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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
Katalog Ana Sayfa
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MATI7251Lattice Ordered Monoids3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 3 hours of lectures per week
LecturerProf. Dr. Funda KARAÇAL
Co-LecturerDoç. Dr. Ümit Ertuğrul, Doç. Dr. Gül Deniz Çaylı
Language of instruction
Professional practise ( internship ) None
 
The aim of the course:
The aim of the course is to investigate the fundamental concepts of po-gropoid, l-grupoid and l-monoid.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : The students will learn the concepts of partially ordered groupoids, lattice ordered groupoids and lattice ordered monoids.1,2,31,
PO - 2 : The students will investigate the basic properties of lattice ordered groupoids, residuation, integral l- groupoids, maximal and prime elements, abstract ideal theory.1,2,31,
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

 
Contents of the Course
Po-groupoids, Examples of l- groupoids and l- monoids, Residuations, Integral l- groupoids, Maximal and prime elements, Abstract Ideal Theory, Fundamental Theorem of Ideal Theory, Frobenius l-monoids, Postulates for relation algebras.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Po-groupoids
 Week 2Divisibility monoids
 Week 3Archimedean monoids
 Week 4Examples of l-groupoids and l-monoids
 Week 5Residuation
 Week 6Elementary applications
 Week 7Integral l-groupoids
 Week 8Commutation lattices
 Week 9Mid-term exam
 Week 10Maximal and prime elements
 Week 11Abstract ideal theory
 Week 12Fundamental theorem of ideal theory
 Week 13Frobenius l-monoids
 Week 14Algebra of relations
 Week 15Postulates for relation algebras
 Week 16End-of-term exam
 
Textbook / Material
1Birkhoff, G. 1948; Lattice Theory, American Mathematical Society Colloquium Publishers, Providence, RI
 
Recommended Reading
1Fuchs, L. 1963; Partially Ordered Algebraic Systems, Pergamon Press, Oxford, New York
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 26/04/2021 2 30
In-term studies (second mid-term exam) 13 24/05/2021 2 20
End-of-term exam 16 21/06/2021 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 3 14 42
Arasınav için hazırlık 10 8 80
Arasınav 2 1 2
Dönem sonu sınavı için hazırlık 9.5 6 57
Dönem sonu sınavı 2 1 2
Total work load225