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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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Matchings and covers
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R1- Chapter 3.1
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2
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Algorithms and applications
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R1- Chapter 3.2
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3
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Cuts and connectivity
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R1- Chapter 4.1
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4
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k-connected graphs
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R1- Chapter 4.2
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5
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Network flow problems
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R1- Chapter 4.3
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6
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Vertex colorings and upper bounds
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R1- Chapter 5.1
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7
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Structures of k-chromatic graphs
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R1- Chapter 5.2
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8
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Counting proper colorings
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R1- Chapter 5.3
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9
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Embeddings and Euler?s formula
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R1- Chapter 6.1
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10
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Characterization of planar graphs
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R1- Chapter 6.2
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11
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Parameters of planarity
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R1- Chapter 6.3
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12
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Line graphs and edge-colorings
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R1- Chapter 7.1
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13
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Hamiltonian cycles
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R1- Chapter 7.2
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14
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Planarity, coloring, and cycles
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R1- Chapter 7.3
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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. Faruk KARAASLAN
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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- West, D. (2017). Introduction to Graph Theory (Classic Version) (2nd Ed.). Pearson, London.
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Supplementary Book
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SR1- Chartrand, G. and Zhang, P. (2020). Chromatic Graph Theory (2nd Ed.), CRC Press, Boca Raton, FL.
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Goals
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To outline basic notions related to graphs, to introduce basic problems of graph theory, also to exemplify some applications of graphs.
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Content
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Matchings and factors, connectivity and paths, colorings of graphs, planar graphs, edges and cycles.
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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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2
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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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3
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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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-
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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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2
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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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