Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
MAT-23-214Advanced Topology IIElective126
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
1Knows the concept of homotopy.
2Obtains fundamental group and covering space of a topological space
3States Jordan Curve Theorem.
4Knows the properties of simplicial complexes.
5Knows the concepts of simplicial and singular homology.
6Knows how to obtain Euler number.
7Classify the surfaces with Euler number.
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
Weekly Detailed Course Contents
WeekTheoreticalPracticeLaboratory
1Topological Concepts
2Homotopi
3Homotopi
4Fundamental Group
5Covering Spaces
6Jordan Curve Theorem
7MID TERM EXAM
8Simplicial Complexes
9Simplicial Complexes
10Simplekssel Homoloji, Singüler Homoloji
11Simplekssel Homoloji, Singüler Homoloji
12Homology in terms of Coefficient Group
13Euler Number
14Euler Number and a Classification of Surfaces
15Final Exam
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
Assessment Methods and Criteria
Term (or Year) Learning ActivitiesQuantityWeight
Midterm Examination1100
SUM100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Final Examination1100
SUM100
Term (or Year) Learning Activities50
End Of Term (or Year) Learning Activities50
SUM100
Language of Instruction
Turkish
Work Placement(s)
None
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination111
Final Examination122
Attending Lectures14342
Question-Answer14342
Individual Study for Mid term Examination15050
Individual Study for Final Examination15050
TOTAL WORKLOAD (hours)187
Contribution of Learning Outcomes to Programme Outcomes
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1
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5
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6
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7
PO
8
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9
PO
10
PO
11
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High
 
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