| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2022W |
| Objectives |
Applications of methods of enumerative combinatorics range from pure mathematical areas (how many objects of a certain type are there?) to areas like computer science (how many steps does my algorithm need?) and natural sciences (e.g., statistical mechanics or chemistry). Often answers to such problems are given in the form of complicated mathematical expressions (multiple-sums or integral, as solutions to difference or differential equations). The simplification of such representation of solutions is of fundamental importance. The lecture introduces to relevant methods, with emphasis on techniques from computer algebra.
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| Subject |
A huge class of enumeration problems are covered by the theory of holonomic functions. The lecture introduces to fundamental notions and ideas: e.g., generating functions and related recurrences and differential equations. Special emphasis is put on algorithmic aspects, in particular, on the usage of methods from computer algebra.
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| Criteria for evaluation |
Oral or written exam at the end of the semester.
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| Methods |
Blackboard- or Zoom-presentation (depending on pandemic situation);
usage of computer algebra tools.
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| Language |
(*)Deutsch - but could be English, provided there is general agreement. |
| Study material |
"The Concrete Tetrahedron" by M. Kauers and P. Paule, also other books.
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| Changing subject? |
No |
| Corresponding lecture |
(*)ist gemeinsam mit 201UCMAAKOU18: UE Algorithmische Kombinatorik (1,5 ECTS) äquivalent zu
TM1PEKVINFO: KV Informationssysteme (3 ECTS) +
[ Lehrveranstaltung aus dem Wahlfach h. Symbolisches Rechnen (1,5 ECTS) oder
Lehrveranstaltung aus dem Wahlfach i. Logik (1,5 ECTS) oder
Lehrveranstaltung aus dem Wahlfach j. Algebra und Diskrete Mathematik (1,5 ECTS) ]
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