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Prerequisites
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Language of Instruction
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Turkish
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Responsible
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Asst. Prof. Dr. Kahraman Esen ÖZEN
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Instructors
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Assistants
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Resources
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R1. Çelik, B. (2018). Soyut Matematik, 3. Baskı. Dora Yayıncılık, Bursa
R2. Güzeltepe, M. (2017). Genel Matematik 1, 1. Baskı. Sakarya Yayıncılık, Sakarya
R3. Yüce, S. (2017). Öklid Uzayında Diferansiyel Geometri, 1. Baskı. Pegem Akademi, Ankara
R4. Hacısalihoğlu, H. H. (2000). Diferensiyel Geometri, Cilt I, 4. Baskı. Ankara Üniversitesi Fen Fakültesi Yayınları, Ankara
R5. Yüksel, Ş. (2008). Genel Topoloji, 6. Baskı. Eğitim Kitabevi, Konya
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Supplementary Book
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SR1. Şahin, B. (2012). Manifoldların Diferensiyel Geometrisi, Nobel Yayıncılık, Ankara
SR2. Sabuncuoğlu, A. (2014). Diferensiyel Geometri, 5. Basım. Nobel Yayıncılık, Ankara
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Goals
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To teach the concept of manifold and to study the basic properties of differential calculus on manifolds
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Content
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Functions, Directional Derivatives, Covariant Derivative, Topological manifolds, Differentiable manifolds, Coordinate neighborhood, Atlas
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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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2
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Ability of abstract thinking
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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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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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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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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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2
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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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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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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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3
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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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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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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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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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