing companies. Bookkeeping entries for general business transactions, initiating joint-stock companies, special transactions (wages and salaries, financial transactions etc…), adjusting entries and year-end closing entries. Practical exercises in applying accounting record-keeping systems and measurement principles to business transactions.

Paoloni M., Paoloni P. (a cura di), Introduzione ed orientamento allo studio delle aziende, Giappichelli, 2009
Paoloni M., Celli, M. (a cura di), Introduzione alla contabilità generale, CEDAM, 2012

1. The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

C. De Vincenti, MACROECONOMIA - ELEMENTI DI BASE, editore Carocci, 2003 (except parr 9.5 e 9.6 and chapt. 10) + macroeconomics hand-outs by prof. Antonella Stirati available at the library

1. National accounts
2. The neoclassical model
3. Aggregate demand and income multipliers
4. Money and interest
5. The IS-LM model
6. The AD-AS model
7. The Phillips curve
8. The new-Keynesian models

- R. Dornbusch, S. Fischer, R. Startz, G. Canullo, P. Pettenati, Macroeconomia, McGraw Hill, Milano, 2014
- J.R. Hicks, “Il processo produttivo, il lavoro e il capitale”, in M. Pivetti (a cura di), Letture di Economia Politica, LED, Milano
- O. Castellino, Introduzione alla contabilità nazionale, Giappichelli editore, Torino, 1991

Structure of the computer. Hardware and Software. General diagram of a data processing system. Type of computers. The use of the computer memories. The processor. The multiprocessor architectures. Input / Output: Ports for input / output of the computer. The units of input. The units of output. Operating systems. Characteristics of the operating systems. The multitasking operating systems. The Windows operating system. The graphical interface. Computer networks.
The communication between computers. Protocols and interfaces. The local networks. The transmission media. The types of network. The network technologies. The wide area networks. Client-server architecture and peer-to-peer networks. Internetwork. Internet. The services of the Internet.
. Word processing and presentation tools. Spreadsheets Use of data bases

ECDL Syllabus 5.0
Lectures notes provided by the teacher

1. Production and prices: general elements
The production process. Production methods and their representation. The social production process. Economy of mere subsistence. Economy producung surplus. Basic and non-basic goods.

2. Fundamentals of the classical theory of distribution and relative prices
The real wage and other circumstances taken as given in the 'core' of the theory. The concept of social surplus. Profits and general profit rate. Distinction and relationship between "normal" and "market" prices. Price equations: simultaneous determination of profit rate and relative prices. Importance and limits of the solutions to the problem attempted by Ricardo and Marx. The inverse wage-profit relationship. The theory of rent.

3. Fundamentals of the marginalist theory of distribution and relative prices
The data of the theory. Consumer theory. Functions of consumption good demand. Production theory. Direct and indirect substitutability as analytical bases for factor demand functions. Determination of distribution and relative prices in terms of supply and demand equilibria. Comparison with the classical theory of distribution. Implications of general economic equilibrium: full employment of available resources; Pareto optimality; efficiency in exchange; efficiency in production; efficiency in the combination of outputs. The notion of capital as a single productive factor and the difficulties that derive from it (mention).

4. Analysis of the single industry and market forms
The analysis of "partial" equilibrium. Short and long term cost curves of the individual enterprise. Equilibrium of enterprise and industry under competitive conditions, in the short and long period. Quantity produced and price, in the short and long period, in monopoly and monopolistic competition. The oligopoly: Cournot model.

■ "Elementi di teoria della produzione", Appunti per il corso di Microeconomia - Dispensa n.1
■ "La teoria classica della distribuzione e dei prezzi relativi", Appunti per il corso di Microeconomia - Dispensa n.2
■ "La teoria marginalista della distribuzione e dei prezzi relativi", Appunti per il corso di Microeconomia - Dispensa n.3

With regard to the other text adopted, the chapters and paragraphs included in the programme are set out below, with reference to the latest edition (2014).

Robert H. Frank e Edward Cartwright, Microeconomia
Milano: McGraw-Hill, VI edizione, 2014
Capitoli e paragrafi in programma:

Capitoli e paragrafi in programma:

Capitolo 3, La scelta razionale del consumatore, p. 51
{paragrafi 3.1, 3.2, 3.3, 3.4 e Appendice 3}

Capitolo 4, Domanda individuale e domanda di mercato, p. 91
{paragrafi: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7}

Capitolo 5, Applicazioni delle teorie della scelta razionale e della domanda, p. 135
{limitatamente al paragrafo 5.7}

Capitolo 9, La produzione, p. 263
{intero capitolo, inclusa l'Appendice 9}

Capitolo 10, I costi, p. 293
{intero capitolo, inclusa l'Appendice 10}

Capitolo 11, La concorrenza perfetta, p. 329
{paragrafi: 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8?, 11.9, 11.12, 11.13}

Capitolo 12, Il monopolio, p. 371
{paragrafi: 12.1, 12.2, 12.3, 12.4, 12.5, 12.6, 12.8}

Capitolo 13, Concorrenza imperfetta: un approccio basato sulla teoria dei giochi, p. 421
{paragrafi: 13.1, 13.2, 13.4 limitatamente al sotto-paragrafo 13.4.1}

Capitolo 15, L'equilibrio generale e l'efficienza dei mercati, p. 515
{paragrafi: 15.1, 15.2, 15.3, 15.4, 15.6, 15.7}

Elements of the theory of production
- inputs, outputs and production methods
- the subsistence economy
- the economy with a surplus
The surplus approach to commodity value and income distribution
- the relevance of social and institutional elements to income distribution
- the explanation of the real wage rate
- the "core" of the classical approach
- the link between profit rate and relative prices
- the price equations
- the classical theory of rent
The theory of consumer choice
- budget set and budget constraint
- preferences
- consumer choice
- consumer-good demand curves
The theory of firm choice
- the function of production
- profit maximisation
- isoquants and isocosts
- the output expansion path and long-term cost curves
Production factors and the marginalist explanation of income distribution
- marginal and average productivity of factors
- the demand curves of factors of production
- equilibrium between supply and demand for factors of production
Market forms
- perfect competition
- monopoly
- Cournot oligopoly
- Stackelberg oligopoly
Introduction to the welfare economics
- allocations and Edgeworth box
- Pareto improvements and Pareto optima
- first theorem of welfare economics

i) "Elementi di teoria della produzione", Appunti per il corso di Microeconomia - Dispensa n. 1 (teaching material written by R. Ciccone, S.M. Fratini e A. Trezzini).
ii) "La teoria classica della distribuzione e dei prezzi relativi", Appunti per il corso di Microeconomia - Dispensa n. 2 (teaching material written by R. Ciccone, S.M. Fratini e A. Trezzini).
iii) "La teoria marginalista della distribuzione e dei prezzi relativi", Appunti per il corso di Microeconomia - Dispensa n. 3 (teaching material written by R. Ciccone, S.M. Fratini e A. Trezzini).
iv) R.H. Frank, Microeconomia. McGraw-Hill Libri Italia, Milano.
v) "Glossario ed Esercizi Svolti di Microeconomia" (teaching material written by S.M. Fratini e D. Pignalosa).

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

The program includes:
Introduction to law
Forms of State and forms of Government
Beyond the State: the EU
The sources of law
Parliament and its functions
Institutes of direct democracy
The abrogative referendum.
The Government and its functions
The President of the Republic and his attributions
Principles on the subject of Administration
The other organs
Local ordering
Rights and freedom
The economic Constitution
Judicial power
Constitutional Justice

It is recommended the study of one of the following books:
R. BIN – G. PITRUZZELLA, Diritto pubblico, Torino, Giappichelli, latest edition
P. CARETTI – U. DE SIERVO, Istituzioni di Diritto pubblico, Torino, Giappichelli, latest edition
F. Modugno (a cura di), Diritto Pubblico, Torino, Giappichelli, latest edition
C. ROSSANO, Manuale di Diritto pubblico, Napoli, Jovene, latest edition

The course is composed by modules. The first two modules include the following legal categories: sources of law; subjective juridical situations; physical and juridical persons; legal assets, real rights in re propria and in re aliena; fact, act and trade; obligations; contracts in general. The third part focuses on the forms of transfer of familial property, with particular emphasis on the discipline of family law and mortis causa succession.

- M. NUZZO, Introduzione alle scienze giuridiche. Norme - Soggetti - Attività, 3ª ed., Giappichelli, 2009
- F. MACIOCE, L’obbligazione e il contratto, 3ª ed., Giappichelli, 2013
- L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, Famiglia e successioni. Le forme di circolazione della ricchezza familiare, 4ª ed., Giappichelli, 2016 (excluding sec. from 6 to 12 Chap. III; Chap. VIII and Chap. X)

The course is composed by modules. The first two modules include the following legal categories: sources of law; subjective juridical situations; physical and juridical persons; legal assets, real rights in re propria and in re aliena; fact, act and trade; obligations; contracts in general. The third part focuses on the forms of transfer of familial property, with particular emphasis on the discipline of family law and mortis causa succession.

- M. NUZZO, Introduzione alle scienze giuridiche. Norme - Soggetti - Attività, 3ª ed., Giappichelli, 2009
- F. MACIOCE, L’obbligazione e il contratto, 3ª ed., Giappichelli, 2013
- L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, Famiglia e successioni. Le forme di circolazione della ricchezza familiare, 4ª ed., Giappichelli, 2016 (excluding sec. from 6 to 12 Chap. III; Chap. VIII and Chap. X)

-Public Budget Revenues: taxes, contributions, and other charges
- The economic effects of Taxes both in closed and in open economies
- A Brief History of Western Public Finances as well as changing methodologies in the analysis of public economic decisions
- Social goods
- Tax design and Tax Incidence
- The Italian Tax System

1) A. DI MAJO, LEZIONI DI SCIENZA DELLE FINANZE, ECIG, GENOVA 2003.
2) A.DI MAJO, QUADERNI DI APPUNTI DI SCIENZA DELLE FINANZE, EDIZIONI PIGRECO, ROMA, 2005. CAPITOLO VI-VII (ESCLUSI I PARAGRAFI VII.5 E VII.6 E LE PAGINE 7-8-9 DEL PARAGRAFO VII.2)
3) P.BOSI, M.C. GUERRA, I TRIBUTI NELL'ECONOMIA ITALIANA, IL MULINO, BOLOGNA EDIZIONE 2015.

-Public Budgeting
-Public Budget Revenues: taxes, contributions, and other charges
- The economic effects of Taxes both in closed and in open economies
- A Brief History of Western Public Finances as well as changing methodologies in the analysis of public economic decisions
- Social goods
- Tax design and Tax Incidence
- The Italian Tax System
- The Long run Growth of Public Expenditure

1) A. DI MAJO, LEZIONI DI SCIENZA DELLE FINANZE, ECIG, GENOVA 2003.
2) A.DI MAJO, QUADERNI DI APPUNTI DI SCIENZA DELLE FINANZE, EDIZIONI PIGRECO, ROMA, 2005. CAPITOLO VI-VII (ESCLUSI I PARAGRAFI VII.5 E VII.6 E LE PAGINE 7-8-9 DEL PARAGRAFO VII.2)
3) P.BOSI, M.C. GUERRA, I TRIBUTI NELL'ECONOMIA ITALIANA, IL MULINO, BOLOGNA EDIZIONE 2011.

a) L’evoluzione dell’attività e delle analisi di Finanza Pubblica;
b) I beni pubblici;
c) Le entrate pubbliche e relative classificazioni;
d) Gli effetti economici dei tributi in economie chiuse ed aperte;
e) Analisi economica dei tributi: tax design e tax incidence;
f) La crescita della spesa pubblica;
g) Le principali forme di prelievo nel sistema tributario italiano.

- DI MAJO A., LEZIONI DI SCIENZA DELLE FINANZE, ECIG, GENOVA 2003, CAPITOLI I, II, III E V.
- DI MAJO A., QUADERNI DI APPUNTI DI SCIENZA DELLE FINANZE, EDIZIONI PIGRECO, ROMA 2005, CAPITOLO VI
- DI MAJO A., QUADERNI DI APPUNTI DI SCIENZA DELLE FINANZE, EDIZIONI PIGRECO, ROMA 2005, CAPITOLO VII
- BOSI P., GUERRA M.C., I TRIBUTI NELL’ECONOMIA ITALIANA, IL MULINO, BOLOGNA EDIZIONE 2010 (ESCLUSO IL CAPITOLO 10).

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website

1. The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

C. De Vincenti, MACROECONOMIA - ELEMENTI DI BASE, editore Carocci, 2003 (except parr 9.5 e 9.6 and chapt. 10) + macroeconomics hand-outs by prof. Antonella Stirati available at the library

1. National accounts
2. The neoclassical model
3. Aggregate demand and income multipliers
4. Money and interest
5. The IS-LM model
6. The AD-AS model
7. The Phillips curve
8. The new-Keynesian models

- R. Dornbusch, S. Fischer, R. Startz, G. Canullo, P. Pettenati, Macroeconomia, McGraw Hill, Milano, 2014
- J.R. Hicks, “Il processo produttivo, il lavoro e il capitale”, in M. Pivetti (a cura di), Letture di Economia Politica, LED, Milano
- O. Castellino, Introduzione alla contabilità nazionale, Giappichelli editore, Torino, 1991

Structure of the computer. Hardware and Software. General diagram of a data processing system. Type of computers. The use of the computer memories. The processor. The multiprocessor architectures. Input / Output: Ports for input / output of the computer. The units of input. The units of output. Operating systems. Characteristics of the operating systems. The multitasking operating systems. The Windows operating system. The graphical interface. Computer networks.
The communication between computers. Protocols and interfaces. The local networks. The transmission media. The types of network. The network technologies. The wide area networks. Client-server architecture and peer-to-peer networks. Internetwork. Internet. The services of the Internet.
. Word processing and presentation tools. Spreadsheets Use of data bases

ECDL Syllabus 5.0
Lectures notes provided by the teacher

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website

1. The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

C. De Vincenti, MACROECONOMIA - ELEMENTI DI BASE, editore Carocci, 2003 (except parr 9.5 e 9.6 and chapt. 10) + macroeconomics hand-outs by prof. Antonella Stirati available at the library

1. National accounts
2. The neoclassical model
3. Aggregate demand and income multipliers
4. Money and interest
5. The IS-LM model
6. The AD-AS model
7. The Phillips curve
8. The new-Keynesian models

- R. Dornbusch, S. Fischer, R. Startz, G. Canullo, P. Pettenati, Macroeconomia, McGraw Hill, Milano, 2014
- J.R. Hicks, “Il processo produttivo, il lavoro e il capitale”, in M. Pivetti (a cura di), Letture di Economia Politica, LED, Milano
- O. Castellino, Introduzione alla contabilità nazionale, Giappichelli editore, Torino, 1991

Structure of the computer. Hardware and Software. General diagram of a data processing system. Type of computers. The use of the computer memories. The processor. The multiprocessor architectures. Input / Output: Ports for input / output of the computer. The units of input. The units of output. Operating systems. Characteristics of the operating systems. The multitasking operating systems. The Windows operating system. The graphical interface. Computer networks.
The communication between computers. Protocols and interfaces. The local networks. The transmission media. The types of network. The network technologies. The wide area networks. Client-server architecture and peer-to-peer networks. Internetwork. Internet. The services of the Internet.
. Word processing and presentation tools. Spreadsheets Use of data bases

ECDL Syllabus 5.0
Lectures notes provided by the teacher

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website

1. The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

C. De Vincenti, MACROECONOMIA - ELEMENTI DI BASE, editore Carocci, 2003 (except parr 9.5 e 9.6 and chapt. 10) + macroeconomics hand-outs by prof. Antonella Stirati available at the library

1. National accounts
2. The neoclassical model
3. Aggregate demand and income multipliers
4. Money and interest
5. The IS-LM model
6. The AD-AS model
7. The Phillips curve
8. The new-Keynesian models

- R. Dornbusch, S. Fischer, R. Startz, G. Canullo, P. Pettenati, Macroeconomia, McGraw Hill, Milano, 2014
- J.R. Hicks, “Il processo produttivo, il lavoro e il capitale”, in M. Pivetti (a cura di), Letture di Economia Politica, LED, Milano
- O. Castellino, Introduzione alla contabilità nazionale, Giappichelli editore, Torino, 1991

Structure of the computer. Hardware and Software. General diagram of a data processing system. Type of computers. The use of the computer memories. The processor. The multiprocessor architectures. Input / Output: Ports for input / output of the computer. The units of input. The units of output. Operating systems. Characteristics of the operating systems. The multitasking operating systems. The Windows operating system. The graphical interface. Computer networks.
The communication between computers. Protocols and interfaces. The local networks. The transmission media. The types of network. The network technologies. The wide area networks. Client-server architecture and peer-to-peer networks. Internetwork. Internet. The services of the Internet.
. Word processing and presentation tools. Spreadsheets Use of data bases

ECDL Syllabus 5.0
Lectures notes provided by the teacher

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

LINEAR ALGEBRA.
MULTIVARIABLE CALCULUS
IMPLICIT FUNCTIONS.
QUADRATIC FORMS.
FREE AND CONSTRAINED OPTIMIZATION THEORY.
ORDINARY DIFFERENTIAL EQUATIONS.
SYSTEMS OF DIFFERENTIAL EQUATIONS.
ECONOMIC AND FINANCIAL APPLICATIONS

C. P. SIMON, L. E. BLUME, MATEMATICA 2 PER L’ECONOMIA E LE SCIENZE SOCIALI, UNIVERSITA’ BOCCONI EDITORE, 2002.

Birth of Marginalism: Jevons and Menger: utility as the foundation of the value of goods; Walras: the system of general economic equilibrium; difficulties connected with the treatment of capital.
Alfred Marshall: specific aspects of Marshall's value theory; claim to continuity with Ricardo's theory.
Spreading marginalism and alternative lines of thought (mention). Development of the marginalist approach between the end of the 19th century and the first part of the 20th century. Two fundamental break points of the prevalence of marginalism: Keynes and Sraffa.
Walras' social-political conceptions: distributive equity and social justice; Walras' criticism of Marx's value theory.
Ricardo's 'macroeconomics': level of social product and Say's law; quantitative theory of money; public debt and taxation.

1. Appunti sulla teoria della distribuzione e del valore negli economisti classici (limited to chaps. 2-6, pp. 7-62), available at the copyshop "Copyando", via Osiense 457/d, Roma;
2. R. Ciccone, Materiale didattico per il corso di Storia del Pensiero Economico, available at the copyshop "Copyando", via Ostiense 457/d, Roma.

1. Social surplus, value and distribution in the classical approach: Quesnay, Smith, Ricardo, Marx.

2. Political economy after Ricardo: the "Ricardian socialists", the critics of Ricardo, Ricardo's disciples; John Stuart Mill.

Appunti sulla teoria della distribuzione e del valore negli economisti classici (only chapters 2-6, pp. 7-62), available at the copy shop "Copyando", via Osiense 457/d, Roma;

Materiale didattico per il corso di Storia del Pensiero Economico a cura del prof. R. Ciccone, available at the copy shop "Copyando", via Osiense 457/d, Roma.

INTRODUCTION
1. Theories of value and distribution: the different theoretical approaches. The connections with the theory of production. Outlines of the surplus approach

I. THE MARGINALIST THEORY: DETERMINATION
OF VALUE IN PURE EXCHANGE EQUILIBRIUM

2. Marginal utility. Individual equilibrium.
3. Individual supply and demand curves (independent and non-independent goods).
4. Collective supply and demand curves. General equilibrium (graphic study): existence; stability; uniqueness/multiplicity.
5. Equations of general equilibrium (2 goods, m individuals; specialization and general case). Walras' law.
6. Possible 'exceptions': superabundance and free goods (or non-existence of equilibrium?); increasing demand curve and instability.

II. THE MARGINALIST THEORY: VALUE AND DISTRIBUTION
IN THE CASE OF PRODUCTION WITHOUT CAPITAL
7. Marginal utility and supply curves of the factors. Indirect substitutability and factor demand curves.
8. Income distribution and price of commodities (supply curves for commodities). Equations of general equilibrium in the case of production with fixed coefficients. Walras' law.
9. The problem of the existence of equilibrium under the hypothesis of fixed coefficients. The hypothesis of variable coefficients: marginal productivity.
10. The problem of product exhaustion.
11. The marginalist theory and the notion of substitutability (plausibility of the notion and its role within the theory). The simultaneous determination of prices and quantities.

III. THE MARGINALIST THEORY: VALUE AND DISTRIBUTION
IN THE CASE OF PRODUCTION WITH CAPITAL

12. Production with capital: the problem of the variability of coefficients; the condition of uniformity of the profit rate.
13. The treatment of capital as a complex of quantities and the absence of a uniform profit rate.
14. The treatment of capital as a single quantity: capital as a sum of value. Problems on the supply side. Problems on the demand side.

Lezioni sulla teoria neoclassica (handouts)

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website

1. The Economic system. Definitions and measurement of the main macroeconomic aggregates
2. Macroeconomic equilibrium and the Keynesian theory of income and employment
3.The public sector
4. The open economy: balance of payments, exchange rate, external constraint
5. Money and financial activities. The Central Bank and the banking sector, Demand and supply of money, interest rate determination.
6. Aggregate investment and the rate of interest. Controversial aspects.
7. The IS-LM model. Economic policy in the IS-LM model in a closed economy. Effects of changes in nominal wages
8. The IS-LM model for the open economy, exchange rate regimes and the effects of economic policy
9.The AD-AS model and its implications for the theory of output and employment
10. Inflation and unemployment some elements towards an interpretation

C. De Vincenti, MACROECONOMIA - ELEMENTI DI BASE, editore Carocci, 2003 (except parr 9.5 e 9.6 and chapt. 10) + macroeconomics hand-outs by prof. Antonella Stirati available at the library

1. National accounts
2. The neoclassical model
3. Aggregate demand and income multipliers
4. Money and interest
5. The IS-LM model
6. The AD-AS model
7. The Phillips curve
8. The new-Keynesian models

- R. Dornbusch, S. Fischer, R. Startz, G. Canullo, P. Pettenati, Macroeconomia, McGraw Hill, Milano, 2014
- J.R. Hicks, “Il processo produttivo, il lavoro e il capitale”, in M. Pivetti (a cura di), Letture di Economia Politica, LED, Milano
- O. Castellino, Introduzione alla contabilità nazionale, Giappichelli editore, Torino, 1991

Structure of the computer. Hardware and Software. General diagram of a data processing system. Type of computers. The use of the computer memories. The processor. The multiprocessor architectures. Input / Output: Ports for input / output of the computer. The units of input. The units of output. Operating systems. Characteristics of the operating systems. The multitasking operating systems. The Windows operating system. The graphical interface. Computer networks.
The communication between computers. Protocols and interfaces. The local networks. The transmission media. The types of network. The network technologies. The wide area networks. Client-server architecture and peer-to-peer networks. Internetwork. Internet. The services of the Internet.
. Word processing and presentation tools. Spreadsheets Use of data bases

ECDL Syllabus 5.0
Lectures notes provided by the teacher

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

An introduction to the fundamental ideas of statistics. Topics include descriptive statistics, probability, confidence intervals, and testing hypotheses, as well as the basics of Chi-square tests, regression and correlation.

1) L. PIERACCINI, A. NACCARATO. LEZIONI DI STATISTICA DESCRITTIVA, GIAPPICHELLI, 2003.
2) L. PIERACCINI. FONDAMENTI DI INFERENZA STATISTICA. II EDIZ. GIAPPICHELLI, 2007.

OR ONE AMONG:
- S.M. ROSS. INTRODUZIONE ALLA STATISTICA, APOGEO, 2008.
- D. PICCOLO. STATISTICA PER LE DECISIONI, IL MULINO, BOLOGNA, EDIZIONE 2010.
- D.S. MOORE. STATISTICA DI BASE, APOGEO, 2005.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

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:
- G. Cicchitelli, Statsitica: Principi e Metodi, Pearson Education, 3/Eds
- 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
Notes and handout (in Italian) are available at the web page of the course.

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Propositional logic. Propositions. Decidable propositions. Logical operations between propositions. Logical implication. Necessity, sufficiency and necessity and sufficiency. Truth tables. Theorem. Methods for proving a theorem. Sets. Operations between sets. Numerical sets:
natural numbers, relative numbers and rational numbers. Infimum and supremum of a numerical set. Irrationality of square root of 2 (with proof). Dedekind's axiom. The real numbers set. Real numbers and their representation on the straight line. Limited and non-limited sets. Maximum and minimum of a numerical set. Intervals and boundary of a point. Elements of line topology: isolated, boundary, internal and accumulation points. Open sets. Closed sets. A set is closed if and only if it contains all its accumulation points.
2) Sums
Definition of summation. Sum of the first natural n (with proof). Sum of the first n terms of a geometric progression (with proof). Summation properties.
3) Real functions of real variable
Real functions of real variable. The Cartesian plane and the graph of a function. Injective and surjective functions. Invertible functions. Even and odd functions. Increasing and decreasing functions. Link between monotony and injectivity. Inverse function. Inverse function graph. Elementary functions. Transformations of elementary functions. Compound function. Multi-law defined functions. Domain of a function.
4) Sequences and numerical series
Converging, diverging and indeterminate sequences. Limits of sequences. Definition of numerical series. Necessary condition for convergence
of a series (with proof). The character of the geometric series (with proof). Mengoli series and its value (with proof).
5) Limits of real functions of real variable
Definition of limits. Right-hand limit and left-hand limit. Vertical and horizontal asymptote. Oblique asymptote. Theorem on uniqueness of limit. (with proof). Theorems on sign permanence (with proof). Rational operations on limits. Indeterminate forms. Notable limits.
6) Infinites and infinitesimals
Definition of infinitesimal and infinite. Comparison between infinitesimal and infinite. Order of infinitesimal and infinite. Cancellation theorems (with proof). Order propagation.
7) Continuity
Definition of continuity in a point. Continuity in a set. Classification of discontinuity points. Continuity of elementary functions. Continuity
of the compound function. Continuity of functions defined by several laws. Theorem of zeros for continuous functions. Weierstrass's theorem. Darboux's theorem (with proof).
8) Differential calculus
Difference quotient. Derivative of a function in a point and its geometric meaning. Derivability implies continuity (with proof). Points of non-derivability.
Derivative function and derivatives of subsequent order. Derivative of elementary functions. The rules of derivation. Derivative of compound functions. De L’Hopital's theorem and its application to indeterminate forms. Taylor polynomial of order 1 and order 2 (with proof). The factorial of n. Taylor polynomial
of order n. Mc Laurin polynomial. Differential and its geometric meaning. First-order error theorem (with proof). Local maxima and minima. Fermat's theorem (with proof). Rolle's theorem (with proof). Lagrange's theorem (with proof). Corollaries to Lagrange's theorem (with proof). Relationship between the sign of the first derivative and the increasing / decreasing functions in an interval (with proof). Concavity and convexity in a point. Relationship between the sign of the second derivative and the convexity / concavity of a function in an interval (with proof). Flex points. Global concavity and convexity conditions.
9) Integral calculus
Primitive of a function. Indefinite integral. Properties of primitives (with proof). Property of the indefinite integral. Immediate indefinite integrals. Integration by parts (with proof). Area subtended by a curve. Superior and inferior integral sum. Definition of definited Riemann integral. Property
of the definite integral. Integral function. The integral mean value theorem (with proof). Torricelli-Barrow's theorem (with proof). Corollary to Torricelli-Barrow's theorem (with proof).
10) Linear algebra
Vectors and their geometric representation. Product of a vector for a scalar. Vectors addition. The vector space Rn: Linear combination of
vectors. Linearly dependent and independent vectors. Matrices. Matrix addition. Matrix multiplication. Determinant of a matrix. Matrix
inverse. Uniqueness of the inverse matrix (with proof). Necessary condition for the existence of the inverse matrix (with proof). Sufficient condition for the existence of the inverse matrix. Transposed matrix. Rank of a matrix. Linear equation systems. Cramer's theorem. Rouché-Capelli theorem. Homogeneous systems. Parametric systems

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only:Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4 .

Functions of One Variable. Properties of Functions. Differentiation. Derivatives in Use. Single-Variable Optimization. Integration. Matrix and Vector Algebra. Determinants and Inverse Matrices. Systems of Linear Equations.

Mathematics for economists Carl P. Simon, Lawrence Blume- W.W. Norton and Company, Inc.
Only: Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Appendix 4.

or

Essential Mathematics for Economic Analysis
Knut Sydsæter, Peter Hammond, Arne Strøm
Only : Chapter1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 15, Chapter 16.

Logica proposizionale ed insiemistica: Proposizioni, operazioni con le proposizioni, insiemi, operazioni con gli insiemi ed applicazioni.
Insiemi numerici: Numeri interi, relativi, razionali, reali; insiemi numerici limitati; intervalli, intorni, punti di accumulazione in R.
Sommatoria e produttoria Somme particolari e proprietà.
Cenni alle successioni e serie numeriche
Funzioni reali di variabile reale: Funzioni iniettive, suriettive, pari e dispari, funzioni elementari, funzioni composte, funzioni invertibili, grafici deducibili da quelli noti; limiti, teoremi di unicità del limite, teoremi della permanenza del segno, teorema del confronto; continuità, Teorema degli zeri, teorema di Weierstrass e di Darboux; infinitesimi, infiniti, ordine, teoremi di cancellazione.
Calcolo differenziale: Rapporto incrementale, derivata, teorema su derivabilità e continuità, regole di derivazione, derivazione funzioni composte e funzioni inverse, differenziale, derivate di ordine superiore, approssimazione con polinomi di Taylor e di Mc Laurin.
Studio di funzioni: Massimi e minimi relativi, teorema di Fermat, teorema di Rolle, teorema di Lagrange e corollari, teorema di De L’Hospital, funzioni concave e convesse.
Calcolo integrale: Funzioni primitive e integrale indefinito, integrazione per parti e per sostituzione, integrale definito: proprietà, teorema della media, teorema di Torricelli Barrow e corollario.
Algebra lineare: Vettori, spazi vettoriali, vettori linearmente dipendenti e non, basi, matrici, operazioni con le matrici, determinante, rango, matrice inversa, sistemi di equazioni lineari, teorema di Cramer e di Rouchè-Capelli, sistemi parametrici.

teaching material on the teacher's website