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; 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 succession.

- M. NUZZO: INTRODUZIONE ALLE SCIENZE GIURIDICHE. NORME - SOGGETTI - ATTIVITÀ, 3ª ED., GIAPPICHELLI, 2009
- F. MACIOCE: L’OBBLIGAZIONE E IL CONTRATTO, 2ª ED., GIAPPICHELLI, 2007
A SCELTA DELLO STUDENTE: - L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, FAMIGLIA E SUCCESSIONI. LE FORME DI CIRCOLAZIONE DELLA RICCHEZZA FAMILIARE, 2ª ED., GIAPPICHELLI, 2009, CAPITOLI: I, II, III, IV (SOLO PARR. 1 E 3), VI, VII, IX, XI, XII, XIII
OPPURE
- A. BELLELLI, A.G. CIANCI, BENI E SITUAZIONI GIURIDICHE DI APPARTENENZA. TRA DIRITTI REALI E NEW PROPERTIES, GIAPPICHELLI, 2008

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

-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 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).

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.

LE ECONOMIE E LE POLITICHE ECONOMICHE DEI PRINCIPALI PAESI ED AREE.
POLITICHE DI BILANCIO E POLITICA MONETARIA NELL’AREA DELL’EURO.
L’ECONOMIA ITALIANA : REDDITO, PREZZI, BILANCIA DEI PAGAMENTI, MERCATO DEL LAVORO E FINANZA PUBBLICA.
I GRANDI NUMERI (DIMENSIONE DEL PIL, PRODOTTO PRO-CAPITE,OCCUPAZIONE, DISOCCUPAZIONE, STRUTTURA PRODUTTIVA, ECC.
EVOLUZIONE DELLE POLITICHE ECONOMICHE DAL DOPOGUERRA AD OGGI.
APPROFONDIMENTI SULLA CRISI FINANZIARIA DEL 2007, SULLA DINAMICA DEI CONSUMI E SUI NODI STRUTTURALI DELL’ECONOMIA ITALIANA.

BANCA D’ITALIA, RELAZIONE ANNUALE, ( PARTE A, B E C ) (WWW.BANCADITALIA.IT).
MATERIALE DISTRIBUITO DURANTE IL CORSO

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

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; 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 succession.

- M. NUZZO: INTRODUZIONE ALLE SCIENZE GIURIDICHE. NORME - SOGGETTI - ATTIVITÀ, 3ª ED., GIAPPICHELLI, 2009
- F. MACIOCE: L’OBBLIGAZIONE E IL CONTRATTO, 2ª ED., GIAPPICHELLI, 2007
A SCELTA DELLO STUDENTE: - L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, FAMIGLIA E SUCCESSIONI. LE FORME DI CIRCOLAZIONE DELLA RICCHEZZA FAMILIARE, 2ª ED., GIAPPICHELLI, 2009, CAPITOLI: I, II, III, IV (SOLO PARR. 1 E 3), VI, VII, IX, XI, XII, XIII
OPPURE
- A. BELLELLI, A.G. CIANCI, BENI E SITUAZIONI GIURIDICHE DI APPARTENENZA. TRA DIRITTI REALI E NEW PROPERTIES, GIAPPICHELLI, 2008

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

-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 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).

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

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.

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.

LE ECONOMIE E LE POLITICHE ECONOMICHE DEI PRINCIPALI PAESI ED AREE.
POLITICHE DI BILANCIO E POLITICA MONETARIA NELL’AREA DELL’EURO.
L’ECONOMIA ITALIANA : REDDITO, PREZZI, BILANCIA DEI PAGAMENTI, MERCATO DEL LAVORO E FINANZA PUBBLICA.
I GRANDI NUMERI (DIMENSIONE DEL PIL, PRODOTTO PRO-CAPITE,OCCUPAZIONE, DISOCCUPAZIONE, STRUTTURA PRODUTTIVA, ECC.
EVOLUZIONE DELLE POLITICHE ECONOMICHE DAL DOPOGUERRA AD OGGI.
APPROFONDIMENTI SULLA CRISI FINANZIARIA DEL 2007, SULLA DINAMICA DEI CONSUMI E SUI NODI STRUTTURALI DELL’ECONOMIA ITALIANA.

BANCA D’ITALIA, RELAZIONE ANNUALE, ( PARTE A, B E C ) (WWW.BANCADITALIA.IT).
MATERIALE DISTRIBUITO DURANTE IL CORSO

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

Notes can be downloaded online from the course website

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 .

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

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.

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

Notes can be downloaded online from the course 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

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

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

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

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.

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 course is composed by modules. The first two modules include the following legal categories: sources of law; subjective juridical situations; physical and juridical persons; 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 succession.

- M. NUZZO: INTRODUZIONE ALLE SCIENZE GIURIDICHE. NORME - SOGGETTI - ATTIVITÀ, 3ª ED., GIAPPICHELLI, 2009
- F. MACIOCE: L’OBBLIGAZIONE E IL CONTRATTO, 2ª ED., GIAPPICHELLI, 2007
A SCELTA DELLO STUDENTE: - L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, FAMIGLIA E SUCCESSIONI. LE FORME DI CIRCOLAZIONE DELLA RICCHEZZA FAMILIARE, 2ª ED., GIAPPICHELLI, 2009, CAPITOLI: I, II, III, IV (SOLO PARR. 1 E 3), VI, VII, IX, XI, XII, XIII
OPPURE
- A. BELLELLI, A.G. CIANCI, BENI E SITUAZIONI GIURIDICHE DI APPARTENENZA. TRA DIRITTI REALI E NEW PROPERTIES, GIAPPICHELLI, 2008

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

-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 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).

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.

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

Notes can be downloaded online from the course website

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 .

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

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.

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

Notes can be downloaded online from the course 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

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

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

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

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.

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 course is composed by modules. The first two modules include the following legal categories: sources of law; subjective juridical situations; physical and juridical persons; 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 succession.

- M. NUZZO: INTRODUZIONE ALLE SCIENZE GIURIDICHE. NORME - SOGGETTI - ATTIVITÀ, 3ª ED., GIAPPICHELLI, 2009
- F. MACIOCE: L’OBBLIGAZIONE E IL CONTRATTO, 2ª ED., GIAPPICHELLI, 2007
A SCELTA DELLO STUDENTE: - L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, FAMIGLIA E SUCCESSIONI. LE FORME DI CIRCOLAZIONE DELLA RICCHEZZA FAMILIARE, 2ª ED., GIAPPICHELLI, 2009, CAPITOLI: I, II, III, IV (SOLO PARR. 1 E 3), VI, VII, IX, XI, XII, XIII
OPPURE
- A. BELLELLI, A.G. CIANCI, BENI E SITUAZIONI GIURIDICHE DI APPARTENENZA. TRA DIRITTI REALI E NEW PROPERTIES, GIAPPICHELLI, 2008

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

-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 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).

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.

DALL’IMPOSTAZIONE CLASSICA A QUELLA NEOCLASSICA: INTERPRETAZIONE DEL CAMBIAMENTO DEL
PARADIGMA TEORICO DOMINANTE
1. SOVRAPPIÙ, DISTRIBUZIONE E VALORE NELL’IMPOSTAZIONE CLASSICA
SCHEMA GENERALE DELLA TEORIA CLASSICA DELLA DISTRIBUZIONE. QUESNAY, SMITH, RICARDO, MARX. LA MODERNA RIPRESA DELLA TEORIA CLASSICA: PIERO SRAFFA
2. L’ECONOMIA POLITICA DOPO RICARDO
I "SOCIALISTI RICARDIANI", I CRITICI DI RICARDO, I DISCEPOLI DI RICARDO. JOHN STUART MILL
3. NASCITA DEL MARGINALISMO
JEVONS E MENGER: L’UTILITÀ QUALE FONDAMENTO DEL VALORE DELLE MERCI. WALRAS: IL SISTEMA DI EQUILIBRIO ECONOMICO GENERALE; DIFFICOLTÀ CONNESSE ALLA TRATTAZIONE DEL CAPITALE.
4. ALFRED MARSHALL
ASPETTI SPECIFICI DELLA TEORIA DEL VALORE DI MARSHALL; PRETESA CONTINUITÀ CON LA TEORIA DI RICARDO.
5. DIFFUSIONE DEL MARGINALISMO E LINEE DI PENSIERO ALTERNATIVE (CENNO)SVILUPPO DELL’IMPOSTAZIONE MARGINALISTA TRA LA FINE DELL’800 E LA PRIMA PARTE DEL ‘900. DUE FONDAMENTALI PUNTI DI "ROTTURA" DELLA PREVALENZA DEL MARGINALISMO: KEYNES E SRAFFA.

APPROFONDIMENTI ED ESTENSIONI
6. NASCITA E OGGETTO DELL’ECONOMIA POLITICA
L’ECONOMIA POLITICA COME SCIENZA DEI FENOMENI ECONOMICI PROPRI DEL MODO DI PRODUZIONE CAPITALISTICO.
7. LA ‘MACROECONOMIA’ DI RICARDO
LIVELLO DEL PRODOTTO SOCIALE E LEGGE DI SAY; TEORIA QUANTITATIVA DELLA MONETA; DEBITO PUBBLICO E TASSAZIONE
8. MARX E L’ANALISI ECONOMICA DEL SUO TEMPO
RAGIONI DELLA LIMITATA INFLUENZA DI MARX SULLA TEORIA ECONOMICA DEL TEMPO.
9. CONCEZIONI POLITICO-SOCIALI DI WALRAS
EQUITÀ DISTRIBUTIVA E GIUSTIZIA SOCIALE. LA CRITICA DI WALRAS ALLA TEORIA DEL VALORE DI MARX.

DISPENSE A CURA DEL DOCENTE

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

Notes can be downloaded online from the course website

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 .

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

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.

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

Notes can be downloaded online from the course 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

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

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

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

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.

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 course is composed by modules. The first two modules include the following legal categories: sources of law; subjective juridical situations; physical and juridical persons; 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 succession.

- M. NUZZO: INTRODUZIONE ALLE SCIENZE GIURIDICHE. NORME - SOGGETTI - ATTIVITÀ, 3ª ED., GIAPPICHELLI, 2009
- F. MACIOCE: L’OBBLIGAZIONE E IL CONTRATTO, 2ª ED., GIAPPICHELLI, 2007
A SCELTA DELLO STUDENTE: - L. ROSSI CARLEO, E. BELLISARIO, V. CUFFARO, FAMIGLIA E SUCCESSIONI. LE FORME DI CIRCOLAZIONE DELLA RICCHEZZA FAMILIARE, 2ª ED., GIAPPICHELLI, 2009, CAPITOLI: I, II, III, IV (SOLO PARR. 1 E 3), VI, VII, IX, XI, XII, XIII
OPPURE
- A. BELLELLI, A.G. CIANCI, BENI E SITUAZIONI GIURIDICHE DI APPARTENENZA. TRA DIRITTI REALI E NEW PROPERTIES, GIAPPICHELLI, 2008

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

-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 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).

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.

GLI ARGOMENTI DEL CORSO SONO:
1. OBIETTIVI, CONTENUTI, UTILIZZI E UTILIZZATORI DELL’ANALISI FINANZIARIA
2. PRINCIPALI BASI-DATI ECONOMICO-FINANZIARIE (NAZIONALI E INTERNAZIONALI): OBIETTIVI, STRUTTURA, MODELLI LOGICI, TECNICHE DI ELABORAZIONE.
3. PERFORMANCE E RISCHIO DELL’IMPRESA:
A) METRICHE:
 CONTABILI (INDICI DI BILANCIO)
 VALUE-BASED (EVA, CFROI, SVA, EM, CVA)
B) DELLE METRICHE SARANNO ANALIZZATI:
 CRITERI DI MISURAZIONE
 CONTENUTI INFORMATIVI E DIAGNOSTICI
 MODELLI LOGICI/ANALITICI DI COLLEGAMENTO E SCOMPOSIZIONE
 TERMINI DI CONFRONTO PER ANALISI CROSS-SECTIONAL
 COERENZA CON VALUE CREATION E CON MISURE DI MERCATO
 DISTORSIONI NEI SISTEMI PREMIANTI E DI INCENTIVO MANAGERIALI
 PROBLEMATICHE APPLICATIVE E ESEMPI DI BIAS/MORAL HAZARD (CASO PARMALAT)
C) ANALISI/COMPARAZIONE DI SETTORI/IMPRESE SU DATI REALI (DA BASI DATI DISPONIBILI)
4. FABBISOGNO FINANZIARIO E SUE DETERMINANTI. ANALISI DELLA DINAMICA FINANZIARIA E RENDICONTI FINANZIARI: FLUSSI DI CAPITALE CIRCOLANTE NETTO (VARIE CONFIGURAZIONI) E DI CASSA
5. SOLVIBILITÀ FINANZIARIA, RISCHIO DI CREDITO E MODELLI DI RATING/SCORING
6. FATTIBILITÀ FINANZIARIA DELLE STRATEGIE
7. GESTIONE DEL CAPITALE CIRCOLANTE: A) GESTIONE DEL CREDITO/DEBITO DI FORNITURA; B) MODELLI DI GESTIONE DELLE SCORTE; C) MODELLI DI GESTIONE DELLA LIQUIDITÀ.

A) LIBRI
1. BERK J. – DE MARZO P., FINANZA AZIENDALE 2, PEARSON-ADDISON WESLEY, 2008, CAPITOLO 7
2. BRUNETTI G., CODA V., FAVOTTO F., ANALISI, PREVISIONI, SIMULAZIONI ECONOMICO-FINANZIARIE D’IMPRESA, ETAS LIBRI 1990, CAPP. 4-6-7-8
3. HORNGREN C.., FOSTER G., DATAR S.M., CONTABILITÀ PER LA DIREZIONE, ISEDI 1998, CAPITOLO 21
4. PAVARANI E., L’EQUILIBRIO FINANZIARIO, MCGRAW-HILL 2006, CAPITOLI 3 E 5
5. PAVARANI E., TAGLIAVINI G., PIANIFICAZIONE FINANZIARIA, MCGRAW-HILL 2006, CAPITOLI 5 E 11
6. VENANZI D., FINANCIAL PERFORMANCE MEASURES AND VALUE CREATION: THE STATE OF THE ART, SPRINGER 2012 (HTTP://WWW.SPRINGER.COM/BUSINESS+%26+MANAGEMENT/FINANCE/BOOK/978-88-470-2450-2)

B) ARTICOLI/DISPENSE
7. CLINTON B.D., CHEN S., “DO NEW PERFORMANCE MEASURES MEASURE UP?”, MANAGEMENT ACCOUNTING, OCTOBER 1998 (COPIA CARTACEA DISPONIBILE IN BIBLIOTECA)
8. MORRESI O., I MODELLI DI GESTIONE DELLA LIQUIDITÀ AZIENDALE – DISPENSA, 2010 (DOWNLOAD DAL SITO WEB DEL CORSO)
9. SIRONI A., “I RATING INTERNI E I MODELLI PER LA GESTIONE DEL RISCHIO DI CREDITO”, IN BANCA D’ITALIA, MODELLI PER LA GESTIONE DEL RISCHIO DI CREDITO – I RATINGS INTERNI, TEMATICHE ISTITUZIONALI, BANCA D’ITALIA, 2000 (DOWNLOAD DAL SITO WEB HTTP://WWW.BANCADITALIA.IT/PUBBLICAZIONI/TEMIST/MODELLI)

C) MATERIALI APPLICATIVI E DI COMPLETAMENTO
DATI, CASI, SLIDES, MATERIALI DEI SEMINARI, ECC., RESI DISPONIBILI DAL DOCENTE SUL SITO WEB DEL CORSO (ACCESSIBILI PER GLI STUDENTI DEL CORSO – FREQUENTANTI E NO – TRAMITE PASSWORD; LE PASSWORD DI ACCESSO SARANNO COMUNICATE DURANTE LE LEZIONI. GLI STUDENTI NON FREQUENTANTI POSSONO RICHIEDERLE AL DOCENTE VIA EMAIL).

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

Notes can be downloaded online from the course website

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 .

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

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.

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

Notes can be downloaded online from the course 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

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

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

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.

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

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

Notes can be downloaded online from the course website

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 .

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

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.

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

Notes can be downloaded online from the course 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

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

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

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

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.

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.