Content:

• Basic terms/concepts: sets, maps, equivalence relations, groups, rings,
• fields
• Linear equation systems: solvability criteria, Gauss algorithm
• Vector spaces: linear independence, generating systems and bases, dimension,
• subspaces, quotient spaces, cross products in R3
• 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

Prerequisites:

Participation in the preparatory course (Brückenkurs) is highly recommended.

• Siegfried Bosch, Lineare Algebra, 4. Auflage, Springer-Verlag, 2008;
• Gerd Fischer, Lernbuch Lineare Algebra und Analytische Geometrie, Springer-Verlag, 2017;
• Bartel Leendert van der Waerden, Algebra Volume I, 9th Edition, Springer 1993;

Zu den Grundlagen

• Kevin Houston, Wie man mathematisch denkt: Eine Einführung in die mathematische Arbeitstechnik für Studienanfänger, Spektrum Akademischer Verlag, 2012