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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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Sets and functions
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R1-Section 1
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2
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Absolute value and some inequalities
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R1-Section 2
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3
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Convergence and continuity in reel numbers
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R1-Section 3
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4
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Metric spaces
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R2-Section 1
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5
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Examples of metric spaces
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R2-Section 2
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6
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Normed spaces and their examples
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R2-Section 2
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7
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Subspaces
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R2-Section 3
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8
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Open and closed sets
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R2-Section 3
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9
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Open and closed sets in subspaces
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R2-Section 3
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10
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Metric topology
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R2-Section 4
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11
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Neighborhoods in metric spaces
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R2-Section 4
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12
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Limit points and closure of a set in metric spaces
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R2-Section 4
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13
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Interior, exterior and boundary of a set in metric and dense set
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R2-Section 4
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14
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Convergence in metric spaces
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R2-Section 5
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Assoc. Prof. Dr. Mustafa ASLANTAŞ
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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. Willard, S. (1970). General Topology, Reading. Mass.: Addison Wesley Pub. Co.
R2. Lecture Notes
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Supplementary Book
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SR1. Lipschutz, S. (1965). Schaum`s outline of general topology (Vol. 37). McGraw Hill Professional.
SR2. Engelking, R. (1989). Sigma series in pure mathematics. In General topology. Berlin: Heldermann.
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Goals
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Identifies the concepts of metric space and norm space. Comments open and closed sets in metric spaces. Explains the relationship between concentration points and convergence in metric spaces.
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Content
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Sets and functions, Absolute value and some inequalities, Convergence and continuity in reel numbers, Metric spaces, Examples of metric spaces, Normed spaces and their examples, Subspaces, Open and closed sets, Open and closed sets in subspaces, Metric topology, Neighborhoods in metric spaces, Limit points and closure of a set in metric spaces, Interior, exterior and boundary of a set in metric and dense set, Convergence in metric spaces.
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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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-
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2
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Ability of abstract thinking
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3
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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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-
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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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3
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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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