Module Number:
| 14085
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Module Title: | Graph Theory |
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Graphentheorie
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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: |
Each winter semester odd year
|
Credits: |
8
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Learning Outcome: | The students
- Know the most important terms and connections of graph theory
- Are able to apply graph theoretical concepts to solve practical problems
- Used the example of graph theroretic topics to attain experience in self-contained scientific working
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Contents: | - Basic concepts, graphs, connectivity, trees
- Matchings, colorings, flows
- Hall's theorem, König's theorem, chromatic number, Menger's theorem
- Planar graphs, Euler characteristic, Kuratowski's theorem, duality, cycle bases
- Ethical responsibility in the application of models, algorithms and results
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Recommended Prerequisites: | Knowledge of the content of the modules
- 11101: Lineare Algebra und analytische Geometrie I
- 11102: Lineare Algebra und analytische Geometrie II
or
- 11112: Mathematik IT-1 (Diskrete Mathematik)
- 11113: Mathematik IT-2 (Lineare Algebra)
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Mandatory Prerequisites: | - No successful participation in module 11415 Graphtheorie
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Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
-
Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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Teaching Materials and Literature: | - D.B. West: Introduction to Graph Theory. (Prentice Hall, 1996)
- R. Diestel: Graphentheorie. (Springer,1996)
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Module Examination: | Final Module Examination (MAP) |
Assessment Mode for Module Examination: | - Written examination, 90 min. OR
- Oral examination, 30 min.
In the first lecture it will announced, wether 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
-
Master (research-oriented) /
Artificial Intelligence /
PO 2022
-
Bachelor (research-oriented) /
Informatik /
PO 2008
- 1. SÄ 2017
-
Master (research-oriented) /
Informatik /
PO 2008
- 2. SÄ 2017
-
Bachelor (research-oriented) /
Künstliche Intelligenz /
PO 2022
-
Master (research-oriented) /
Künstliche Intelligenz Technologie /
PO 2022
-
Bachelor (research-oriented) /
Mathematik /
PO 2023
-
Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Mathematik - dual /
PO 2023
-
Bachelor (research-oriented) /
Wirtschaftsmathematik /
PO 2023
-
Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Wirtschaftsmathematik - dual /
PO 2023
|
Remarks: | - Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
- 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 B.Sc.: Compulsory elective module in „Praktische Mathematik“ or in field of application „Mathematik“
- Study programme Informatik M.Sc.: Compulsory elective module in „Mathematik“ or in field of application „Mathematik“
- Study programme Künstliche Intelligenz B.Sc.: Compulsory elective module in complex „Wissensakquise, -repräsentation und -verarbeitung“
- Study programme Künstliche Intelligenz Technologie M.Sc.: Compulsory elective module in complex „Software-basierte Systeme“
- Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Knowledge Acquisition, Representation, and Processing“
- Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
|
Module Components: | - Lecture: Graph Theory
- Accompanying exercises
- Related examination
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Components to be offered in the Current Semester: | |