Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
GEOMETRIC TOPOLOGY MAT 571 0 3 + 0 3 6
Ön Koşul Dersleri Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II, Topology I and Topology II.
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. SOLEY ERSOY Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı The aim of this course is to give some differential topological fundamental notions for the studies of graduate students who study at geometry and topology branch. Dersin İçeriği Toplogy of subsets of Euclidean space, open and closed subsets of sets in , continuous maps, homeomorphims, connectedness, compactness, arcs, discs, 1-spheres, surfaces in , surfaces via gluing, properties of surfaces, connected sum and the classification of compact connected surfaces, simplices, simplicial complexes and simplicial surfaces (simplicial complexes with underlying spaces that are topological surfaces), the Euler characteristic, simplical curvature and the Gauss Bonnet thoerem
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she recalls the fundamental notions of topology 1 - 2 - 3 - A - C - 2 - He/she defines the fundamental notions of surface theory 1 - 2 - 3 - A - C - 3 - He/she interprets connectedness, compactness notions on subsets of Euclidean space 1 - 2 - 3 - 8 - 15 - A - C - 4 - He/she investigates properties of surfaces 1 - 2 - 3 - 8 - 15 - A - C - 5 - He/she defines simplices, simplicial complexes and simplicial surfaces 1 - 2 - 3 - 8 - 15 - A - C - 6 - He/she classifies compact connected surfaces 1 - 2 - 3 - A - C - 7 - He/she explains and proves the theorem of Gauss Bonnet 1 - 2 - 3 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 8:Group Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Toplogy of subsets of Euclidean space
2 Open and closed subsets of sets in
3 Continuous maps, homeomorphims,
4 Connectedness, compactness
5 Arcs, discs, 1-spheres,
6 Surfaces in , surfaces via gluing,
7 Properties of surfaces
8 Connected sum
9 The classification of compact connected surfaces,
10 Simplices, simplicial complexes
11 Simplicial surfaces (simplicial complexes with underlying spaces that are topological surfaces),
12 The Euler characteristic,
13 Simplical curvature
14 Gauss Bonnet thoerem

#### Kaynaklar

Ders Notu

1. Ethan D. Bloch, "A First Course in Geometric Topology and Differential Geometry" Birkhäuser Boston, 1996.

Ders Kaynakları

2. Daverman R.J. and Sher R.B., Editors, Handbook of Geometric Topology, North- Holland, Amsterdam 2002.
3. Armstrong, M.A. Basic Topology, Springer Verlag, 1983.

#### 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 understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 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 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 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 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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
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 20 20
Assignment 1 10 10
Final examination 1 30 30
Toplam İş Yükü 156
Toplam İş Yükü /25(s) 6.24
Dersin AKTS Kredisi 6.24
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