| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Topology and Category | MAT 617 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Topology I, Topology II |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. METİN BAŞARIR |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | Knowing of topological spaces, connectedness spaces and topolojical groups, The concepts of category, morfizm, functor and grupoid |
| Dersin İçeriği | Connectedness,curvature connectedness, homotopy, fundemental groups, cover spaces, topological groups, seperation axioms in topological groups, topological cover spaces, category, special objects and morfizm, product spaces, Pullback and Pushout diagrams, functors, grupoids, grupoid cover morfizms. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 2 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 3 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 4 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 5 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, | |
| 6 | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Connectedness spaces | |
| 2 | Homotopy | |
| 3 | Topological groups | |
| 4 | Topological group homomofizm | |
| 5 | Connectedness topological groups | |
| 6 | Seperation axioms in topological groups | |
| 7 | Topological groups | |
| 8 | Topological cover groups | |
| 9 | Mid Exam | |
| 10 | Category | |
| 11 | Special objects | |
| 12 | Product spaces | |
| 13 | Pullback and Pushout diagrams, functors | |
| 14 | Grupoids, grupoid cover morfizms |
| Kaynaklar | |
|---|---|
| Ders Notu | [1] Mucuk, O., Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. |
| Ders Kaynakları | [2] Brown, R., Topoloji ve Grupoids, Bokksurge LLC, U.K, 2006. [3] Lipschutz, S., General Topology, Schaum's Outline Series, New York, 1965. [4] Massey, W. S., Algebraic Topology: An Introduction, Sipringer-Verlag, New York, 1990. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
| 2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
| 3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
| 4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
| 5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
| 6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
| 7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
| 8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
| 9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
| 10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
| 11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 60 |
| 1. Ödev | 10 |
| 2. Ödev | 10 |
| 1. Kısa Sınav | 20 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 18 | 18 |
| Assignment | 2 | 15 | 30 |
| Final examination | 1 | 18 | 18 |
| Toplam İş Yükü | 162 | ||
| Toplam İş Yükü / 25 (Saat) | 6,48 | ||
| Dersin AKTS Kredisi | 6 | ||