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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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Basic notations about proositions and introduction to algebra of propositions (conjunction and disjunction)
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R1-Section 1
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2
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Implication (Conditional) and equivalence (biconditional)
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R1-Section 1
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3
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Quantifiers
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R1-Section 1
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4
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The notions of axioms, theorem and proof, introduction to methods of proof (proof by truth table and direct proof)
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R1-Section 1
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5
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Indirect proof methods, proof by contrapositive and proof by contradiction, falsification methods (giving counterexample, finding conflict)
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R1-Section 1
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6
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Mathematical induction
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R1-Section 1
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7
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More examples about methods of proof
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R1-Section 1
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8
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Basic notions of sets, Boolean operations on sets
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R1-Section 2
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9
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Finite-infinite intersections and unions, product of sets and basic notions about product sets
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R1-Section 4
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10
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Relations and their basic properties
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R1-Section 5
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11
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Equivalence relation
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R1-Section 5
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12
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Order relations
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R1-Section 5
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13
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Functions and their basic notions
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R1-Section 5
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14
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Functions of several variables
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R1-Section 5
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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. Gonca DURMAZ GÜNGÖR
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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. Akkaş, S., Hacısalihoğlu, H. H., Özel, Z., & Sabuncuoğlu, A. (1998). Soyut matematik. Ankara: Gazi Üniversitesi Yayınları.
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Supplementary Book
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SR1. Karaçay, T. (2013). Soyut Matematik, Seçkin Yayıncılık. SR2. Arıkan, A. ve Halıcıoğlu, S. (2018). Soyut Matematik. Palme Yayınevi.
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Goals
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Learning of theorems and concepts related to propositions, sets, relation and functions in detail.
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Content
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Propositions, quantifiers, proof methods, set, relations, and functions.
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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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4
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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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-
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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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-
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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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