Corso di studio in Economia

The course of Mathematics for Economics I gives the basic mathematical techniques commonly used in economic applications. In particular,  the fundamental concepts of mathematical analysis are introduced, both for functions of one variable and for functions of several variables. The objective of the course is to learn to reason in an analytical and rigorous way in the decision problems. We will discuss how to solve an optimization problem in its simplest formulations. The emphasis will be given to the economic applications of the concepts introduced.

At the end of the course, the student is expected to be capable of:

- knowing the techniques and the basic mathematical tools commonly used in the solution of problems of economic nature;

- using such techniques and tools to formalize and solve problems;

- being able to communicate the results obtained using a clear and appropriate mathematical notation and language.

Students affected by Specific Learning Disorders (SLD) or disability are invited to read carefully the supporting tools and facilities made available by the University of Turin (SLD: https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld Disability: https://en.unito.it/services/students-special-needs/students-disabilities), and, in particular, the procedures to follow in order to receive support for the exams (SLD: https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld/support-students-sld-taking Disability: https://en.unito.it/services/students-special-needs/students-disabilities/support-students-disability-taking-exams). 

- Review of basic concepts. Set operations. Natural numbers, integer relative numbers, rational numbers, real numbers.

- Vector spaces and subspaces. Operations with vectors and matrices.

- Topology in R and in Rn: distance, norm, spheric neighbourhoods, open and closed sets.

- Functions of real variable and their properties, sequences and numerical series. Functions of several variables.

- Notion of limit and techniques of calculation, continuity and discontinuity in R and in Rn.

- Differential calculus and fundamental theorems in R and in Rn.

- Unconstrained optimization in R and in Rn.

- Integral calculus. Riemann integral and indefinite integral, fundamental theorems. Integration methods.

The course is organized in 96 hours of formal in‐class lectures, of 3 hours each according to the academic calendar. The attendance of lectures is not compulsory but is strongly recommended, and the final exam will be the same for students who attend and for students who do not attend the lectures.

The course grade is determined solely on the basis of a written examination. The examination (2 hours and 15 minutes) tests the student's ability to do the following:

1) present briefly the main concepts and results developed in the course (also through proofs);

2) use these results to solve exercises of numerical nature.

This is accomplished requiring the answer to:

- 10 multiple-choice questions, each of which requires the solution of a numerical exercise delivered through the Moodle platform (each exercise has a value of 1/30, and to pass this part the correct answer to at least 6 questions is required);

- 4 open-answer questions, of theoretical nature,  that require to illustrate one or more concpets, eventually also through proofs (maximum grade: 22/30).

The total mark of the exam is given by the sum of the grades of the 2 parts.

Each week a 3-hour session is devoted to the solution of exercises that apply in practice the theoretical concepts presented in the course. 

The course material is available on the Moodle page of the course.

The teacher is available, upon appointment, for student reception in presence or on-line, through the Webex platform.

Students affected by Specific Learning Disorders (SLD) or disability are invited to read carefully the supporting tools and facilities made available by the University of Turin (SLD: https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld Disability: https://en.unito.it/services/students-special-needs/students-disabilities), and, in particular, the procedures to follow in order to receive support for the exams (SLD: https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld/support-students-sld-taking Disability: https://en.unito.it/services/students-special-needs/students-disabilities/support-students-disability-taking-exams).