• Getting to know and to understand the axiomatic structure of mathematics and the importance of mathematical reasoning • Mastering basic mathematical proof techniques and their logical structure • Recognizing the relevance of premises in mathematical theorems: Localization of premises within proofs and possible consequences if premises are not met • Learning the significant ideas and methods of linear algebra • Mastering the fundamental concepts of algebra, such as groups, rings, fields • Mastering the fundamental concepts and significant methods of linear algebra, such as systems of linear equations, Gaussian algorithm, vector spaces, dimension, linear maps, matrices, determinants • Mastering of further notions and methods of linear algebra, e.g. eigenvectors, eigenvalues, diagonalization