Mathematics for Economics | Università degli Studi di Milano Statale

A.Y. 2020/2021

Max ECTS

Overall hours

SSD

MAT/06

Language

English

Included in the following degree programmes

Environmental and Food Economics (Classe LM-76)-Enrolled from 2014/15 Academic Year

Learning objectives

The aim of the course is to provide basic mathematical methods for solving a wide range of applications in economics.
Main topics of the course are: Linear Algebra, Functions of Several Variables and Optimization Problems.

Expected learning outcomes

Basic mathematical methods and tools required to read and understand contemporary literature and modelling in economics.

Lesson period: First semester

Lessons timetable

Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi

Exams calendar

Single course

This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.

Search a single course

Course syllabus and organization

Single session

Responsible

Benfenati Alessandro

Lesson period

First semester

Lectures will be held on MS Teams both in classroom (respecting social distancing rules, by reserving seats by the employment of the UNIMI app) and in streaming, and they can be followed synchronously.

Lectures will be recorded and uploade on the Ariel website, in order to allow non present students to attend them at a later time. The teacher will use a virtual whiteboard for the lecture, together with slides and other softwares to ease the comprehension.

The exam will be a written test: MS Teams or an analogous software will be used for surveillance.

Course syllabus

Linear systems: matrix representation. Rank of a matrix. Linear independency. Inverse of a matrix. Gaussian elimination method (linear system solution, determinant and inverse matrix computation). Symmetric matrices. Eigenvalues and eigenvectors. Norm of a vector. Basis and dimension in R^n. Geometry of the 3D space.
Multivariable functions. Special case: graphs of functions of two variables. Level curves. Quadratic forms. Continuity and differentiability of multivariable functions. Partial derivatives, gradient and Hessian matrix. Two variable functions: tangent plane and gradient vector. Convex and concave functions. Optimization problems: first and second orderd conditions for unconstrained problems. Constrained optimization: equality constraints and method of the Lagrangian multipliers. Constrained optimization: inequality constraints and Karush-Khun-Tucker conditions. Linear programming (base concepts).

Prerequisites for admission

Numerical sets. Intervals of the real line. Monomials, polynomials, power function with rational exponent, power function with negative exponent. Elementary functions: sine, cosine, exponential functions, logarithms, natural logarithms. Functions composition. Real functions and their properties. Plot of real functions. Limits of real functions. Continuity and differentiability. Derivatives of elementary functions. Maxima and minima of real functions. Linear Algebra: vector, matrices, vector operations. Scalar product, matrix-vector multiplication, determinant of a matrix. Solution of 2x2 and 3x3 linear systems. Geometry: circumference, ellipse, parabola, hyperbola.

Teaching methods

Lecture-style instruction, integrated with slides created by the teacher. Usage of multimedia (video) and advanced software for improving the learning experience. Use of theoretical and real--life examples to show how the topics addressed in class can be directly applied in an economic framework.

Teaching Resources

K. Sydsæter, P. Hammond with A. StrØm; Essential Mathematics for Economic Analysis; Pearson.
R. A. Adams, C. Essex; Calculus: a complete course; Pearson
Teacher's notes.

Assessment methods and Criteria

The exam consists of a written test.
The test consists of theoretical questions (both open and mutiple choice questions) aimed to verify the comprehension of the topics studied in class. The test includes also exercises devoted to check the ability of applying independently the methodologies studied in class. The duration of the test depends on the number and on the structure of the questions, but it will not exceed 3 hours. An oral test is mandatory for students that achieve an assessment between 15 and 17 (endpoints included) at the written test.
Results will be communicated via personal e-mail and on the UNIMIA web portal.

MAT/06 - PROBABILITY AND STATISTICS - University credits: 6

Practicals: 16 hours
Lessons: 40 hours

Professor: Benfenati Alessandro

Professor(s)

Benfenati Alessandro

Web site

Reception:

By appointment

We use a selection of our own and third-party cookies on the pages of this website: Essential cookies, which are required in order to use the website; functional cookies, which provide better easy of use when using the website; performance cookies, which we use to generate aggregated data on website use and statistics; and marketing cookies, which are used to display relevant content and advertising. If you choose "ACCEPT ALL", you consent to the use of all cookies. You can accept and reject individual cookie types and revoke your consent for the future at any time at "Settings".