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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2025W |
| Learning Outcomes |
Competences |
| The students understand basic algorithms in computer algebra and how they can be applied for problem solving in mathematics.
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| Skills |
Knowledge |
- Learning basic structures and algorithms in computer algebra [K2,K5];
- Analyzing the complexity of algebraic algorithms [K4,K5];
- Properties of the extended Euclidean algorithm in Euclidean domains [K2] and its application [K3] (operations in algebraic field extensions, partial fraction decomposition, Chinese Remainder Theorem, Pade approximation, rational function reconstruction, rational number reconstructions);
- Understanding of modular algorithms in the context of the Euclid algorithm [K2,K5];
- Basic understanding of Gröbner bases [K2,K4] with a special focus on algorithms (Buchberger's algorithm) and solving ideal theoretic problems in mathematics [K3].
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Extended Euclidean algorithm with applications, resultant, Mignotte bound, modular algorithms of the Euclidean algorithm, algorithmic Gröbner bases theory with applications.
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| Criteria for evaluation |
Depending on the needs of the participants there will be a written or oral exam.
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| Methods |
The different algorithms will be presented on the blackboard. Concrete examples will be carried out with the computer.
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| Language |
English |
| Study material |
Joachim von zur Gathen and Jürgen Gerhard, "Modern Computer Algebra", Cambridge University Press, 2013 (or earlier versions).
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| Changing subject? |
No |
| Corresponding lecture |
(*)ist gemeinsam mit 201ALGECALU12: UE Computer Algebra (1,5 ECTS)
äquivalent zu
TM1WHKVCASY: KV Computeralgebra (4,5 ECTS)
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
201ALGECALV12: VL Computer Algebra (2013W-2018S)
201ALGECALV12: VL Computer Algebra (2012W-2013S)
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