Algebraic Topology I
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Algebraic Topology I | MAT502 | Elective | Master's degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Abdülkadir AYGÜNOĞLU
Prof. Dr. Çiğdem GÜNDÜZ
Associate Prof. Dr. Vildan ÇETKİN
Learning Outcomes of the Course Unit
1) Knows basic concepts of algebraic topology.
2) Knows the concepts of transformation that preserves objects and structures.
3) Knows the concepts of category, functor and natural transformations.
4) Explains the concept of homotopy relation in the category of topological spaces
5) Explains the concepts of chain complexes, homoloji and cohomoloji theory, simplicial complexes.
6) Applies basic concepts of algebraic topology.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Topology
Course Contents
This course provides candidates with profound knowledge on axioms and general theorems, category, functor and morphism of functor, homotopy, the category of inverse and direct sequences of groups, chain complexes, homology groups of chain complexes, homology theory and cohomology theory, simplicial complexes, homology theory of simplicial complexes.
Weekly Schedule
1) Category and functor2) Morphism of functor
3) Homotopy relation in the category of topological spaces
4) Inverse and direct sequences of groups
5) Chain complexes
6) Chain complexes category
7) Homology groups of chain complexes
8) Midterm examination/Assessment
9) Homology and cohomology theory
10) Homology and cohomology theory
11) Homology and cohomology theory
12) Simplicial complexes
13) Simplicial complexes
14) Homology theory of simplicial complexes
15) Homology theory of simplicial complexes
16) Final examination
Recommended or Required Reading
1- Sadi Bayramov, Çiğdem Gündüz (Aras), Genel Topoloji, Çağlayan Kitabevi, 2004.
2- Steenrod N. and Eilenberg S., Foundations of Algebraic Topology, Princeton Univ. Press, NJ,Princeton.
3- Spanier H.E. Algebraic Topology, McGRAW-HILL, New York, 1966
4- Ders notları
5- Lecture notes
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Planned Learning Activities and Teaching Methods
1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required