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| Detailed information |
| Original study plan |
Master's programme Computer Science 2025W |
| Learning Outcomes |
Competences |
| Students are familiar with basic skills and techniques that are relevant to simplify formulas related, e.g., to the analysis of algorithms (worst case and average case) or data structures such as binary trees. They know the relevant computer algebra algorithms and can apply them to non-trivial examples.
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| Skills |
Knowledge |
- Introduction into the theory of formal power series [K2,K5];
- Manipulation of formal power series with classical and algorithmic tools to concrete problems [K3,K4,K6];
- Understanding of the basic properties of C-finite sequences and the most relevant algorithms (rational representation, closure properties, recurrence solving) [K2,K3,K6];
- Applying closure properties to holonomic functions/sequences and understanding of the underlying algorithmic toolbox [K3,K4];
- Understanding and applying of basic aspects in asymptotics [K2, K3];
- Algorithmic treatment of simplifying sums (symbolic summation and recurrence solving) [K2,K3];
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- Algorithmic and mathematical thinking;
- Classical and algorithmic manipulation of mathematical objects such as formal power series and Laurent series;
- Basic principles of computer algebra methods for concrete problem solving.
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| Criteria for evaluation |
Oral exam.
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| Methods |
Blackboard presentation combined with Mathematica sessions where the introduced computer algebra tools are applied to non-trivial problems combing from combinatorics and the analysis of algorithms.
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| Language |
English |
| Study material |
Detailed lecture notes will be provided.
In addition, many of the topics discussed in the lecture can be found in the book "Concrete Mathematics - A Foundation for Computer Science" by R.L.Graham, D.E.Knuth und O.Patashnik (Addison-Wesley, 1994) and
"The Concrete Tetrahedron" by Manuel Kauers and Peter Paule (Springer Wien, 2011).
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| Changing subject? |
No |
| Corresponding lecture |
TM1WHVOANKO: VO Analytische Kombinatorik (3 ECTS)
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
201SYMRCACV12: VL Computer Algebra for Concrete Mathematics (2012W-2020S)
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