Mathematical Methods for Economics and Finance A.Y. 2016-2017


22) Results of the written exam of 05/06/2017

Risultati esami INGLESE 5_6_2017AV

and solutions


21) Results of the written exam of 06/02/2017



20) Solutions of the written exam of 06/02/2017



19) Results of the written exam of 19/12/2016

Risultati esami 19-12-2016ENGfinal


18) Solutions of the written exam of 19/12/2016



(17) About the final program:

The exercises on symmetric matrices and their sign are in the second part. On the other hand the exercises on first integrals of ODE systems (e.g. predator-prey) are in the first part.


(16) Office hours:

Antonio Veredice Monday 12  h.15

Elena Bandini Tuesday 13 h.11.30

Vanessa Raso Thursday 15 h. 11


(15) Additional TA sessions (EB) next two Thursdays, November 24 and December 1, h 16-18, Room 210. Please come!

(14) No lectures in the week from 31/10 till 5/11.

(13) Additional TA session (AV) next Thursday, October 27, h 16-18. Please participate!

(12) Tomorrow, Tuesday 25 October, bring the slides on symmetric matrices (from p. 125 to p. 142 of the slides of weeks 1-5) and the slides of weeks 7-8.

(11) Next Wednesday, October 26, Office Hours will not be in the morning but in the afternoon from 15.15 to 16.30, in my office at floor 5.

(10) Now you find the notes on nonlinear dynamical systems. Please bring them at the lectures this week.

(9) Tomorrow, Friday 14 October, MATLAB sessions start. The time table is the following


Fri. 14 oct. h   9-11
Wed. 19 oct. h 18-20
Fri. 21 oct. h   9-11
Fri. 28 oct. h   9-11

Fri. 04 nov. h  9-11
Fri. 11 nov. h  9-11
(8) You now find the revised slides. Today, Tuesday 11 October, and in the next days, bring from page 105 to page 142.


(7) Now you find new slides for Thursday, September 29.


(6) Now you find further notes for the lecture of tomorrow Thursday September 22.


(5) In the point (A) below you find a new communication about academic gym and tutoring.


(4) The slides of the first week have been slightly modified with respect to the ones given before the lectures.


(3) Now you find the slides of the first week in point F1.


(2) Here below you find the slides and the tutorial of the TA session of today, Monday, September 12, 2016.


(1) The TA session of Monday, September 19, 2016 is canceled due to exceptional events (“Festa della Matricola”). Hence there will be a TA session (by dr. Veredice) Thursday, September 22, 15-17. Everybody is warmly invited!




In this page you can find, beyond all up-to-date news about the course, the following material.

(A) Teachers and time table

(B) Office hours

(C) Textbooks

(D) Preliminary program and effective one

(E) Exam rules

(F) The material for the first part of the course

(G) The material for the second part of the course

(H) The material for the Matlab course


(A) Teachers and time table.

Teacher: prof. Fausto Gozzi; Assistants: dr. Antonio Veredice and dr. Elena Bandini; Matlab lectures: dr Roeland De Koek.

The course starts Monday, September 12 and ends Friday, December 2 with the following schedule:

Monday 18.15 – 20, Room A210, EXERCISES;

Tuesday 17.45 – 19.45 Room AT02, LECTURE;

Wednesday 12 – 13.30 Room A202, LECTURE;

Thursday 8.30 – 10, Room A406, LECTURE;

The course contemplate also MATLAB lectures on Fridays (but not all Fridays) from 9.30 to 11.30, room INFO A306. Such lectures will be made only from October 7 on.

Students which have problems in following the course may take advantage of the so-called “academic gym”

and of the tutoring

Indeed, in the “academic gym”, 1 hour per week (probably on Mondays evening from September 26 on, but see the time table on the site) will be devoted to exercises related to this course.

Moreover, within the tutoring it will be possible ask for clarifications on the prerequisites of the course which are not treated at the lectures and at the TA sessions.



(B) Office hours.

Fausto Gozzi: Wednesday 10.30-11.30 till December 3 (Office at fifth floor). Moreover after the lectures or by appointment (to agree personally or by email at fgozzi at luiss dot it).

Antonio Veredice and Elena Bandini: after the lectures, or by appointment (to agree personally or by email at a_veredice at yahoo dot it or ebandini at luiss dot it).

Dr. Roeland De Koek: after the lectures, or by appointment (to agree personally or by email).


(C) Textbooks

Main textbooks
Authors: Simon, Blume,
Title: Mathematics for economists
Editor: Norton

Autori: C. Pocci, G. Rotundo, R. de Kok
MATLAB for economics ans financial applications.
Maggioli Editore, 2016, forthcoming.


Other textbooks

Authors: Lawrence E. Spence, Arnold J. Insel, Stephen H. Friedberg Title: Elementary Linear Algebra
Editor: Pearson Education

Author: James Stewart
Title: Calculus (International Metric Edition)
Editor: Brooks/Cole; International Edition

Author: Michael C. Delfour
Title: Introduction to Optimization and Differential Calculus
Editor: SIAM


(D) Preliminary program and effective one

Here is the line to the preliminary program published on the Luiss site:

Here is the program effectively taught with reference to the textbook and other didactic material (updated almost every week).









It is fundamental to recall that the program taught or summarized at the precourse will not be repeated during the course. Such program will be part of the basic knowledge needed to understand the course. People who did not follow the precourse is invited to study carefully (solving the exercises) the material found at the precourse site.


(E) Exams rules

The exam  is written and oral.

The part of the exam concerning MATLAB is not compulsory and is only oral.

There will be no mid term exam.

Written test: the time available is 3 hours. the written test is divided in 2 parts (approximately 20 points each). The test is sufficient if in each part the grade is at least 7.5 and if the sum is at least 18.

If the sum is at least 18 (with each part at least 7.5) then, at the time of the oral exam the student can choose one of the following two options: either to register without the oral exam or to make the oral exam. If the student decides to register then she/he can register the minimum between its grade and 25. If she/he wants to get more than 25 he must do the oral exam. It is possible that the final grade after the oral exam be lower than the grade of the written test.

At the written test the student can decide to do only 1 part. In such a case she/he will have 1.5 hours to do it. As a consequence, a student may decide to do the two parts in different dates.

There are 4 standard exam dates every year (1 in December, 1 in January-February, 1 in June-July, 1 in September) and one restricted exam date (in October). The time available is 3 hours: 1.5 for each part (i.e. after 1.5 hours the students must deliver the first part and, after that, the text of the second part is given).

The written test can be repeated at each available date but every delivery cancels the previous grades. The oral exam (or the registration) can be done at every available date (but in the same academic year), not necessarily the same of the written exam.

The written test contains questions concerning both theory and exercises and it is completely “closed-book”: the students can only bring brains and pens (white sheets will be provided by the teachers). Hence no books, no sheets, no electronic devices like pocket calculators, cell phones, tablets, electronic clocks, pens or glasses. People using any of such devices or violating rules will be carefully prosecuted.

The oral exam consists in various questions on the whole course, including exercises. The Matlab part of the exam can be made only during the days formally devoted to the oral exam. It is not compulsory and the grade is binary (Pass or Fail). Students who get Pass will earn 1 point on the final grade but only if the final grade of the oral exam is greater or equal to 26 (if not the student will not earn any point but will still have the satisfaction of learning a useful thing).


(F) The material for the first part of the course

(F1) Slides









Notes on nonlinear dynamical systems



(F2) Tutorials








(F3) TA sessions






(F4) More material on the first part

– seminar of Gianna Del Corso on ranking algorithm of search engines


– Notes on phase portraits of dynamical systems




(G) The material for the second part of the course

(G1) Slides


Updated slides weeks 7-8. For week 8 bring from p. 57 till p. 92






(G2) Tutorials












(G3) TA Sessions

TA session Topology

TA session Differential calculus

TA session Implicit Function1

TA session Unconstrained Optimization

TA session Constrained Optimization_1

TA session Constrained Optimization_2


(H) The material for the Matlab course









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