The course proper starts on Tuesday, 17 October, with the lecture at 8 am in S2|04 / 213.

There will be a mock exam on Thursday, 25 January, at 14:30-16:30. It will take place in room S103|123. You are free to use books, lecture notes, notes of your own, problem sheets and their solutions, but do not use any electronic device. See mock exam questions and their solutions

The core topic of linear algebra is the investigation of vector spaces and linear maps. Linear algebra has close links with geometry and with various application areas inside mathematics and beyond.

Techniques and methods from linear algebra are ubiquitous in many branches of pure and applied mathematics, as well as for instance in physics and engineering, in computer graphics, or in information theory.

The first part of this first-year course in linear algebra, Linear Algebra I, introduces students to the relevant algebraic notions and concepts, like vector spaces, groups, fields, linear maps and matrices, linear independence, dimension, and lays the foundation for more advanced topics in part II. At the same time it provides some general training in mathematical methods and techniques.

The course is taught in English. Exercise groups and tutorial sessions from an integral part of the course. Students are strongly encouraged to participate actively in the exercises and tutorials and to hand in weekly homework assignments. These components of the course are essential not only for understanding the material taught, but in order to experience and practice the core mathematical activities of problem analysis, problem solving and rigorous presentation of mathematical thought.

Group work during exercises and tutorials, with guidance by tutors and demonstrators, as well as feedback on written solutions to the assignments are particularly important parts of the learning experience, and as essential for satisfactory performance on the course as the actual lectures. Students are also encouraged to ask questions during the lectures and contact hours. Course notes, as well as exercise sheets and related material are being made available electronically, via the links provided on this page.

Exercise sheets are provided both for Tuesday tutorials and Thursday exercise groups. The sheet for the exercise group will typically comprise five or six exercises. The first few of these are primarily intended for group work during the exercises, with the remainder serving as homework assignments to be submitted on the following Tuesday and discussed the Thursday after.

It is extremely important that students train their skills in writing up solutions and formulating mathematical thought and argument (also for the exam, but by no means only for that reason). Written solutions to any of the Thursday exercises, including those covered in group work, can be handed in as homework. These will be marked and returned with feedback.

Participation will be monitored, including performance in homework submissions; successful participation/performance will be certified with an "Übungsschein" (which, although not a formal requirement in the course, may be counted as an additional bonus).

Some suggestions (from the library):

Anton: Elementary Linear Algebra, 7th edition, Wiley also in German translation, Spektrum Verlag.

Artmann: Lineare Algebra, Birkhäuser

Beutelsbacher: Lineare Algebra, Vieweg

Brieskorn: Lineare Algebra und Analytische Geometrie (I,II), Vieweg

Bröcker: Lineare Algebra und Analytische Geometrie, Birkhäuser

Curtis: Linear Algebra - An Introductory Approach, Springer

Fischer: Lineare Algebra, 11. Aufl., Vieweg

Greub: Linear Algebra, Springer

there is also a German edition

Jänich: Lineare Algebra, 10. Aufl., Springer also in English translation, Springer

Kaye, Wilson: Linear Algebra, Oxford University Press

Klingenberg, Klein: Lineare Algebra und Analytische Geometrie, BI

Koecher: Lineare Algebra und Analytische Geometrie, Springer

Kwak, Hong: Linear Algebra, Birkhäuser

Lingenberg: Lineare Algebra, BI

Strang: Linear Algebra and its Applications, Academic Press