Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Algebraic Topology | MAT 592 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | YUKSEK_LISANS |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. İSMET ALTINTAŞ |
Dersi Verenler | |
Dersin Yardımcıları | |
Dersin Kategorisi | Diğer |
Dersin Amacı | The Algebraic Topology course aims to make students comprehend the topics that provide a basis for the work of Master and PhD students working in the field of topology. |
Dersin İçeriği |
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# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | Lecture, Brain Storming, Self Study, | Testing, Homework, | |
2 | Problem Solving, Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Self Study, | Testing, Homework, | |
3 | Lecture, Discussion, Drilland Practice, Group Study, Self Study, Problem Solving, | Testing, Homework, | |
4 | Lecture, Discussion, Drilland Practice, Group Study, Self Study, Problem Solving, | Testing, Homework, | |
5 | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Self Study, Problem Solving, | Testing, Homework, | |
6 | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Self Study, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Basic topological concepts | |
2 | Topological manifolds and surfaces | |
3 | Compact connected surfaces and surface forms | |
4 | Connected sums of compact surfaces | |
5 | Classification of compact surfaces and classification theorem | |
6 | Simplex complexes | |
7 | Triangulation of compact surfaces, Euler characterization | |
8 | Notation matrix and its properties | |
9 | Simple closed curves and their properties, homotopy curves, homotopy type | |
10 | Homotopy groups | |
11 | Homology, homologous curves, type of homology | |
12 | Cell subdivisions of cells and surfaces, Betti numbers | |
13 | Homology groups | |
14 | Cover spaces |
Kaynaklar | |
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Ders Notu | 1. R.A. Piccinini, Lectures on homotopy theory, Elsevier science publ., Nort-Holland, 19922. |
Ders Kaynakları | 1. W.S. Massey, Singular homology theory, Springer-Verlag, New York, 1980. |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |||
2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | ||||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | ||||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 70 |
1. Ödev | 30 |
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 | 14 | 14 |
Assignment | 1 | 14 | 14 |
Final examination | 1 | 14 | 14 |
Toplam İş Yükü | 138 | ||
Toplam İş Yükü / 25 (Saat) | 5,52 | ||
Dersin AKTS Kredisi | 6 |