Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MODERN GENERAL TOPOLOGY MAT 515 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHPEYKER ÖZTÜRK Dersi Verenler Doç.Dr. MAHPEYKER ÖZTÜRK Dersin Yardımcıları Dersin Kategorisi Diğer Dersin Amacı Betraying the relation of topology between other branches of mathematics. Dersin İçeriği Fundamental notions, set theory, functions, continuity, topological transformations, choice axioms, connectedness, compact spaces,countable compact spaces, compactinization, Stone-Cech compactness, metric spaces, function spaces, Peano spaces, simple closed curves, manifolds, general dynamics, fixed points.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she recalls the fundamental notions of topology. 1 - 4 - 15 - A - C - 2 - He/she learns the useage of the notions of topology in other areas. 1 - 4 - 15 - A - C - 3 - He/she understands the theorems related to continuity and topological transformations and he/she gains the ability to prove other theorems related to the subject. 1 - 4 - 15 - A - C - 4 - He/she recalls the notions of axiom of choice and connectedness 1 - 4 - 15 - A - C - 5 - He/she has knowledge about compact spaces, countable and false compact spaces. 1 - 4 - 15 - A - C - 6 - He/she proves theorems of compactness. 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 Fundamental notions
2 Set theory and functions
3 Continuity and topological transformations
4 Choice axioms and connectedness
5 Compact spaces, Countable compact spaces
6 Compactness
7 Stone-Cech compactness
8 Metric spaces
9 Function spaces
10 Peano spaces
11 Simple closed curves
12 Manifolds
13 General dynamics
14 Fixed points

#### Kaynaklar

Ders Notu
Ders Kaynakları

1-Scott W. Williams, Modern General Topology with Dynamics and Homotopy, John Wiley, 1996.
2- James R. Munkers, Topology, Printice Hall, 2000.

#### 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. X
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 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
20 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 1 100
Toplam 100
Yıliçinin Başarıya Oranı 40
Finalin Başarıya Oranı 60
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 30 30
Assignment 1 15 15
Performance Task (Laboratory) 1 20 20
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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