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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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Open and closed sets in IR^{n}
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R1-Section-2
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2
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Relative neighborhoods, continuity
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R1-Section-2
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3
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Compact and connected sets
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R1-Section-2
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4
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Product and quotient spaces, identification space
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R1-Section-3
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5
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Complexes
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R1-Section-4
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6
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Surfaces, surfaces with boundary
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R1-Section-4, R2-Section-5
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7
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Connected sum, classification of surfaces
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R1-Section-4, R2-Section-6
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8
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Triangulations, simplicial complexes
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R1-Section-4, R2-Section-5
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9
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Graph and trees
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R1-Section-5, R2-Section-8
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10
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The Euler characteristic and the sphere
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R1-Section-5
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11
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The Euler characteristic and surfaces
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R1-Section-5, R2-Section-10
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12
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Directed Complexes
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R1-Section-6
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13
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The algebra of chains
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R1-Section-6, R2-Section-12
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14
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Homology groups
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R1-Section-6, R2-Section-13
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Prerequisites
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Topology I, Topology II, Algebra I
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Language of Instruction
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English
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Responsible
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Asst. Prof. Dr. Hanife Varlı
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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. Kinsey. L. C. (1993). Topology of Surfaces, Springer-Verlag
R2. Introduction to Geometric Topology Lecture notes
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Supplementary Book
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SR1. Bozhüyük, M. E. (1984). Genel Topolojiye Giriş (Uzaylar Bilimi), Atatürk Üniversitesi Basım Evi
SR2. Bloch, E. D. (1997). A first course in Geometric Topology and Differential Geometry, Birkhauser Boston Inc.Div. of Springer-Verlag N.Y., Inc. 675 Massachusetts Avenue Cambridge, MAUnited States
SR3. Karaca, İ. Geometrik Topology ders notları
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Goals
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To introduce the concept of the surface and show its construction. To demonstrate the invariants used for the classification of the surfaces.
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Content
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Surfaces, connected sums, classification of the surfaces and some invariants, simplicial complexes, and homology groups
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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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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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-
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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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-
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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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3
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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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