Schedule: 16.04.2019 - 23.05.2019
Contact information for the course (applies in this implementation):
Department of Mathematics and Systems Analysis
Aalto University School of Sciences
Details on the course content (applies in this implementation):
Abstract Algebra II is a kind of
continuation of Abstract Algebra I, which has been taught in the 3rd
teaching period of Year 2018/19, but also one year before, with
essentially the same content.
We seek to have a closer look into
the algebraic structure of a group and will use (simple) combinatorial
tools to understand more about the structure of its lattice of normal
subgroups, all typically in the finite case. This will in the end lead
to Sylow's theorems, which are powerful as they allow statements about
existence and non-existence, hence characterization problems in group
Should time allow (and I believe it will), we will then
have a first look into the very colourful world of rings and modules. I
will do my best to make the audience familiar with a few basic elements
of the theory, and I believe I can promise, it will not be boring.
This is the schedule for the course so far. Looking forward to see the audience.
Details on the course materials (applies in this implementation):
I will distribute mostly latex-typset written materials in class.
Apart from that, I recommend several good textbooks beyond my written notes. For this purpose,
have a look at the following:
- Dummit and Foote: Abstract Algebra. ISBN 978-0471433347.
- Hungerford: Algebra. ISBN 978-0387905181.
- Biggs: Discrete Mathematics. (a lot of the basics of this course can be found in this book as well).
- Lang: Undergraduate Algebra. Springer 2004. ISBN 987-1441919595.
- Lang: Algebra. Springer Graduate Texts 2002. ISBN 987- 038795385X.
these books are expensive, however the library might have them for you.
Some of them seem to be available as pdf-files in the web. I am not
completely sure about the legal status of such copies, so take this serious enough.
Course Homepage (valid 01.08.2018-31.07.2020):
Grading Scale (valid 01.08.2018-31.07.2020):