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Module Number:
| 13911
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| Module Title: | Algebra: Structures and Algorithms |
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Algebra: Strukturen und Algorithmen
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| Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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| Responsible Staff Member: | -
Prof. Dr. rer. nat. Averkov, Gennadiy
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| Language of Teaching / Examination: | English |
| Duration: | 1 semester |
| Frequency of Offer: |
On special announcement
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| Credits: |
6
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| Learning Outcome: | After successfully completing the module, students are able to work with basic algebraic concepts and know basic algebraic facts and constructions. They are able to use this knowledge to solve algebraic problems, with our without the assistance of computer-algebra systems. Students understand the basic algebraic algorithmic machinery of computational algebra. |
| Contents: | - Commutative rings and ideals
- Affine varieties
- Groebner basis and the Hilbert basis theorem
- Elimination of variables with Groebner bases and resultsants
- Hilbert's Nullstellensatz
- Selected applications (e.g. global optimization, solution of kinematic problems, automated theory proving)
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| Recommended Prerequisites: | Knowledge of the content of the modules
- 11101: Lineare Algebra und analytische Geometrie I
or
- 11112: Mathematik IT-1 (Diskrete Mathematik), and
- 11113: Mathematik IT-2 (Lineare Algebra)
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| Mandatory Prerequisites: | None |
| Forms of Teaching and Proportion: | -
Lecture
/ 3 Hours per Week per Semester
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Exercise
/ 1 Hours per Week per Semester
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Self organised studies
/ 120 Hours
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| Teaching Materials and Literature: | - D. Cox, J. Little, and D. O’Shea: Ideals, Varieties, and Algorithms–An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer Publishing Company, 2010
- D. Cox, J. Little, and D. O’Shea: Using Algebraic Geometry, Springer Publishing Company, 2005
- S. Lang: Algebra, Springer Publishing Company, 2002
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| Module Examination: | Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | Final module examination:
- Written examination, 90 min. OR
- Oral examination, 30 - 45 min. (with small number of participants)
In the first lecture it will introduced, if the examination will organized in written or oral form. |
| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | -
Master (research-oriented) /
Angewandte Mathematik /
PO 2019
- 1. SÄ 2021
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Master (research-oriented) /
Artificial Intelligence /
PO 2022
- 1. SÄ 2024
-
Master (research-oriented) /
Cyber Security /
PO 2017
- 1. SÄ 2024
-
Bachelor (research-oriented) /
Informatik /
PO 2008
- 2. SÄ 2024
-
Master (research-oriented) /
Informatik /
PO 2008
- 3. SÄ 2024
-
Master (research-oriented) /
Mathematical Data Science /
PO 2025
-
Master (research-oriented) /
Mathematics /
PO 2025
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Bachelor (research-oriented) /
Wirtschaftsmathematik /
PO 2023
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Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Wirtschaftsmathematik - dual /
PO 2023
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| Remarks: | - Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
- Studiengang Mathematics M.Sc.: Wahlpflichtmodul im Komplex „Analysis / Algebra / Combinatorics“
- Studiengang Mathematical Data Science M.Sc.: Wahlpflichtmodul im Komplex „Advanced Mathematical Methods in Data Science“
- Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
- Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
- Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Advanded Methods“
- Study programme Informatik B.Sc.: Compulsory elective module in „Praktische Mathematik" or in field of application „Mathematics"
- Study programme Informatik M.Sc.: Compulsory elective module in „Mathematik" or in field of application „Mathematik"
- Study programme Cyber Security M.Sc.: Compulsory elective module in complex „Computer Science“
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| Module Components: | - Lecture Algebra: Structures and Algorithms, with integrated exercise
- Related examination
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| Components to be offered in the Current Semester: | |
