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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, absolute value, and some inequalities (Hölder and Minkowski inequalities)
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R1-Section 1
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2
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Convergence in real numbers
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R1-Section 1
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3
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Continuity in real numbers
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R1-Section 1
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4
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Metric spaces
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R1-Section 1
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5
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Normed spaces
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R2-Lecture Notes
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6
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Subspaces
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R2-Lecture Notes
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7
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Open and closed sets
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R1-Section 2
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8
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Open and closed sets in the subspace
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R1-Section 2
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9
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Neighborhoods and Limit Points
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R1-Section 2
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10
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Equivalent Metrics
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R1-Section 2
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11
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Convergence in metric spaces
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R1-Section 3
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12
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Continuity in metric spaces
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R1-Section 3
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13
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Convergence in normed space
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R1-Section 3
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14
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Continuity in normed space
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R2-Lecture Notes
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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. Mustafa ASLANTAŞ
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Instructors
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1-)Doçent Dr Mustafa Aslantaş
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Assistants
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The related lecturers of the department
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Resources
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R1) Shirali, S., Vasudeva, H. L., Metric spaces. Springer Science & Business Media, 2005., Lecture notes
R2) Lecture Notes
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Supplementary Book
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K1) S.A. Kılıç, M. Erdem, Metrik Uzaylar ve Genel Topoloji, Nobel Yayın Evi, 2008, Ankara.
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Goals
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To teach metric spaces and their basic properties.
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Content
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Metric spaces and their basic properties
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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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-
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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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3
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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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