Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
TOPOLOGICAL VECTOR SPACES I MAT 507 0 3 + 0 3 6
Ön Koşul Dersleri Topology I-II
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHPEYKER ÖZTÜRK Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Temel Öğretim Dersin Amacı To apprehend the properties of the topological vector spaces,to learn the local convex topological vector spaces,Convex sets and semi-norms, normed spaces and normable spaces,Hahn-Banach theorem,local convex spaces,projective topologies,reductive topologies,Barrelled spaces,Bornological spaces,Compact Convex sets. Dersin İçeriği Topological vector spaces(TOPOLOGY OF VECTOR SPACES,product spaces,subspace,direct sum,quotient space,topological vector spaces with finite dimension,Linear manifolds and hyperplanes,bounded sets,metrizable,complexification),Local convex topological vector spaces(convex sets and semi norms, normed and normable spaces Hahn-Banach theorem,local convex spaces,projective topologies,reductive topologies,Barrelled spaces,Bornological spaces,Compact Convex sets.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/ she recognizes the Topological vector spaces 1 - 2 - 3 - 14 - A - C - 2 - He/ she explains the local convex topological vector spaces 1 - 2 - 3 - 14 - A - C - 3 - He/ she interprets the convex sets and semi-norms, normed and normable spaces. 1 - 2 - 3 - 14 - A - C - 4 - He/ she recognizes the Local convex spaces, ,Barrelled spaces,Bornological spaces 1 - 2 - 3 - 14 - A - C - 5 - He/ she defines projective topologies and reductive topologies. 1 - 2 - 3 - 14 - A - C - 6 - He/she recognizes the compacy convex sets. 1 - 2 - 3 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 14:Self Study Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Topological vector spaces
2 TOPOLOGY OF VECTOR SPACES
3 product spaces,subspace
4 direct sum,quotient space,
5 topological vector spaces with finite dimension
6 Linear manifolds and hyperplanes
7 bounded sets,metrizable,complexification,
8 Local convex topological vector spaces
9 ıntermediate examination
10 convex sets and semi norms
11 normed and normable spaces Hahn-Banach theorem,
12 local convex spaces,projective topologies,reductive topologies
13 Barrelled spaces,Bornological spaces
14 Compact Convex sets.

#### Kaynaklar

Ders Notu

[1][1] H. H. Schaefer, M. P. Wolff, Topological Vector Spaces, Springer, New York, NY, 1999

Ders Kaynakları

[2] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul

[3] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London.
[4] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul
[5] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.

#### 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.
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.
10 Student follows the current journals in his/her field and puts forward problems. X
11 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
12 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
13 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
14 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
15 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
16 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
17 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
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 80
Odev 1 10
Odev 2 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 20 20
Assignment 2 10 20
Final examination 1 25 25
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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