As a team, Prof. Köster, Prof. Ruckert, and I will introduce freshmen (“Erstsemester”) to the basics of this beautiful subject. Our list of contents is based on the famous video lectures of Gilbert Strang who teaches linear algebra from a more practical point of view and hence avoids becoming too formal too quickly. This approach perfectly fits to the general program of the department, i.e., the emphasis lies on the application of concepts rather than their theory.
The core concepts that we like them to learn and experience are the following:
- Linear systems and matrices (Gaussian elimination, LU decomposition, inversion)
- Basis and dimension of a subspace (linear independence, span)
- The four fundamental subspaces of a matrix
- Orthogonality and projections (least squares, Gram-Schmidt)
- Eigenvalues and eigenvectors (diagonalization)
- Complex numbers
The lectures will be held online only, whereas the exercises are offered in person and online. I am especially curious as this course is my first experience with freshmen and since they had to finish their time at high school under rather difficult conditions due to the Corona crisis. My hope is that our team is able to provide a stimulating environment for them and contributes to a successful start into their time as college students.