UCL - Mathematics and Statistics for Economics

[ECON2500]

[30h] 5 credits

Teacher(s): Luc Bauwens, Julio Davila Muro

Language: English

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

The purpose is that students learn the most important mathematical and statistical tools needed for advanced courses in macroeconomics, microeconomics and econometrics. The course serves mostly to refresh students' knowledge in certain topics, and to ensure that all students taking the advanced courses have a common mathe-matical and statistical level.

Main themes

For the mathematics part, the themes of matrix algebra, functions, optimization, and difference/differential equations. For the statistics part: multivariate distributions and related concepts.
The two parts are linked in particular by matrix algebra.

Content and teaching methods

Mathematics :
Matrix algebra (inverse, rank, derivatives, eigenvalues, diagonalization and factorization, quadratic forms). Met-ric and topological spaces, vector spaces. Real functions on Rn (continuity, concavity, differentiability, Taylor expansion, mean value theorem, implicit function theorem). Static optimization (constrained and uncon-strained). Difference and differential equations (steady states, stability).

Statistics:
Multivariate distributions: joint, marginal and conditional distributions, (conditional) moments (variance-covariance matrices), independence in probability and linear independence. Law of iterated expectations. Transformation of random vectors. Multivariate normal distribution.
Quadratic forms in normal vectors and related distributions (Student, chi-squared, Fisher)

Methods:
Lectures and home works

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Basic background in mathematics.

Written exam. Evaluation of the home works enters in the final note.