Mathematics for economics

A.Y. 2017/2018
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
Course syllabus
System of Linear equations: examples. General form, Matrix
and Vector representation, basic techniques for solving linear
system. Rank of matrix and Rouché-Capelli Theorem. Matrix
algebra: basic operations, scalar and matrix multiplication.
Transpose Matrix. Square Matrix. Determinant. Inverse Matrix.
Special kind of matrices. Quadratic Form. Eigenvalues and

Real vector spaces. Linear combination, dependence and linear
independence. Basis and dimension in R^n. Algebra of vectors,
inner product and Norm. Linear Transformation and Linear
subspaces. Basic Calculus functions of one variable. Functions
of several variables: graphs of functions of Two Variables, Level
Curves. Special Kinds of functions: linear functions, quadratic
functions. Domain, continuity and partial derivatives.
Differentiability. Directional
derivatives. Gradients. Second order Derivatives. Hessian
matrix. Concave and convex functions.

Optimization problems: Definition of local and global
minimum/maximum. First and Second order conditions for
unconstrained problems. Constrained optimization: equality
constraints and Lagrange Multipliers. Inequality constraints and
Kuhn¿Tucker conditions. Linear programming (Basic)
Teaching methods
Readings: Simon, C.P. and Blume, L.E. (1994): ¿Mathematics for
Economists¿, Norton, W. W. & Company, Inc.
MAT/06 - PROBABILITY AND STATISTICS - University credits: 6
Practicals: 16 hours
Lessons: 40 hours
Professor: Naldi Giovanni