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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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Operations, definition and examples
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R1 - Section 7
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2
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Properties of an operation (commutative property, associative property, inverse element, identity element)
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R1 - Section 7
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3
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Groups, Examples of Groups and Ring
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R1 - Section 8
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4
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Cardinalities of sets, numerically equivalent sets
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R1 - Section 8
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5
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Countable and uncountable sets
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R1 - Section 9
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6
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Comparing cardinalities of sets and Schröder-Bernstein Theorem
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R1 - Section 9
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7
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Construction of natural number set
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R1 - Section 9
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8
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Addition and multiplication for natural numbers
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R1 - Section 9
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9
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Mathematical induction, addition and multiplication symbol
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R1 - Section 9
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10
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Construction of integers set
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R1 - Section 10
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11
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Division algorithm, least common multiple, greatest common divisor
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R1 - Section 10
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12
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Construction of rational numbers, addition and multiplication for rational numbers
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R1 - Section 11
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13
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Properties of rational numbers
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R1 - Section 11
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14
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Construction of real numbers and properties
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R1 - Section 12
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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 - Arıkan, A. ve Halıcıoğlu, S. (2018). Soyut Matematik. Palme Yayınevi.
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Supplementary Book
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SR1- Karaçay, T. (2013). Soyut Matematik, Seçkin Yayıncılık. SR2 - Hacısalihoğlu, H. H. ve Özel, Z. (2020). Soyut Matematik. Seçkin Yayıncılık.
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Goals
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It is a reality that a subtantial number of students who do well in the calculus courses have difficulty with their first theoretical upper-division course.The transition from the rather routine problem solving involved in the study of calculus to abstract proof-oriented advanced courses is too abrupt for these students. The aim of this course is to bridge the gap referred to above,to teach what a valid proof is, and to enable the student to construct simple proofs.
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Content
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Binary operations and properties of binary operations Cayley table and examples of binary operation Construction of natural numbers Addition and multiplication for natural numbers Mathematical induction Construction of integers, addition and multiplication for integers Division algorithm, least common multiple, greatest common divisor Construction of rational numbers, addition and multiplication for rational numbers Properties of rational numbers Cardinalities of sets, numerically equivalent sets, uncountable sets Comparing cardinalities of sets and Schröder-Bernstein Theorem
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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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4
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2
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Ability of abstract thinking
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-
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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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-
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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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