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Module Number:
| 14273
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| Module Title: | Special Topics of Discrete Mathematics |
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Spezielle Kapitel der Diskreten Mathematik
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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. habil. Köhler, Ekkehard
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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 have in-depth knowledge of structures and algorithms in discrete mathematics. They are able to understand, analyze and apply essential algorithms in discrete mathematics. In addition, they have the skill to think structurally, use abstraction and modelling. |
| Contents: | The lecture is read with changing main focuses, e.g.:
- Integer Programming: formulations, relaxation, optimality and bounds, integer polyeders, complexity of integer problems, cutting-plane method, branch-and-bound method, Lagrange duality, column generation
- Network Optimization: essential flow algorithms and their complexity, formulation of flows as LP, IP, path based formulations, special network flows, k-splittable flows, unsplittable flows, dynamic flows, approximation algorithms
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| Recommended Prerequisites: | Knowledge of the content of the module
- 12868: Algorithmische Diskrete Mathematik
- 11101: Lineare Algebra und Analytische Geometrie I
or of the modules
- 11112: Mathematik IT-1 (Diskrete Mathematik)
- 11113: Mathematik IT-2 (Lineare Algebra)
- 12215: Theoretische Informatik
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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: | Depending on the specific focus specific references will be provided during the first week of the course. |
| Module Examination: | Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | - Oral examination, 30-45 min.
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| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | |
| Remarks: | - Study programme Mathematics M.Sc.: Compulsory elective module in complex „Analysis/Algebra/Combinatorics“
- 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 Informatik M.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“
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| Module Components: | - Lecture: Special Topics of Discrete Mathematics
- Accompanying exercise
- Related examination
The exercise may be partially replaced by guided self organised studies. |
| Components to be offered in the Current Semester: | |
