MM540: Mathematical methods for economics

The aim of the course is to enable the student to apply mathematical reasoning, mathematical methods and proof techniques and that the student achieves a basic understanding of philosophy of science. Moreover, it is the aim that the student acquires fundamental skills within the discipline of linear algebra in relation to applications in economy and linear models. The material covered is important in almost all aspects of mathematics and has wide-reaching applications in economics and throughout the natural sciences.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Knowledge: Give the students knowledge about proof techniques and fundamental concepts in abstract mathematics (logic, sets, functions, relations). Moreover, it is the focus of the course that the student obtains knowledge about fundamental concepts and techniques in linear algebra (vector spaces, linear operators, bases, diagonalization). Finally, the course will give an introduction to philosophy of science.

Skills: Give the students the skills to solve problems in linear algebra (solve systems of linear equations, find eigenvectors and eigenvalues, find matrices for linear operators). Give the students skills to apply mathematical terminology and symbols and to formalize mathematical statements in a logically correct way.

Competences: Give the students the competences to 1) Discuss and collaborate with others around mathematical-economical problems, solution methods, results, applying standard mathematical terminology. 2) Relate examples of mathematical-economic models to real problems (within for example linear algebra, linear programming, job assignment, game theory).

The learning objective of the course is that the student demonstrates the ability to:

• Apply mathematical theory and results to solve concrete problems in linear algebra
• Argue in a mathematically correct and stringent way about the steps and techniques in the solution of given problems
• Assess whether achieved results are correct
• Prove
  assertions by applying proof techniques such as direct proof, indirect
  proof and proof by induction. Use concepts, results and techniques
  learned in this course on known as well as new concrete problems.
• Understand principles of mathematical thinking, argumentation and ability to carry out and understand proofs
• Ability to handle abstract mathematical concepts
• Ability to present in written form precise mathematical arguments.

The following main topics are contained in the course:

The lectures, where the literature (curriculum) for the course will be explained, will be supplemented by exercise classes, where relevant exercises, relating to the lectures, will be solved and explained. Both of these events are supported by the students' independent work (or group-work) on the material as described in the study phase.

• 4 hours lectures and 2 hours exercise classes in 15 weeks
• Read the literature for the course

• Solve exercises