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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
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R1-Section 1.1, Section 1.2
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2
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Algebra of propositions
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R1-Section 1.3
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3
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Quantifiers
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R1- Section 1.5
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4
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Method of Proof: Direct proof, Proof by contrapositive
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R1- Section 2.1, Section 2.2
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5
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Method of Proof: Proof by contradiction, falsification methods
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R1- Section 2.3
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6
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Method of Proof: Mathematical induction
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R1- Section 6.3, R3- Section 2.4
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7
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Sets and Operation on sets
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R1- Section 3.2, Section 3.3, R2-Section 2.2
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8
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Power set and Family of Sets
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R1- Section 3.4
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9
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Cartesian Products
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R2- Section 2.3
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10
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Relations and their basic properties
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R1- Section 5.1, R2- Section 3.1
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11
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Equivalence relation
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R1- Section 5.3, R2- Section 3.3,
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12
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Order relations
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R2- Section 3.2, R3-Section 4.2
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13
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Functions
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R1- Section 4.1, R3-Section 4.3
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14
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Operation on Functions
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R1- Section 4.2, Section 4.3
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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. Bloch, E. D. (2011). Proofs and fundamentals: a first course in abstract mathematics. Springer Science & Business Media.
R2. Galovich S. (1989). Introduction to Mathematical Structures, Harcourt Brace Jovanovich Publishers.
R3. Krantz S. G. (2011). The Elements of Advanced Mathematics, Third Edition.
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Supplementary Book
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SR1. Maddox, R. B. (2002). Mathematical Thinking and Writing, A transition to Abstract Mathematics, HARCOURT/ACADEMIC PRESS Massachusetts, USA.
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Goals
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The course will learn logical and rigorous mathematical background for study of advanced math course. Topics include formal logic, set theory, proofs, mathematical induction, functions, partial ordering and relations.
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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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-
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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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