Course contents:

• introduction to the open source programming environment R, R as a calculator, named vectors in R
• functions of one variable, defining and evaluating functions in R
• brief introduction to functions of several variables
• graphs of functions, graphing functions in R
• special functions and their properties: linear, quadratic, polynomial, power, exponential, logarithmic
• concatenation and composition of functions, inverse of functions
• analytical and numerical rootfinding
• elementary financial mathematics (discounting and compounding, simple annuities): computation and visualization using R
• elementary matrix algebra and its usage in R
• systems of linear equations and their representation using matrix algebra
• analytical and numerical differentiation
• single-variable optimization
• basic concepts of probability
• important probability distributions: uniform, binomial, Gaussian
• simulation methods using R

After completing the course, students should be familiar with basic concepts, methods and tools in mathematics and computing that are necessary for the quantitative analysis of problems in modern business and economics. Moreover, students will have acquired basic programming skills in the open-source computer language R, enabling them to independently conduct simple mathematical analyses.

100% physical, emotional, and intellectual participation is strongly recommended in both the lectures as well as the practical sessions. However, attendance in the lectures will not be formally checked. Note that there will be no chance to make up for any points which were lost due to missing practical sessions.

The course will be taught as a lecture accompanied by practicals in small groups (VÜ). There will be 10 lectures with 120 participants, lasting 90 minutes each. Concerning the practicals, there will be one introductory session (90 minutes, 4 x 30 participants) and 6 further exercise sessions (60 minutes, 4 x 30 participants), where students will use their own computers. Additionally, there will be tutorials held by senior students.

Course evaluation consists of three parts:

• final exam (50 points)
• homework assignments (6 in total, 5 points each)
• case study (group work to be handed in in written form, 20 points)

Mathematical skills and knowledge at high school level.