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MATH-S400

Mathematics and economic modelling

academic year
2024-2025
2025-2026

Course teacher(s)

Thomas DEMUYNCK (Coordinator), Bram DE ROCK and Luca Paolo MERLINO

ECTS credits

5

Language(s) of instruction

english

Course content

The course covers the following topics:

  • Basic introduction into logic and proofs.
  • What are the different proof techniques, how and when to apply them.
  • Introduction into real analysis; supremum and infimum, sequences, limits, Cauchy sequences, subsequences, open, closed and compact sets 
  • Extreme value theorem & intermediate value theorem,
  • Correspondences, upper and lower hemi-continuity
  • Berge's maximum theorem.
  • Fixed point theorems:
    • Contraction mappings,
    • Sperner's lemma and Brouwer's fixed point theorem 
    • Existence of general equilibrium in an exchange economy, 
    • Kakutani's fixed point theorem
    • Existence of Nash equilibrium.

Objectives (and/or specific learning outcomes)

The main goal of this course are:

  • Provide the student with some necessary mathematical skills while learning about important results in economic theory.
  • Improve the technical/mathematical skills and to understand how proofs are structured/organized
  • Make sure students understand verify and construct proofs. 

Prerequisites and Corequisites

Required and Corequired knowledge and skills

The course is self contained but has a rapid pace. It is advised that students have some prior knowledge in terms of mathematics..

Teaching methods and learning activities

  • Lectures
  • Podcasts of the main proofs are available on the website
  • Exercise sessions
  • Q&A sessions at the end of the semester
  • Assignments.

Course notes

  • Syllabus
  • Université virtuelle

Contribution to the teaching profile

Mastering the theoretical tools used in economics such that the student can use them for his/her own research. Knowledge of the essential mathematical tools used in contemporary economic research. Select and apply the theoretical tools of economics to specific problems in order to provide relevant solutions. Be able to understand and follow a proof.
The learning objectives relevant for the MATH-S400 course are:

  • LO1.2: Identify and apply the relevant analytical tools and scientific knowledge to analyse an economic problem in depth
  • LO2.1: Adopt a scientific approach to data collection, research and analysis and communicate results with clear, structured and sophisticated arguments

Other information

Contacts

Thomas Demuynck (thomas.demuynck@ulb.be). Office R42.6.220

Campus

Solbosch

Evaluation

Method(s) of evaluation

  • written examination
  • Other

written examination

  • Open question with developed answer

Other

The exam is a written open book exam. Various assignments (usually 4) are given throughout the semester. 

Mark calculation method (including weighting of intermediary marks)

90% (written exam); 10% (exercises; provisionary).

Language(s) of evaluation

  • english

Programmes