Dear participants of the autumn school,
In our lectures we will deal with binomial ideals (ideals which are
generated by polynomials with at most two terms) and we will use
computers to do so. To prepare for the school, if necessary, please
review basic commutative algebra, such as the definitions of rings,
ideals, fields, modules, etc. Any slightly more advanced algebra book
can be source for this. I like “Abstract Algebra” by Dummit and Foote.
An introduction more tuned to Gröbner bases and algorithms is the
popular “Ideals, Varieties, and Algorithms” by Cox, Little, O’Shea.
I also have two concrete homework tasks for you
1) Keep your eyes open for a binomial ideal that you encounter in your
daily life. Bring to the summer school one page on which you describe
that binomial ideal. Please give some context. Where did you find the
ideal? Why did you find it interesting? What properties does the ideal
have? Please also put your name on the page and give it to me when you
first see me in Lukecin.
2) Bring a laptop on which you have installed Macaulay2
(http://www.math.uiuc.edu/Macaulay2/), Singular
(https://www.singular.uni-kl.de/), and Sage (http://www.sagemath.org/)
and make sure that you are familiar with at least one of these systems,
thoroughly studying a tutorial, if necessary.
With this I wish you a great week and see you soon in Lukecin.
Thomas