This learning unit is not open to incoming exchange students!
Teacher(s)
Language
English
Prerequisites
Basic background in mathematics
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.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
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. |
Content
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
0. Idealized statistics versus constructive analysis
1. Databases
2. Operations on a database
3. Conditional expectation
4. Introduction to induction
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
0. Idealized statistics versus constructive analysis
1. Databases
2. Operations on a database
3. Conditional expectation
4. Introduction to induction
Teaching methods
Methods: Lectures and home works
Evaluation methods
STATISTICS is evaluated continuously, 3 to 4 times during the semester.
MATHEMATICS : written exam during session
MATHEMATICS : written exam during session
Bibliography
STATISTICS :
Errett Bishop (1967). Foundations of Constructive Analysis. New York: McGraw-Hill.
Andrei N. Kolmogoroff (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Heft 3. Berlin: Julius Springer.
Errett Bishop (1967). Foundations of Constructive Analysis. New York: McGraw-Hill.
Andrei N. Kolmogoroff (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Heft 3. Berlin: Julius Springer.
Teaching materials
- STATISTICS : Lecture notes by S. Van Bellegem
Faculty or entity
