Graduate Program

__Credit hours__

In-class work per week |
Practice per week |
Credits |
Duration |
Total |

6 |
2 |
8 |
10 weeks |
120 hours |

__Instructor__

Adriano Júlio de Barros Vicente de Azevedo Filho

Mirian Rumenos Piedade Bacchi

Vitor Augusto Ozaki

__Objective__

The objective is to introduce mathematical knowledge within the context of quantitative and

computational methods, focusing on their applications in theories and methodologies used in studies in

economics. Specifically, the course include training the student in understanding, modeling and solving

problems involving mathematics and mathematical models in order to improve their ability to analyze,

model and solve problems within the field of economics.

__Content__

1. Mathematical models: fundamental ideas and applications. 2. Review of fundamentals and

applications: set theory, functions, polynomials, equations, series, limits, derivatives and integrals. 3.

Equations and systems of linear and non-linear equations: theory, solution methods, computational

implementation and applications. 4. Linear and matrix algebra: fundamentals, computational

implementation and applications. 5. Differential and integral calculus in the multivariate context:

fundamentals and applications. 6. Linear and non-linear optimization: introduction to theory, algebraic

and computational solutions, and applications. 7. Differential equations and difference equations:

introduction and applications. 8. Optimal control theory and dynamic programming: introduction and

applications.

__Bibliography__

Amemiya, T. 1994. Introduction to Statistics and Econometrics. Harvard University Press, Cambridge.

Azevedo-Filho, A. 2010. Principios de Inferência Dedutiva e Indutiva: Noções de Lógica e Métodos de

Prova. CreateSpace (EUA). Azevedo-Filho, A. 2011. Introdução à Estatística Matemática Aplicada - Vol I:

Fundamentos. CreateSpace (EUA). Azevedo-Filho, A. 2011. Introdução à Estatistica Matemática Aplicada

- Vol II: Distribuições Paramétricas e Simulação. CreateSpace (EUA). Azevedo-Filho, A. 2007.

Probabilidades III - Distribuições Paramétricas Discretas e Contínuas. USP/DEAS - Série Didática, No. D-

133, 150p, Berger, J. 1993. Statistical Decision Theory and Decision Analysis, 2nd Edition, Springer,

617p, Berger, J. 2003. Could Fisher, Jeffreys and Neyman have agreed on testing? Statistical Science,

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Wesley, 702p. DeGroot, M. 1986. Probability and Statistics. Addison-Wesley. Drake, A. 1967.

Fundamentals of Applied Probabilistic Analysis. McGraw-Hill, New York. Greene, W. H. 2007.

Econometric Analysis. 6th Edition, Prentice Hall, Englewood Cliffs. Hoffmann, R. 2006. Estatística para

Economistas. 4ª. Edição, Editora Thomson Learning, São Paulo. Hoffmann, R. e Vieira, S. 1977. Análise

de Regressão: uma Introdução à Econometria. Hucitec-Edusp Hubbard, R. e Amstrong, J. 2006. Why we

don't really know what statistical significance means: Implications for educators. Journal of Marketing

Education, Volume 28, no. 2, 2006, Pages 114-120. Intriligator, Bodkin e Hsiao 1996. Econometric

Models, Techniques and Applications. 2nd Edition, Prentice-Hall. Mood, A., Graybill, F. A and Boes, D.

1989. Introduction to the Theory of Statistics. McGraw-Hill, New York. O'Haggan, A. e Luce, B. 2003. A

Primer on Bayesian Statistics. Centre for Bayesian Statistics in Health Economics, MEDTAP International,

2003. Spanos 1999. Statistical Foundations for Econometric Modelling with Observational Data.

Cambridge University Press.