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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
PROJECTIVE GEOMETRY MAT 467 7 2 + 0 2 5
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Lisans
Dersin Türü SECMELI
Dersin Koordinatörü Dr.Öğr.Üyesi İBRAHİM ÖZGÜR
Dersi Verenler
Dersin Yardımcıları Research assistants of Mathematics Department
Dersin Kategorisi
Dersin Amacı
Acquainted with the non-Euclidean geometry and speciality projective geometry.
Dersin İçeriği
Euclidean geometry and other geometries. Several geometric structures. Affine planes. Projective planes. The relations between affine and projective planes, and subplanes. Desarguesian, Pappian and Fano planes. Projective planes on division rings. Projective planes which are supply Fanos axiom or are not supply Fanos axiom.
Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - He/She questions deficiencies of Euclidean geometry, 1 - 2 - 4 - A - C -
2 - He/She examines non-Euclidean geometries, 1 - 4 - A - C -
3 - He/She defines affine space, uses the theorems related to affine spaces and illustrates them, 1 - 2 - 3 - A - C -
4 - He/She illustrates and interprets especially finite projective geometry via axiomatic or algebraic ways, 1 - 3 - A - C -
5 - He/She examines various coordinate systems and the different geometric structures, 1 - 4 - A - C -
6 - He/She examines Desarguesian and Pappian planes, 1 - 3 - 4 - A - C -
7 - He/She interprets division rings and projective planes on division rings, 1 - 2 - 3 - 4 - A - C -
8 - He/She questions Fanos axiom and projective planes which supply Fanos axiom or are not supply Fanos axiom, 1 - 2 - 4 - A - C -
9 - He/She interprets Desarguesian and Pappian planes, 1 - 3 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 3:Discussion
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Euclidean geometry and other geometries.
2 Several geometric structures.
3 Affine planes. Theorems and examples.
4 Projective planes. Theorems and examples.
5 The relations between affine and projective planes, and subplanes.
6 Other geometric structures.
7 Desarguesian planes.
8 Pappian planes.
9 Division rings and projective planes on division rings.
10 Fanos axiom. Projective planes which are supply Fanos axiom or are not supply Fanos axiom.
11 The relations between Desarguesian and Pappian planes, and theorems.
12 Transformations in projective planes. Isomorphism and automorphism.
13 One-dimensional transformations. Perspectives and projection.
14 Perspectives and projection.

Kaynaklar

Ders Notu Prof. Dr. Rüstem KAYA, Projektif Geometri, Üçüncü Baskı, Osmangazi Üniversitesi, 2005.
Ders Kaynakları

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 80
KisaSinav 1 5
Odev 1 10
KisaSinav 2 5
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 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 10 10
Quiz 2 5 10
Assignment 1 3 3
Final examination 1 20 20
Toplam İş Yükü 107
Toplam İş Yükü /25(s) 4.28
Dersin AKTS Kredisi 4.28
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