Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Rıght Topologıcal Semı Groups | MAT 603 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | Doktora |
Dersin Türü | Seçmeli |
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. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/she investigates the properties of Beta-N semigroups. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
2 | He/she proves the finite sums theorem. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
3 | He/she investigates the Beta-S subgroup that is one of Stone-cech compactization of an S subgroup. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
4 | He/she learns the usega areas of Beta-S subgroup. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
5 | He/she knows the fundamental notions of Ramsey Theory. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
6 | He/she has knowledge about minimal dynamic systems. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
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. |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
---|---|---|---|---|---|---|---|
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. | ||||||
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. | X | |||||
2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
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. | ||||||
3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
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. | X | |||||
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. | ||||||
5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
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. | X | |||||
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. | ||||||
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. | X | |||||
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. | X | |||||
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. | ||||||
9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
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. |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 100 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 40 |
1. Final | 60 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (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 (Saat) | 6,44 | ||
Dersin AKTS Kredisi | 6 |