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Linear Algebra I (MCS)



There will be an opening lecture in the
orientation week on Monday, 9 October.
OWO lecture handout.
The course proper starts on Tuesday,
17 October, with the lecture at 8 am in S204 / 213.
There will be a mock exam on Thursday, 25 January, at 14:3016:30. It will take place in room S103123. 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



Name  Office  additional contact information  Prof. Dr. Martin Otto  S215 / 207  
Sven Herrmann  S215 / 221  tel: 163953; LZM: Monday 10:40 
Dr. Benno van den Berg  S215 / 203  berg@...; LZM: Wednesday 9:4510.35 
Andreas Mars   mars@mathematik... 



Course notes are available here.



Linear algebra is one of the fundamental areas of mathematics.
Together with calculus it forms one of the cornerstones
in first year undergraduate education in mathematics.
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 firstyear 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.



Time  Place 
Tuesday, 8.009.40 am  S204 / 213 
Wednesday, 9.50  11.30 am  S103 / 223 
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.



Group  Time  Place  Tutor  office hours 
Exercises  Thursday, 2.25  4.05 pm  S103 / 9  Andreas Mars  Mon 910, room 217 
Tutorial 1  Tuesday, 9.50  11.30 am  S102 / 144  Sven Herrmann  LZM: Monday 10:40 
Tutorial 2  Tuesday, 9.50  11.30 am  S114 / 265  Dr.Benno van den Berg  Mon 13:1514.15, room 203 
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).



Note that the required exam for MCS bachelor students is the module exam
covering
Linear Algebra I and II, primarily offered in September.



There are plenty of textbooks both in German and in English on the
topic of linear algebra, at various levels but also differing widely
with respect to comprehensiveness and structure.
Students are encouraged to explore which books suit their tastes.
Most relevant books are available in the mathematics library, which has
a shelf in the reading room dedicated to linear algebra and one with
English books especially for the MCS students. (There is also a
section with mathematical dictionaries.)
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





