- Docente: Paolo Negrini
- Credits: 9
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 20, 2023 to May 22, 2023
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 limits, continuity and derivability of functions of one real variable. The birth of differential and integral calculus: historical information. Different methods for a rigorous construction of elementary functions. First elements of the calculation of variations: the brachistochronous curve, the catenary, the isoperimetric problem. Elementary notions on test functions and on distributions and applications. The Dirac delta distribution. Derivatives of distributions. Convergence in the space of distributions. Approximations of delta with function type distributions. Pseudo-functions: 1 / x ^ n distributions.
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 e altri: 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.
W.Rudin: Analisi reale e complessa, Bollati Boringhieri. Torino 1978
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