# MSc Economics

## Bridging Course Mathematics

### Winter Semester 2018/19

Mathematics is the language for the description of relations in
economics. Students will learn the most important elements of
this language in our course *Foundations of Economics*.
However, basic knowledge of mathematical methods are
prerequisites for mastering this course. It is assumed that
students already have gained these basic skills during their
time in high school and in the introductory course in their
Bachelor programmes.

For various reasons (e.g., different syllabi in high schools or
different interpretation of this syllabi by teachers) the
knowledge vary considerably among students of the master
programme *Economics*. It also may have happened that
one's personal expectation during high school of the importance
of the culture technology called Mathematics has not been
compatible with the latter studies of economics.

Mastering the basis mathematical methods is mandatory for the
master programme *Economics* and thus it is relevant in a
couple of courses. This bridging course in Mathematics offers
the opportunity to get feedback about your knowledge and your
level of expertise and helps you to close possible subject
related knowledge gaps.

The following problems cause issues for quite a few students:

- drawing (or sketching) of graphs of functions,
- transform equations into equivalent ones,
- handling inequalities,
- correct handling of fractions,
- calculations with exponents and logarithms,
- using of mathematical notation.

Presented "solutions" of such problems are surprisingly often wrong.

### Learning Outcomes

In this course we will practice the following skills:

- computations with mathematical terms
- polynomials, fractions, exponents and logarithms
- equalities and inequalities
- functions and their graphs
- derivatives and their applications
- antiderivative and integral
- basic matrix algebra

### Organisation and Course Design

In each of the 10 units the basics concepts and methods are shortly recapitulated, problems are solved collectively. Furthermore students are asked to do some homework problems. These problems are provided by the course instructor. However, students are explicitly invited to suggest their own problems they are interested in. It is expected that students actively participate in the course.

### Grades

There will be no explicit exams.
However, it is expected that students **actively
participate** in the course.

For a positive grade ("erfolgreich teilgenommen") students must
be *present* in at least *8 units*.

### Maxima - A Computer Algebra System

Computer Algebra Systems (CAS) allaw the manipulation of
mathematical expressions.
*Maxima*
is a freely available CAS. If there is some interest a very
short introduction can be given.

### Course Materials

### Preview on Courses on Mathematis in MSc Economics

- Mathematische Methoden (in German; English version in preparation)
- Mathematics 1: Linear Spaces and Metric Concepts (scientific track only)
- Mathematics 2: Analysis and Dynamic Optimization (scientific track only)

### Literature

- J. Leydold (2012). Mathematik - Grundlagen (in German)
- E. Mendelson (2003). Beginning Calculus, McGraw Hill, 3rd ed.
- J. Leydold: Mathematik für Ökonomen, 3. Auflage, Oldenbourg Verlag, München Wien, 2003. (in German)

Last change: 2018-09-14 by josef leydold