This lecture - as well as the corresponding basic lecture Analysis II - sets the fundaments for the whole study of mathematics. On general grounds, it introduces to most important mathematical notions and concepts needed for the courses of the curriculum; in particular, the students should develop an understanding for linear (and non-linear) problems. The students should develop a working knowledge of fundamental methods; in addition, the connection between algebra and geometry should be made transparent.

Subject

Contents of Linear Algebra I and II: Fundamental concepts of algebra; numbers, functions, and maps. Vector spaces and vector calculus. Matrices, determinants, inner product spaces and eigenvalue problems. Solutions of systems of linear equations. Foundations
of group theory.