66741 - Advanced Operative Research and Analysis Elements

Learning outcomes

After completing this course, students: - have advanced knowledge about the foundations of mathematical analysis in their classic and modern development - have knowledge about the fundamentals of operational research, in their modern development - is able to independently conduct a critical study of founding principles of mathematical analysis, classical and modern, and operational research.

Course contents

Insights on continuity and differentiability of functions of one variable.  Exercises and insights on elementary mathematical analysis topics (definition of limit, examples and applications of the main theorems on the functions of a variable).
The birth of differential and integral calculus: historical information.
Various methods for the construction of elementary functions.
Elements of the calculus of variations and some classical examples.
Developments of the concepts of function, limit, derivative.
A short survey on the spaces of test functions and distributions.

Application of differential methods, in particular the Taylor formula, for the local study of plane curves defined by implicit equations. Examples of some classic curves. 

Elements of financial mathematics: simple and composed capitalization laws; Interest, Upright, Current Value. Annuities. Amortization of loans.  Decision theory. Decisions under certainty and decisions under uncertainty.
The criterion of mathematical expectation; strengths and weaknesses. The St. Petersburg paradox and its variants.
The criterion of utility. Examples about some simple problems in finance.
Linear programming. The simplex algorithm.

 

Readings/Bibliography

L.Daboni et al.: Ricerca Operativa.  Zanichelli, Bologna 1985;

P.Agnoli-F.Piccolo: Probabilità e scelte razionali. Una introduzione alla teoria delle decisioni.
Armando, Roma 2008;

 

Costantini, Giorgi, Herzel, Monari, Scardovi. (1994). Metodi statistici per le scienze economiche e sociali. Bologna: Monduzzi.

lecture notes by the teacher.

Teaching methods

frontal lessons

Assessment methods

The examination consists of a written test followed by an individual interview; the candidate exposes a topic of his choice among those covered in the course; he must then answer a few questions, or solve simple exercises on various topics of the course

Office hours

See the website of Paolo Negrini