Mathematics for economics

A.Y. 2020/2021
Overall hours
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.
Course syllabus and organization

Single session

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
Educational website(s)
By appointment