Mathematics

Course goals

Learning objectives
At the end of the course, the student:

• has strengthened his or her fluency in mathematics;
• uses mathematical techniques to solve a range of problems and to understand their application to various economic models.

Content

Students who are not enrolled in the research master Multidisciplinary Economics should contact the course coordinator for enrollment in this course.

The course aims at developing mathematical skills to understand and solve problems by using advanced mathematical methods.
 
The following topics will be covered:

• Static Optimisation: derivatives in Rn, directional derivatives, implicit function theorem, Taylor expansion, unconstrained optimisation in Rn, optimisation under equality and inequality constraints.
• Multiple integrals
• Complex numbers
• Dynamical systems: first order differential and difference equations, higher order differential and difference equations, nonlinear differential and difference equations. Systems of differential and difference equations.

Students are expected to be familiar with the following topics:

• Limits
• Inverse functions
• Logarithmic and exponential functions
• Basic linear algebra (vectors and matrices, matrix addition, multiplication, trace, determinant, inverse, eigenvalues and eigenvectors, diagonalisation)
• Integrals (definite and indefinite integrals, integrals by parts and substitution)
• Optimisation in R

Intended Learning Outcomes
The graduate:
3a)    can think in a logical way
3b)    can summarize and identify common themes in the literature on a specific topic, and keep track of recent developments
3c)    can critically appraise literature

In case online access is required for this course and you are not in the position to buy the access code, you are advised to contact the course coordinator for an alternative solution. Please note that access codes are not re-usable meaning that codes from second hand books do not work, as well as access codes from books with a different ISBN. Separate or spare codes are usually not available.