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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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Metric and Metric spaces, neighborhood of a point , open and closed sets in metric spaces
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R1. Section 1.1
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2
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Sequences in metric spaces and their convergence, Hölder and Minkowski inequalities, Classical sequence spaces
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R1. Section 1.2
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3
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Complete metric spaces, First and second countable metric spaces, Baire Category Theorem
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R1. Section 1.3
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4
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Continuous functions between metric spaces and their properties
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R1. Section 2.1
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5
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Vector space, subspace, norm, normed space, Banach space, examples of normed spaces
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R1. Section 2.2
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6
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Finite dimensional normed spaces
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R1. Section 2.3
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7
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Bounded and continuous linear operators
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R1. Section 3.1
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8
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Linear operators and functionals in finite dimensional spaces, Normed operator spaces, Dual space
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R1. Section 3.2
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9
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Hahn-Banach Teorem, Hahn-Banach Theorem for normed spaces
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R1. Section 3.3
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10
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Applications of bounded linear functionals defined on continuous function spaces, Reflexive spaces
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R1. Section 4.1
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11
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Banach-Steinhaus Theorem and its applications
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R1. Section 4.2
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12
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Open Mapping Theorem and its applications
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R1. Section 4.3
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13
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Closed linear operators
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R1. Section 5.1
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14
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Closed Graph theorem and its applications
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R1. Section 5.2
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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. Gülsüm Ulusoy Ada
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Instructors
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-
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Assistants
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-
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Resources
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R1. Lecture notes
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Supplementary Book
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SR1. Kreyszig, E. (1978). Introductory functional analysis with applications (Vol. 1). New York
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Goals
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The aim of the course is to show norm concept, normed space, linear bounded operators between normed saces together with some applications of them
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Content
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Metric spaces, normed spaces, linear functionals, linear bounded operators on normed space,Hahn-Banach theorem, Banach Steinhauss theorem, Open mapping and closed graph theorem
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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3
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2
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Ability of abstract thinking
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-
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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2
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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-
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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3
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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-
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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-
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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-
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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-
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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