The lecture takes places on Thu, 15:30-17:00 in S2 059 starting on March 9 and will be held in English.

The goal of the course is to understand the underlying principles of algorithms typically used in computer algebra systems for computing closed forms of integrals, or for solving differential equations. Participants are expected to be acquainted with the basic notions from analysis (differentiation, integration, power series expansions, etc.) and linear algebra (finite dimensional vector spaces, solving linear systems of equations, etc.). It might be an advantage, although it is not a formal requirement, to do the courses computer algebra and/or algorithmic combinatorics (or computer algebra for concrete mathematics) before this course.

- Examples for Hermite reduction and Rothstein Trager: Mathematica Notebook and pdf-version of MMA-nb
- Lecture notes on solutions of linear ODEs
- Video 1 introduction and solution to linear ODEs with constant coefficients
- Video 2 polyonomial solutions of linear ODEs with rational function coefficients
- Video 3 rational function solutions of linear ODEs with rational function coefficients
- Examples for right division, least common left multiple, uni- and multivariate closure properites: Mathematica notebook and pdf-version of MMA-nb
- Take home exam posted on Monday July 10, 2023 and due by email to Veronika Pillwein on Monday July 17, 2023. If there are any questions or you prefer to hand in a hard copy version just email me. Good luck!

Related literature:

- Bronstein: Symbolic Integration I, Transcendental Functions
- von zur Gathen, Gerhard: Modern Computer Algebra
- Geddes, Czapor, Labahn: Algorithms for Computer Algebra
- Winkler: Polynomial Algorithms in Computer Algebra