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Week
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Topics
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Study Metarials
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1
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Set theory, metric spaces, complete metric spaces
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R1. Section 1.1
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2
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Definition of norm and some basic theorems
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R1. Section 2.1
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3
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Banach spaces
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R1. Section 2.2
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4
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Finite dimensional spaces
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R1. Section 2.3
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5
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Continuous and bounded linear operators
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R1. Section 3.1
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6
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Dual space and operator norm
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R1. Section 3.2
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7
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Hahn-Banach Theorem
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R1. Section 3.3
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8
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Open mapping theorem, Closed graph theorem
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R1. Section 3.4
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9
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Dual spaces
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R1. Section 4.1
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10
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Dual operators, weak convergence
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R1. Section 4.2
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11
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Inner product spaces
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R1. Section 5.1
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12
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Orthogonality, Orthogonal complement
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R1. Section 5.2
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13
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Hilbert spaces
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R1. Section 6.1
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14
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Fourier series
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R1. Section 7.1
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Assoc. Prof. Dr. Müfit ŞAN
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Instructors
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1-)Profesör Dr. Gonca Durmaz Güngör
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Assistants
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Assoc. Prof. Dr. Gonca DURMAZ GÜNGÖR
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Resources
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R1. Lecture Notes
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Supplementary Book
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SR1. Soykan Yüksel, (2008). Fonksiyonel Analiz, Nobel yayın dağıtım.
SR2. Lusternik, L. A., & Sobolev, V. J. (1974). Elements of Functional Analysis, Hindustan Pub. Corp., Delhi and New York.
SR3. Kolmogorov, A. N., & Fomin, S. V. (1975). Introductory real analysis. Courier Corporation.
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Goals
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The aim of this course is to teach basic concepts and theorems of functional analysis; to investigate basic spaces like Banach space.
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Content
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Complete metric spaces and completion of metric spaces, Normed spaces, Linear continous operators and functionals, Banach spaces, Hilbert spaces, Hahn-Banach Theorem, Weak and Weak* convergence
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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3
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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4
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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3
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4
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Analyze mathematical problems by using the gained research methods
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-
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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-
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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-
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Uses computer software and information technologies related to the field of mathematics at an advanced level.
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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