Course Name Code Semester T+U Hours Credit ECTS
Right Topological Semi Groups MAT 603 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. REFİK KESKİN
Course Lecturers
Course Assistants
Course Category Other
Course Objective

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.

Course Content

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.

# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes
Course Resources

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

Order Program Outcomes Level of Contribution
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.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6