Advanced Mathematics

Course goals

Learning objectives
At the end of this course, students are able to:

• use mathematical tools correctly;
• apply mathematical techniques to solve a range of different economic problems;
• understand why mathematical tools work;
• understand mathematical proofs and be able to prove simple results

Content

Mathematics is an important tool for economics. Most of the economic theories are formalised using mathematical models. As a result, knowledge of mathematical techniques that are often used in economics is a prerequisite for reading and understanding many of the papers published in economic journals.

The course builds on the knowledge acquired in the first-year course Mathematics for economists. This course explores the following topics: linear algebra (vectors and matrices), functions, differentiation, integration (integrals by substitution, by parts, improper integrals, multiple integrals), unconstrained optimisation, constrained optimisation with equality constraints, concave programming, envelope theorem, Taylor series expansion, differential equations, difference equations, systems of differential equations. Particular attention is given to abstract thinking.

The course prepares for many quantitative masters in economics and finance and, in particular, for the Research Master in Multidisciplinary Economics at USE.

Academic skills
This course focuses on the following academic skills:
 
Analytical skills

• Being able to solve problems (identifying the problem, devising a path towards the solution, follow this path, verify the outcome) for more complex assignments.
• Being able to identify, interpret and critically evaluate the main line of reasoning, for more complex problems.

Effort requirement
In week 1, 2, 3, 6, 7, 8 students have to hand in individual assignments on the material of that week. If the students submit at least five sufficient assignments, the effort requirement will be checked off.


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 reusable 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.