Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Combinatorial Geometry II | MAT 533 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | YUKSEK_LISANS |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Dr.Öğr.Üyesi İBRAHİM ÖZGÜR |
Dersi Verenler | |
Dersin Yardımcıları | Research assistants of geometry |
Dersin Kategorisi | Diğer |
Dersin Amacı | To introduce non-Euclidean finite geometries and its combinatorial properties. |
Dersin İçeriği | Polar spaces, Quadrics, Linear subspaces, Generalized quadrangles, Subquadrangles, Partial geometries, Strongly regular graphs, Subgeometries, Paschs axiom. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/She designs polar spaces, | Lecture, Question-Answer, Motivations to Show, | Oral Exam, Homework, |
2 | He/She defines absolute points and quadrics, | Lecture, Question-Answer, | Oral Exam, Homework, |
3 | He/She explains linear subspaces, | Lecture, Question-Answer, | Homework, |
4 | He/She constructs projective spaces inside polar spaces, | Lecture, Question-Answer, | Homework, |
5 | He/She formulates polar spaces and generalized quadrangles | Lecture, Question-Answer, Drilland Practice, | Homework, |
6 | He/She suggests generalized subspace, generalized subspaces with s=t=3 and some properties of them, | Lecture, Question-Answer, Drilland Practice, | Homework, |
7 | He/She constitutes the construction of partial geometries and some Partial geometries, | Lecture, Question-Answer, | Homework, |
8 | He/She generates Strongly regular graphs and subgeometries, | Lecture, Question-Answer, | Homework, |
9 | He/She constitutes subgeometries, Paschs axiom. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Polar spaces | |
2 | Absolute points , Quadrics | |
3 | Linear subspaces | |
4 | Irreducibility | |
5 | Projective spaces inside polar spaces | |
6 | Some combinatorial properties | |
7 | Generalized quadrangles , definition and some basic results | |
8 | Generalized quadrangles with s=t=3 | |
9 | Subquadrangles | |
10 | Collineations of generalized quadrangles | |
11 | Partial geometries | |
12 | A method of constructing proper partial geometries | |
13 | Strongly regular graphs | |
14 | Subgeometries, Paschs axiom |
Kaynaklar | |
---|---|
Ders Notu | Combinatorics of Finite Geometries, Lynn. M. Batten, Cambridge, 1986. |
Ders Kaynakları | Finite Geometries, Tosiro Tsuzuko, 1990. The Theory of Finite Linear Spaces, L.,M., Batten ve A. Beutelspacher, 1993. |
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 | |||||
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 | |||||
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 | |||||
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 | |||||
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 | |||||
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 | |||||
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 | |||||
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. | 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. | 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 | |||||
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. Kısa Sınav | 10 |
2. Kısa Sınav | 10 |
1. Ödev | 10 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 40 |
1. Final | 60 |
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 | 4 | 64 |
Mid-terms | 1 | 15 | 15 |
Final examination | 1 | 15 | 15 |
Toplam İş Yükü | 142 | ||
Toplam İş Yükü / 25 (Saat) | 5,68 | ||
Dersin AKTS Kredisi | 6 |