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Module Number:
| 14380
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| Module Title: | Special Topics of Algebra |
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Spezielle Themen der Algebra
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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: |
8
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| Learning Outcome: | After successfully completing the module, students deeply understand advanced algebraic structures and concepts. They are able to apply this knowledge to solve more complex algebraic problems using computatinal algebra systems and advanced algorithmic techniques. |
| Contents: | Students can choose from the following topics depending on their interests:
- Correspondence between varieties and ideals
- Polynomial and rational functions on a variety
- Robotics Automatic theorem proving
- Symmetric polynomials and invariant theory
- Projective algebraic geometry
- The dimension of a variety
- Real root location and isolation
- Solving equations with Eigenvalues and Eigenvectors
- Berstein's theorem
- Syzygies
- Algebraic coding theory
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| Recommended Prerequisites: | Knowledge of the content of module
- 11101: Lineare Algebra und Analytische Geometrie I
- 11102: Lineare Algebra und Analytische Geometrie II
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| Mandatory Prerequisites: | None |
| Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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| Teaching Materials and Literature: | - DA Cox, J Little, D O’Shea: Using Algebraic Geometry (2005)
- S Bosch: Algebra (2013)
- S. Lang: Algebra (2005)
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| Module Examination: | Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | - Written examination, 90 min. OR
- Oral examination, 30-45 min.
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) /
Mathematics /
PO 2025
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| Remarks: | - Study programme Mathematics M.Sc.: Compulsory elective module in complex „Analysis/Algebra/Combinatorics“
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| Module Components: | - Lecture: Special Topics of Algebra
- Accompanying exercise
- Related examination
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| Components to be offered in the Current Semester: | |
