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| MAT7251 | Lattice Ordered Monoids | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Gül Deniz ÇAYLI | | Co-Lecturer | Prof. Dr. Cevat Hacıoğlu | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to work the fundamental concepts of po-gropoid , l-grupoid and l-mon |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | familiar with the notions of partially ordered groupoids , lattice ordered groupoids and lattice ordered monoids. | 1,2 | 1 | | PO - 2 : | work with the basic concepts of lattice ordered groupoids:Residuation, Integral l- groupoids, Maximal and Prime elements, Abstract İdeal Theory | 2,3,4 | 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), PO : Learning Outcome | | |
| Po-groupoids, Examples of l- groupoids and l- monoids, Residuation, Integral l- groupoids, Maximal and Prime elements, Abstract Ideal Theory, Funda mental Theorem of Ideal Theory, Frobenius l-monoids, postulates for Relation Algebras. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | po-groupoids | | | Week 2 | Divisibility Monoids | | | Week 3 | Archimedean monoids | | | Week 4 | Examples of l-groupoids and l-monoids | | | Week 5 | Residuation | | | Week 6 | Elementary Applications | | | Week 7 | Integral l-groupoids | | | Week 8 | Commutation Lattices | | | Week 9 | Mid-term exam | | | Week 10 | Maximal and prime elements | | | Week 11 | Abstract Ideal Theory | | | Week 12 | Fundamental Theorem of Ideal theory | | | Week 13 | Frobenius l-monoids | | | Week 14 | Algebra of Relations | | | Week 15 | Postulates for Relation Algebras | | | Week 16 | End-of-term exam | | | |
| 1 | Birkhoff, G., Lattice Theory, American Mathematical Socıety | | | |
| 1 | Fuchs L., Partially ordered Algebraic systems, Addison -Wesley Publishing company, inc.Oxford-London-New York-Paris | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 21/11/2012 | 2 | 50 | | End-of-term exam | 16 | 0101/2012 | 2 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 9 | 14 | 126 | | Arasınav için hazırlık | 8 | 1 | 8 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 194 |
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