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Course Description Course Name : Semigroup Structures and Presentations Course Code : MT-550 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Prof.Dr. GONCA AYIK Learning Outcomes of the Course : Recognizes semigroups and semigroups structures finds the generating sets of semigroups finds the ranks of semigroups Recognizes some special semigroups finds presentations of semigroups finds presentations of monoids Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : MT-551 Semigroup Theory Recommended Optional Programme Components : None Aim(s) of Course : Recognize semigroups and semigroups structures. Finding generating sets of semigroups, Finding ranks of semigroups, Recognizing some special semigroups , Finding presentations of semigroups, Finding presentations of monoids Course Contents : Fundamental definitions and theorems in semigroup theory, Generating sets, Rank of a semigroup, Generating sets of some semigroup structures , Rees Matrix Semigroups, Simple semigroups and zero simple semigroups, Green equivalence, Generating sets of subsemigroups, Semigroup presentations, Finding presentations of semigroup, Direct method for finding presentations of semigroup, Tietze transformations, Coset enumeration , Presentations and word problem for strong semilattices of semigroups, Monoid presentations Language of Instruction : Turkish Work Place : Department of Mathematics, Seminar Room   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Fundamental definitions and theorems in semigroup theory Reviewing the relevant chaptes in the Sources Lecture and discussion 2 Generating sets Reviewing the relevant chaptes in the Sources Lecture and discussion 3 Rank of Semigroups Reviewing the relevant chaptes in the Sources Lecture and discussion 4 Generating sets of some semigroup constructions Reviewing the relevant chaptes in the Sources Lecture and discussion 5 Rees Matrix Semigroups Reviewing the relevant chaptes in the Sources Lecture and discussion 6 Simple semigroups and zero simple semigroups Reviewing the relevant chaptes in the Sources Lecture and discussion 7 Green Equivalence, Generating sets of sub semigroups Reviewing the relevant chaptes in the Sources Lecture and discussion 8 Mid term Exam Review Written exam 9 Semigroup presentations Reviewing the relevant chaptes in the Sources Lecture and discussion 10 Finding presentations of semigroup Reviewing the relevant chaptes in the Sources Lecture and discussion 11 Direct method for finding presentations of semigroup Reviewing the relevant chaptes in the Sources Lecture and discussion 12 Tietze transformations Reviewing the relevant chaptes in the Sources Lecture and discussion 13 Coset Enumaration Reviewing the relevant chaptes in the Sources Lecture and discussion 14 Presentations and word problem for strong semilattices of semigroups Reviewing the relevant chaptes in the Sources Lecture and discussion 15 Monoid presentations Reviewing the relevant chaptes in the Sources Lecture and discussion 16/17 Final Exam Review Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Fundamentals of Semigroup Theory, Oxford Science Publications,J.M. Howie 2003. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   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 2 Learns theoretical foundations of his/her field thoroughly 5 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 3 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).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 20 20     Final Exam 1 20 20 Total Workload: 138 Total Workload / 25 (h): 5.52 ECTS Credit: 6