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Course Description Course Name : Topological Groups Course Code : MT-526 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. ALİ ARSLAN ÖZKURT Learning Outcomes of the Course : Can explain the concept of topological group Know global and local properties of topological groups Investigate the action of a topological group on a topological space Know the structure of the continuous real valued functions on the topological groups Know the existence of Haar integral on a compact group and its consequences Know some knowledge about the representation of compact groups Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : to give the concept of topological groups and investigate the actions of a topological group on a topological space, in particular to investigate representations of topological groups. Course Contents : Definition of topological group and some examples, global and local properties of topological groups, actions of topological groups on a topolocial space, continuous real valued functions on a topological groups, Haar integration and representation of topological groups Language of Instruction : Turkish Work Place : classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Definition of topological group and neighbourhood system of the identity Read the relevant sections in the textbook and solving problems Lecture and discussion 2 Subgroups, normal subgroups and factor groups Read the relevant sections in the textbook and solving problems Lecture and discussion 3 Subgroups, normal subgroups and factor groups Read the relevant sections in the textbook and solving problems Lecture and discussion 4 topological homomorphisms and topological isomorphisms Read the relevant sections in the textbook and solving problems Lecture and discussion 5 direct product of topological groups Read the relevant sections in the textbook and solving problems Lecture and discussion 6 connected and totally disconnected topological groups Read the relevant sections in the textbook and solving problems Lecture and discussion 7 local properties of topological groups and local isomorphisms Read the relevant sections in the textbook and solving problems Lecture and discussion 8 evaluation and solutions of homeworks Review of the topics discussed in the lecture notes and source again Lecture and discussion 9 local properties of topological groups and local isomorphisms Read the relevant sections in the textbook and solving problems Lecture and discussion 10 topological transformation groups Read the relevant sections in the textbook and solving problems Lecture and discussion 11 topological transformation groups Read the relevant sections in the textbook and solving problems Lecture and discussion 12 continuous real valued functions on topological groups Read the relevant sections in the textbook and solving problems Lecture and discussion 13 Haar integration on compact topological groups Read the relevant sections in the textbook and solving problems Lecture and discussion 14 Schur lemma Read the relevant sections in the textbook and solving problems Lecture and discussion 15 Peter-Weyl theorem Read the relevant sections in the textbook and solving problems Lecture and discussion 16/17 evaluation and solutions of homeworks Review of the topics discussed in the lecture notes and source again Lecture and discussion   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Topological Groups, L.S. Pontryagin Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 0 0     Homeworks/Projects/Others 2 100 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 4 2 Learns theoretical foundations of his/her field thoroughly 5 3 Uses the knowledge in his/her field to solve mathematical problems 4 4 Proves basic theorems in different areas of Mathematics 3 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 3 6 Uses technical tools in his/her field 3 7 Works independently in his/her field requiring expertise 4 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 4 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 4 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 4 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 1 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 2 25 50     Mid-term Exams (Written, Oral, etc.) 0 0 0     Final Exam 0 0 0 Total Workload: 148 Total Workload / 25 (h): 5.92 ECTS Credit: 6