MATHEMATICAL METHODS

Single discipline educational activity

Course Sheet

Academic Year of enrolment:

2018/2019

Type of Course:

Characterising

Optional/Mandatory:

Compulsory

Degree:

Master's Degree Programme in ECONOMICS

Disciplinary Sector:

MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Credits:

Programme Year:

Professor and Collaborators:

RUSSU Paolo

Hours of classroom activity:

Prerequisites:

General and basic concepts of calculus.

AF code:

40002781

Assessment Methods

Verification of learning:

The learning test consists in a written exam to solve in 2 hours. This exam is composed by 3 execises. The first execise concerns the topics described in modules 1 and 2. The second exercise deals with topics described in module 3, finally the third exercise concern the topics of the module 4. During the exam it is not permitted to use the calculator, books and notes. It is attributed on average 10 points to each exercise. The students pass the exam with a score not lower than 18 points.

Teaching period

First semester

Objectives

The course provides the advanced notions of mathematical analysis useful for the analysis and understanding, through mathematical models, of economic phenomena.
Teaching Unit 1-2
1) Knowledge and Understanding: knowing how to perform the oprations between matrices, know how to use the properties of a symmetric matrix, know how to determine the "sign" of a quadratic form, know how to calculate maximum and minimum of a function of several variables unconstrained.
2) Applying Knowledge and Understanding: knowing how to apply to simple economic problems.
3) making judgements: ability to analyze and interpret the numerical results obtained in relation to the specific application or to the theorems.
4) Learning skills: ability to extend the concepts seen in 2 dimensions to n dimensions.

Teaching Unit 3
1)Knowledge and Understanding: nowing Khun Tucher's theorems for constrained optimization.
2)Applying Knowledge and Understanding: being able to apply applying the theorems to the resolution of non-linear problems.
3) making judgements: ability to analyze and interpret the numerical results obtained in relation to the specific application or to the theorems.
4) Learning skills: ability to extend the theorems from the 2-dimensional space to n dimensions.
Teaching Unit 4
1)Knowledge and Understanding: knowing how to identify a problem of PL, know the steps necessary to formulate a mathematical model of PL.
2)Applying Knowledge and Understanding: being able to apply the necessary steps for the formulation of a PL model to real problems such as: production, maketing, assignment problems, once assigned the text of the problem.
3) making judgements: ability to analyze and interpret the numerical results obtained in relation to the specific application or to the theorems.
4) Learning skills: ability to model some real problems.
For all Teaching Units
Communication skills: although the teaching does not foresee specific activities aimed at developing communication skills, the student will be able to operate within heterogeneous working groups.

Contents

T.U. 1. Elements of linear algebra.
T.U. 2. Unconstrained Optimum of a Function of Many Variables
2.1 First Order Conditions
2.2 Second Order Conditions (Hessian)
T.U. 3. Constrained Optimum of a Function of Many Variables
The Lagrangean Multiplier Method and Khun Tucker Theorem
3.1 First Order Conditions
3.2 Second Order Conditions (Bordered Hessian)
T.U. 4. Elements of Linear Programming
4.1 Optimal solutions
4.2 Applications

Recommended Bibliography

Allevi, Bertocchi, “Manuale Modulare Metodi Matematici-Modulo 6”, Giappichelli Editore.
Lecture Notes provided by the teacher and downloadable from the teacher's web site on Moodle

Teaching Methods

Face to face lessons are supported by lecture notes, which are made downloadable from the teacher's web site on Moodle.
Use of computer software (open source) in the classroom, in particular with reference to the drawing of the graphs and to the problems of optimizing the functions with several variables (Wolfram Alpha).

Contacts/More Information

Office hours: during the semester of the course,
the teacher will meet students to help them to solve problems and to give them all the information they need after lessons concerns the solution of exercises; in the semester where no lessons will be held, the office hours will be announced.
Availability to provide a tutoring service also in English for Erasmus students or in mobility and availability of teaching materials and bibliographic references.
Further information about office hours, please consult
www.edisea.uniss.it
Contact MAIL russu@uniss.it Tel. 079213016

MATHEMATICAL METHODS

Course year: 1

Course year: 2

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MATHEMATICAL METHODS