Algebraic Topology II
Mathematics
Institute of Natural and Applied Sciences
Third Cycle (Doctorate Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Algebraic Topology II | MAT605 | Elective | Doctorate degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Çiğdem GÜNDÜZ
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 concepts of Singular homology theory, systems of groups and their limits, and Cech homology theory.
5) Applies the 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 | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Topology
Course Contents
Candidates are provided with in-depth knowledge on axioms and general theorems, category, functor and morphism of functor, homology theory, the singular homolgy theory, systems of groups and their limits, the Cech homology theory.
Weekly Schedule
1) Kategory and functor2) Morphism of functors
3) Morphism of functors
4) The singular homology theory
5) The singular homology theory
6) The singular homology theory
7) Systems of groups
8) Midterm examination/Assessment
9) Systems of groups
10) Systems of groups and their limits
11) Systems of groups and their limits
12) Systems of groups and their limits
13) Cech homology theory
14) Cech homology theory
15) Cech homology theory
16) Final examination
Recommended or Required Reading
1- Sadi Bayramov, Çiğdem Gündüz (Aras), Genel Topoloji, Çağlayan Kitabevi, 2004.
2- Ali Bülbül, Genel Topoloji, Hacettepe Üniversitesi Yayınları, 2004.
3- Steenrod N. and Eilenberg S., Foundations of Algebraic Topology, Princeton Univ. Press, NJ,Princeton.
4- Spanier H.E. Algebraic Topology, McGRAW-HILL, New York, 1966
5- Ders notları
6- 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