| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Knot Theory I | MAT 593 | 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 | Knot Theory I course aims to comprehend basic topics which are the bases for the studies of Master and PhD students working in topology algebraic topology, knot theory and related fields. |
| Dersin İçeriği | Fundamental concepts of knot theory, simple knot movements, rings, knot diagrams, regular diagrams and alternate knots, knot graphs, basic problems of knot theory, global problems, local problems, classical knot invariants, Reidemeister movements, minimum intersection number, torsion number , number of bridges, number of unknots, number of rings, number of colors, knot groups. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She learns the simple moves of knot diagrams | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| 2 | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, | |
| 3 | Lecture, Question-Answer, Discussion, Drilland Practice, Role Playing, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, | |
| 4 | Lecture, Question-Answer, Discussion, Drilland Practice, Demonstration, Brain Storming, Self Study, Problem Solving, | Testing, Homework, | |
| 5 | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Basic concepts of knot theory | |
| 2 | Simpleknot movements, knot equations, Rings | |
| 3 | Knot tables, Regular diagrams and alternate diagrams | |
| 4 | Knot graphs | |
| 5 | Simple problems of knot theory, Global problems, | |
| 6 | Local problems | |
| 7 | Classical knot invariants, Reidemeister movements, minimum number of intersections | |
| 8 | Number of bridges, Number of non-knotting, Number of ringing, Number of torsion | |
| 9 | Colors | |
| 10 | Knot groups, tunnel neighborhood | |
| 11 | Dehn representation, Wirtinger representation | |
| 12 | Meridians and paralels | |
| 13 | Surgical manifolds | |
| 14 | Homotopy and homology groups of surgical manifolds |
| Kaynaklar | |
|---|---|
| Ders Notu | 1.D. Rolfsen, Knots and Links, Math. Lecture series 7, Publ. Of Perish, 1976. |
| Ders Kaynakları | 1.L.Kauffman, Knots and physics, World Scientific Pub., 1991. |
| 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. | X | |||||
| 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 | ||