Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT-23-214 | Advanced Topology II | Elective | 1 | 2 | 6 |
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Level of Course Unit |
Third Cycle |
Objectives of the Course |
To introduce the concepts of homotopy, fundamental group and covering space; to introduce simplicial complexes; to show the concepts of simplicial and singular homology; to introduce Euler number and to obtain a classification of surfaces. |
Name of Lecturer(s) |
Dr. Öğr. Üyesi Alkan ÖZKAN |
Learning Outcomes |
1 | Knows the concept of homotopy. | 2 | Obtains fundamental group and covering space of a topological space | 3 | States Jordan Curve Theorem. | 4 | Knows the properties of simplicial complexes. | 5 | Knows the concepts of simplicial and singular homology. | 6 | Knows how to obtain Euler number. | 7 | Classify the surfaces with Euler number. |
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Mode of Delivery |
Daytime Class |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Topological Concepts
Homotopy
Homotopy
Fundamental Group
Covering Spaces
Jordan Curve Theorem
Simplicial Complexes
Simplicial Homology, Singular Homology
Simplicial Homology, Singular Homology
Homology in terms of Coefficient Group
Euler Number
Euler Number and a Classification of Surfaces
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Weekly Detailed Course Contents |
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1 | Topological Concepts | | | 2 | Homotopi | | | 3 | Homotopi | | | 4 | Fundamental Group | | | 5 | Covering Spaces | | | 6 | Jordan Curve Theorem | | | 7 | MID TERM EXAM | | | 8 | Simplicial Complexes | | | 9 | Simplicial Complexes | | | 10 | Simplekssel Homoloji, Singüler Homoloji | | | 11 | Simplekssel Homoloji, Singüler Homoloji | | | 12 | Homology in terms of Coefficient Group | | | 13 | Euler Number | | | 14 | Euler Number and a Classification of Surfaces | | | 15 | Final Exam | | |
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Recommended or Required Reading |
1. Martin D. Crossley, “Essential Topology”, Springer, 2007. 2. V. V. Prasolov, “Elements of Combinatorial and Differential Topology”, AMS, 2006. 3. James R. Munkres, “Elements of Algebraic Topology”, Westview Press, 1993. |
Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 50 | End Of Term (or Year) Learning Activities | 50 | SUM | 100 |
| Language of Instruction | Turkish | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 1 | 1 |
Final Examination | 1 | 2 | 2 |
Attending Lectures | 14 | 3 | 42 |
Question-Answer | 14 | 3 | 42 |
Individual Study for Mid term Examination | 1 | 50 | 50 |
Individual Study for Final Examination | 1 | 50 | 50 |
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Contribution of Learning Outcomes to Programme Outcomes |
LO1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO2 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO6 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO7 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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