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 R^3,
• 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 matrices, 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

• Whiteboard: Signing up for the course with the FU Whiteboard system is mandatory for participating. Whiteboard will also serve as a course homepage.
• Active participation: A problem set will be published every week. Each problem set has to be solved within one week. Submissions are allowed by groups of max. two students. For active participation, 50% of the total possible amount of points have to be reached. Moreover, we expect active participation in the tutorials.
• Regular participation: Participating in the lectures is recommended. Participation in the tutorials is required.
• Covid: The modus operandi of the course (online, hybrid, presence) will be determined at the beginning of the semester depending on the Covid situation. Please follow the Whiteboard homepage and announcements.