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| Course Description |
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| Course Name |
: |
Semigroup Theory |
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| Course Code |
: |
MT-551 |
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| Course Type |
: |
Optional |
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| Level of Course |
: |
Second Cycle |
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| Year of Study |
: |
1 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
6 |
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| Name of Lecturer(s) |
: |
Prof.Dr. GONCA AYIK
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| Learning Outcomes of the Course |
: |
Recognizes semigroups and semigroup constructions
Recognizes semigroups homomorphism
Recognizes congruences
Recognizes semigroup and monoid presentations
Recognizes Ideals and Rees congruences
Recognizes simple and zero simple semigroups
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Recognize semigroups and semigroup structures , Recognize semigroups homomorphism, Recognize congruences, Recognize semigroup and monoid presentations, Recognize Ideals and Rees congruences, Recognize simple and zero simple semigroups
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| Course Contents |
: |
Semigroups and examples of semigroups, Monogenic semigroups,Ordered sets , semilattices and lattices, Equivalence relations, Congruences, Semigroup homomorphism, free semigroup, Presentations of semigroups and monoids, Ideals and Rees congruences, Green Equivalences, Structure of D-classes, Regular D-classes, Regular semigroups, Simple and zero simple semigroups, Completely simple semigroups |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Department of Mathematics, seminar room |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Semigroups and examples of semigroups |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
2 |
Monogenic semigroups |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
3 |
Ordered sets , semilattices and lattices |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
4 |
Equivalence relations |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
5 |
Congruences |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
6 |
Semigroup homomorphism, free semigroup |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
7 |
Presentations of semigroups and monoids |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
8 |
Mid term Exam |
Review and Problem solving |
Written Exam |
|
9 |
Ideals and Rees congruences |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
10 |
Green Equivalences |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
11 |
Structure of D-classes |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
12 |
Regular D-classes |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
13 |
Regular semigroups |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
14 |
Simple and zero simple semigroups |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
15 |
Completely simple semigroups |
Reviewing the relevant chaptes in the Sources |
Lecture, Problem Solving |
|
16/17 |
Final exam |
Review and problem solving |
Exam |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Fundamentals of semigroup theory, Oxford Science Publication,J.M. Howie, 2003
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| |
| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
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Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Aquires sufficient knowledge to enable one to do research over and above the undergraduate level |
5 |
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2 |
Learns theoretical foundations of his/her field thoroughly |
5 |
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3 |
Uses the knowledge in his/her field to solve mathematical problems |
5 |
|
4 |
Proves basic theorems in different areas of Mathematics |
5 |
|
5 |
Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. |
5 |
|
6 |
Uses technical tools in his/her field |
5 |
|
7 |
Works independently in his/her field requiring expertise |
5 |
|
8 |
Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process |
5 |
|
9 |
Argues and analyzes knowledge in his/her field and applies them in other fields if necessary |
5 |
|
10 |
Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders |
5 |
|
11 |
Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary |
5 |
|
12 |
Knows and abides by the ethical rules in analyzing, solving problems and publishing results |
5 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
|
Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
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Out of Class Study (Preliminary Work, Practice) |
14 |
4 |
56 |
| Assesment Related Works |
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Homeworks, Projects, Others |
0 |
0 |
0 |
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Mid-term Exams (Written, Oral, etc.) |
1 |
20 |
20 |
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Final Exam |
1 |
20 |
20 |
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Total Workload: | 138 |
| Total Workload / 25 (h): | 5.52 |
| ECTS Credit: | 6 |
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