KECD 2240 - INTRODUCTION TO MATHEMATICS FOR ECONOMICS

Abstract :

The aim of this course is to :

• make students more comfortable with basic mathematical concepts and methods that are commonly used in contemporary economic research
• allow them to take the fundamental courses (microeconomics, macroeconomics, and econometrics) of the Research Master’s in Economics with greater confidence

Students learn how to apply the mathematical concepts by manipulating concrete examples and economic models. This course adapts to the level/expectations of students.

Week 1 Real Analysis; Optimisation; Integral Calculus (by Aurélien) :

Preliminaries of Real Analysis: sets, relations, real numbers, real sequences, real functions

Introduction to Real Analysis: open and closed sets, convergent sequences, compactness, con-tinuity, convexity, multivariate analysis, applications;

Optimization: Unconstrained optimization, constrained optimization, applications to economics

Integral Calculus: Definite and indefinite integrals, applications

Week 2 Matrices, Linear Algebra, and their Applications (by Daniel) :

Basic Matrix Calculus:

• Solving Systems of Linear Equations using Elementary Row Operations

Linear Algebra and Square Matrices:

• Introduction to Linear Maps and Vector Spaces: basis, linear independence
• Matrix Inverse, Determinant, Rank, Eigenvalues & Eigenvectors, Definiteness
• Application to Optimization: gradient, Jacobian, Hessian
• Application to Ordinary Least Squares