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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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Division algorithm, arithmetic in other bases
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R1-Section 2
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2
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Greatest common divisor, the Euclidean algorithm
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R1-Section 2
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3
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Linear Diophantine equations, lowest common divisor
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R1-Section 2
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4
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Divisibility in integers and primes
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R1-Section 2
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5
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The fundamental theorem of arithmetic
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R1-Section 2
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6
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Modular arithmetic, residue classes
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R1-Section 3
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7
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Euler`s Phi function
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R1-Section 4
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8
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Fermat and Euler theorems
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R1-Section 4
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9
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Properties of congruence equations
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R1-Section 5
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10
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Linear congruences and their relations with linear Diophantine equations
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R1-Section 5
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11
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Linear congruences and Chinese remainder theorem
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R1-Section 3, 5
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12
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Number of roots of Linear congruence equations, Lagrange and Wilson theorems
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R1-Section 5
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13
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Quadratic congruences and quadratic residue
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R1-Section 5
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14
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Primitive roots,indices, solving congruence equations
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R1-Section 6
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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. Lecture Notes
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Supplementary Book
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SR1. Hardy, G.H., Wright, E.M.,(2010), An Introduction to the Theory of Numbers, 6th edition, by Contemporary Physics, 51:3, 283, DOI: 10.1080/00107510903184414.
SR2. Silvermann, J. H., (2001), A Friendly Introduction to Number Theory, Prentice-Hall Inc..
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Goals
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Teachs fundamental properties of integers to explain some problems that are easy to ask and still unsolved. Provides some idea about why generalizations have to be made.
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Content
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-
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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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-
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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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