| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2023W |
| Objectives |
In the last decades big parts of mathematics has been algorithmized and many mathematical problems (or problems coming from natural and technical sciences that can be modeled in mathematics) can be solved with the computer. A major contribution for this algorithmic revolution is the computer algebra. This lecture aims at introducing the most crucial algorithms in this field and illustrating how they can be used for non-trivial applications.
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| Subject |
We discuss constructive symbolic methods for simplification of expressions and solving algebraic (i.e., polynomial) systems of equations.
Among others, the following algorithms are explored:
- basic structures and algorithms
- the extended Euclidean algorithm, polynomial remainder sequences and applications
- modular methods based on Hensel lifting and the Chinese Reemainder Theorem (resultants, gcd, factorization)
- a gentle introduction to Gröbner bases
- symbolic summation and integration
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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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