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Course Description Course Name : Functional Analysis Course Code : MT-545 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Learning Outcomes of the Course : Fully understands the completeness of a metric space. Knows the relationship between normed spaces and completeness. Understands the importance of the Banach spaces Understands the importance of the Hilbert spaces. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : to provide knowledge about complete metric spaces, Banach spaces, Hilbert spaces, Hahn-Banach theorem, open mapping theorem and the Banach-Steinhaus Course Contents : Complete metric spaces, Kategory, normed spaces, Banach spaces, Hahn-Banach theorem, Baire category theorem, Hilbert spaces, conjugate spaces, Riez Representation Theorem, Banach Algebras. 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 Complete metric spaces Review of the relevant pages from sources Narration and discussion 2 Completion of a metric space Review of the relevant pages from sources Narration and discussion 3 Category and separable spaces. Review of the relevant pages from sources Narration and discussion 4 Normed spaces Review of the relevant pages from sources Narration and discussion 5 Banach spaces and examples. Review of the relevant pages from sources Narration and discussion 6 Hahn-Banach theorem Review of the relevant pages from sources Narration and discussion 7 The results of Hahn-Banach Theorem Review of the relevant pages from sources Narration and discussion 8 Mid-term exam topics discussed in the lecture notes and sources again Written Exam 9 Some consequences of Baire´s Theorem. Review of the relevant pages from sources Narration and discussion 10 Hilbert spaces. Review of the relevant pages from sources Narration and discussion 11 Some results on Hilbert spaces. Review of the relevant pages from sources Narration and discussion 12 Conjugate spaces Review of the relevant pages from sources Narration and discussion 13 Riesz Representation Theorem. Review of the relevant pages from sources Narration and discussion 14 Banach Algebras. Review of the relevant pages from sources Narration and discussion 15 Problem solving Review of the relevant pages from sources Narration and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Funtional Analysis, G. Bachman ve L. Narici, Academic Press, 1966.  Fonksiyonel Analizin Yöntemleri, Tosun Terzioğlu, 1984. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 1 10 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 3 2 Learns theoretical foundations of his/her field thoroughly 4 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 2 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 3 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 3 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 3 * 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 1 15 15     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 20 20 Total Workload: 143 Total Workload / 25 (h): 5.72 ECTS Credit: 6