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| MAT3038 | Introduction to Semigroup Theory | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Sultan YAMAK | | Co-Lecturer | Doç. Dr. Gül Deniz ÇAYLI | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to enable students to gain knowledge about semigroup theory and its applications and to use this knowledge. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Comprehend algebraic structures more easily.
| 2,6 | 1 | | LO - 2 : | Can comprehend more sub-algebraic structures | 2,6 | 1 | | LO - 3 : | Students will be able to develop and deepen their knowledge of semigroup theory. | 2,6 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| The main objective of this course is to provide the students with a clear and comprehensible knowledge of elementary semigroup theory, commutative, regular, and inverse semigroups, congruence relations in semigroups, and ideals. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Groupoid, semigroups | | | Week 2 | Ordered semigroups | | | Week 3 | Regular Semigroups | | | Week 4 | Left and right cancellable semigroups | | | Week 5 | Left and right unit element, inverse element, | | | Week 6 | zero element, idempotent element | | | Week 7 | Subsemigroups, ideals | | | Week 8 | Quasi ideals | | | Week 9 | Midterm Exam | | | Week 10 | İnterior ideals | | | Week 11 | Ideals produced by sets | | | Week 12 | Congruence Relations | | | Week 13 | Quotient Sets | | | Week 14 | Green relations | | | Week 15 | General overview | | | Week 16 | General overview | | | |
| 1 | Ruskuc N., Semigroups, Course Notes, 2001. | | | |
| 1 | Howie J. M., Fundamentals of Semigroup Theory, Oxford University Press, 1995. | | | 2 | Ganyushkin O., Mazorchuk V., Classical Finite Transformation Semigroups: An Introduction, Springer, 2009. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 15/05/2025 | 1,5 | 50 | | End-of-term exam | 17 | 06/06/2025 | 1,5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 3 | 14 | 42 | | Arasınav için hazırlık | 23 | 1 | 23 | | Arasınav | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 25 | 1 | 25 | | Dönem sonu sınavı | 1.5 | 1 | 1.5 | | Diğer 1 | 17 | 1 | 17 | | Total work load | | | 166 |
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