| Detailinformationen |
| Quellcurriculum |
Bachelorstudium Technische Mathematik 2022W |
| Ziele |
(*)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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| Lehrinhalte |
(*)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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| Beurteilungskriterien |
(*)Depending on the needs of the participants there will be a written or oral exam.
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| Lehrmethoden |
(*)The different algorithms will be presented on the blackboard. Concrete examples will be carried out with the computer.
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| Abhaltungssprache |
Englisch |
| Literatur |
(*)Joachim von zur Gathen and Jürgen Gerhard, "Modern Computer Algebra", Cambridge University Press, 2013 (or earlier versions).
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| Lehrinhalte wechselnd? |
Nein |
| Sonstige Informationen |
Bis Semester 2018S bezeichnet als: 201ALGECALV12 VL Computer Algebra
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| Äquivalenzen |
ist gemeinsam mit 201ALGECALU12: UE Computer Algebra (1,5 ECTS)
äquivalent zu
TM1WHKVCASY: KV Computeralgebra (4,5 ECTS)
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| Frühere Varianten |
Decken ebenfalls die Anforderungen des Curriculums ab (von - bis)
201ALGECALV12: VL Computer Algebra (2013W-2018S)
201ALGECALV12: VL Computeralgebra (2012W-2013S)
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