Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
COMBİNATORİAL GEOMETRY I MAT 532 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Dr.Öğr.Üyesi İBRAHİM ÖZGÜR Dersi Verenler Dersin Yardımcıları Research Assistants Dersin Kategorisi Dersin Amacı To introduce non-Euclidean finite geometries and its combinatorial properties. Dersin İçeriği Approximated linear spaces, dimension, linear functions, linear spaces, hyperplanes, projective planes, affine planes, finite projective planes, Desargues and Pappus configurations, embedding affine planes to projective planes
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She constitutes a finite geometrical structure and analysis its properties 1 - 4 - 15 - A - C - 2 - He/She analysis approximated linear spaces and its properties, 1 - 4 - 15 - A - C - 3 - He/She formulates approximated linear spaces and its combinatorial properties, 1 - 4 - 15 - A - C - 4 - He/She designs hyperplanes, 1 - 4 - 15 - A - C - 5 - He/She defines the finite an infinite projective planes, 1 - 4 - 15 - A - C - 6 - He/She generates the Desargues configurations in affine plane, 1 - 4 - 15 - A - C - 7 - He/She defines finite and infinite affine planes, 1 - 4 - 15 - A - C - 8 - He/She designs the embedding of an affine plane into the projective plane, 1 - 4 - 15 - A - C - 9 - He/She constructs the Desargues and Pappus configurations 1 - 4 - 15 - A - C - 10 - He/She designs affine paces. 1 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Near-linear spaces
2 Dimensions
3 Linear functions
4 Linear spaces
5 Hyperplanes
6 Projective planes
7 Finite projective planes
8 The Desargues configuration
9 The Pappus configuration
10 Affine planes
11 Finite affine planes
12 Embedding affine planes to projective planes
13 The Desargues configuration in affine planes
14 Affine spaces

#### Kaynaklar

Ders Notu [1] Lynn Margaret BATTEN, Combinatorics of Finite Geometries Cambridge Univ.
Press, 1986
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 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
4 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
5 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
6 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
7 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
8 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
9 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
10 Student determines the problems to be solved within his/her field and if necessary takes the lead.
11 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
12 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
13 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
14 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
15 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
16 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
17 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
18 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
19 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(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 15 15
Quiz 2 5 10
Assignment 1 5 5
Final examination 1 20 20
Toplam İş Yükü 146
Toplam İş Yükü /25(s) 5.84
Dersin AKTS Kredisi 5.84
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