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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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Definition and examples of binary operattion
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R1-Section 2.6,2.7,2.8
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2
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Properties of the binary operations
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R1-Section 2.7,2.8
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3
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Construction of Natural Numbers, definition of addition and multiplication
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R1-Section 3.1,3.2,3.3.
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4
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Properties of addition and multiplication of natural numbers
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R1-Section 3.1,3.2,3.3.
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5
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Countable, finite and infinite sets
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R2- Section 13
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6
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Construction of Integer number sets, properties of addition and multiplication in Z
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R1-Section 4
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7
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Additional properties of addition and multiplication in integer number set
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R1-Section 5
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8
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Construction of Rational Number set as equivalence class, definitions of addition and multiplication in rational number set
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R1-Section 6.1
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9
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Construction of Rational Number set and properties of addition and multiplication.
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R1-Section 6.2,6.3, 6.4
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10
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Additional properties of Rational numbers
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R1-Section 6.5
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11
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Order relation on rational numbers
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R1-Section 6.5, 6.6
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12
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Groups
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R1-Section 9.1,9.2
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13
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Examples of group (Z, Z_m, Q)
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R1-Section 9.1,9.2
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14
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Ring, definition and properties (Z, Z_m, Q)
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R1-Section 11.1,11.2
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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. Jaisingh, L. R., & Ayres, F. (2003). Schaum`s Outline of Abstract Algebra. McGraw Hill Professional.
R2.Hammack, R. H. (2013). Book of proof. Virginia: Richard Hammack.
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Supplementary Book
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SR1) The Elements of Advanced Mathematics, Steven G. Krantz, Third Edition, 2011
SR2) Proofs and Fundamentals, A First Course in Abstract Mathematics Second Edition Springer New York Dordrecht Heidelberg London, 2011.
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Goals
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To develop students` ability to comprehend and interpret mathematical definitions and theorems
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Content
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Binary operation, countable set, the construction of sets of natural numbers, integers and rational numbers and their algebraic properties.
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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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4
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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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3
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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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