Computer algebra (Spring term 2025)
Content
In this class we discuss computer algebra, which is relevant for theoretical purposes, e.g. in algebraic geometry, but which has concrete applications (such as in robotics) as well. Concretely, we will study the theory of Gröbner bases, which roughly speaking generalize the division algorithm for polynomials in one variable to higher dimensions. Along the way, I will introduce some concepts of commutative algebra. The class can be considered as a rather down-to-earth introduction to algebraic geometry, with emphasize on concrete computations. Some applications (such as those to robotics, as mentioned) will be given towards the end of the lecture.Prerequisits are the content of the Linear algebra lectures. Knowledge of abstract algebra is helpful, but not strictly speaking required for the class.
Literatur
- David A. Cox, John Little, Donal O'Shea: "Ideals, Varieties, and Algorithms", Springer-Verlag, Undergraduate Texts in Mathematics
- David A. Cox, John Little, Donal O'Shea: "Using Algebraic Geometry", Springer-Verlag, Graduate Texts in Mathematics
Lectures and exercises
There will be a one exercise class every week, notice that working on the exercises is an essential part of the class. Understanding the material is not possible without solving exercises.- Lecture: Monday 11:30-13:00, room C46.633, first lecture: 7.4.2025
- Exercise class: Friday 09:15-10:45, room C10.006, first exercise class: 11.4.2025