AI Summary
This content was summarized and structured with AI support based on the official competency profile of the Studienkollegs.
Competency Profile: Mathematics
1. Self-Conception of the Subject and its Contribution to Competency Development
Mathematical competencies create essential prerequisites for gaining knowledge in a wide variety of disciplines and subjects, making them fundamental for natural sciences and engineering. Furthermore, mathematical methods in economics, politics, and social sciences serve to objectify and structure complex issues. The central task of mathematics instruction at Studienkollegs is for students to further develop concrete mathematical knowledge and working methods as part of building mathematical competencies.
2. Competency Areas
- Modeling: Capturing and structuring increasingly complex factual situations regarding a specific question to find solution approaches.
- Representing: Translating increasingly complex factual situations into mathematical models and solving a given problem within a mathematical model.
- Problem Solving: Analyzing and structuring a problem situation, developing a solution strategy, selecting and applying appropriate procedures to find a solution.
- Arguing: Linking arguments into complete chains of argumentation and using various argumentation strategies.
- Communicating: Capturing, structuring, and formalizing information from increasingly complex texts and representations containing mathematics.
- Using Tools: Executing operations with mathematical objects and purposefully and efficiently working on mathematical tasks.
3. Competency Expectations
Students will be able to…
- increasingly independently apply basic technical terms and calculation techniques of algebra and analysis.
- distinguish between relation and function as well as the respective form of representation.
- apply proof techniques to present logical argumentations.
- (Depending on the course T, M, W, different focuses in analysis, linear algebra, stochastics, and financial mathematics).
4. Course Content
a) Basic Content
- Analysis: Sets of numbers, basic arithmetic operations, equations/inequalities, systems of linear equations, real functions, limits, differential and integral calculus.
- Linear Algebra / Analytic Geometry (T-Course): Vectors, lines, planes, scalar product, cross product.
- Statistics and Probability (W-Course): Descriptive and exploratory statistics, concept of probability.
b) Possible Differentiations or Extensions
- Complex numbers, Taylor series, differential equations (T-Course).
- Special probability distributions, hypothesis tests (M-Course).
- Multivariate analysis, econometrics (W-Course).