Basic terms/concepts: sets, maps
Linear equation systems: solvability criteria, Gauss algorithm
Vector spaces: linear independence, generating systems and bases, dimension,
subspaces
Linear maps: image and rank, relationship to matrices, behaviour under
change of basis
Dual vector spaces: multilinear forms, alternating and symmetric bilinear
forms, relationship to matices, change of basis
Determinants: Cramer's rule, Eigenvalues and Eigenvectors
Equivalence relations, groups, rings, fields
Prerequisites:
Participation in the preparatory course (Brückenkurs) is highly recommended.