|Lecture Course WS2018/19|
In the winter term 2018/19 I will read a lecture course
(with exercises) for bachelor and master students in mathematics. Prerequisite is only knowledge from a basic course in algebra, as one can obtain in the lecture course Grundlagen der Algebra und Computeralgebra. Knowledge about Gröbner bases are of advantage but not necessary.
The course will mainly introduce the Ritt-Kolchin theory of differential polynomials. Thus the main emphasis will be on differential ideal theory, which extends the classical algebraic theory of ideals in commutative rings to differential polynomials, and related algorithms. In the last years, the Ritt-Kolchin theory could help in the solution of many algorithmic problems based on sets of algebraic differential equations. It is of interest for both pure and applied mathematics. If time permits, we will also discuss some basic notions of the differential Galois theory of linear ordinary differential equations.
Time/Place: Tuesday 11:00-13:00, SR 0450a, Wednesday 09:00-11:00,
I will read the exercises for the course myself. They are every Wednesday 11:00-13:00 in SR 0450. The exercise sheets will be available here. The first sheet will be published on October 30th after we have actually started with differential algebra.
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