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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
RIGHT TOPOLOGICAL SEMI GROUPS MAT 603 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Doktora
Dersin Türü SECMELI
Dersin Koordinatörü Prof.Dr. REFİK KESKİN
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi Diğer
Dersin Amacı

Finite sums theorem can be proved in a simple way by using the properties of Beta-N subgroup. It is shown that many Theorems known as Ramsey Theory can be proven simply by analysing Beta-S subgroup that is one of Stone-cech compactization of an S subgroup. Our aim is to analyse this topic that is studied during last 40 years consistently.

Dersin İçeriği

Subgroups and their ideals, Right topological subgroups, ultrafilters, Stone-Cech compactinization of a discrete space, Beta-S subgroup, Beta-S and Ramsey Theory, İdempotents and finite products, sums and products in N, commutativeness in Beta-S, abbreviation in Beta-S, minimal dynamic systems, dynamic center sets.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - He/she investigates the properties of Beta-N semigroups. 1 - 4 - 15 - A - C -
2 - He/she proves the finite sums theorem. 1 - 4 - 15 - A - C -
3 - He/she investigates the Beta-S subgroup that is one of Stone-cech compactization of an S subgroup. 1 - 4 - 15 - A - C -
4 - He/she learns the usega areas of Beta-S subgroup. 1 - 4 - 15 - A - C -
5 - He/she knows the fundamental notions of Ramsey Theory. 1 - 4 - 15 - A - C -
6 - He/she has knowledge about minimal dynamic systems. 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 Subgroups and their ideals
2 Right topological subgroups
3 Ultrafilters
4 Stone-Cech compactinization of a discrete space
5 Beta-S subgroup
6 Beta-S and Ramsey Theory
7 İdempotents and finite products
8 İdempotents and finite products
9 Sums and products in N
10 Commutativeness in Beta-S
11 Abbreviation in Beta-S
12 Mminimal dynamic systems
13 Mminimal dynamic systems
14 Dynamic center sets

Kaynaklar

Ders Notu
Ders Kaynakları

1-Neil Hindman, Dona strauss, Algebra in the Stone-Cech Compactification, Walter De Gruyter, 1998.


Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application.
2 Student completes the missing or limited knowledge by using the scientific methods.
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result.
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field.
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches.
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity.
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters.
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work.
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
10 Student follows the necessary technological developments in his/her field, and s/he uses them.
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data.
12 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
13 Student completes the missing or limited knowledge by using the scientific methods. X
14 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
15 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
16 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
17 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
18 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
19 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
20 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
21 Student follows the necessary technological developments in his/her field, and s/he uses them. 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 20 20
Assignment 1 15 15
Performance Task (Laboratory) 1 30 30
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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