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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 of Ring and Elementary Properties of Rings
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R1: Section 10.1
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2
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Some Important Rings
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R1: Section 10.2
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3
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Subring and Subfields
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R1: Section 11.1
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4
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Ideals and Quotient Rings
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R1: Section 11.2
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5
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Homomorphisms and Isomorphims
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R1: Section 11.3
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6
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Direct Sum of Rings
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R1: Section 13.1
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7
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Polynomial Rings
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R1: Section 14.1
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8
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Euclidean Domains
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R1: Section 15.1
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9
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Greatest Common Divisors
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R1: Section 15.2
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10
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Prime and Irreducible Elements
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R1: Section 15.3
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11
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Unique Factorization Domains
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R1: Section 16.1
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12
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Factorization of Polynomials over a UFD
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R1: Section 16.2
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13
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Ireducibility of Polinomials
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R1: Section 16.3
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14
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Maximal, Prime, and Primary Ideals
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R1: Section 17.1
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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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Dr. Hanife Varlı
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Resources
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R1. Malik, D. S., Mordeson, J. N., & Sen, M. K. (2007). MTH 581-582: Introduction to Abstract Algebra. United States of America.
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Supplementary Book
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SR1. Fraleigh, John B. (2014). A First Course in Abstract Algebra (7th Edition). Pearson Education Limited, England.
SR2. Herstein, I. N. (1996). Abstract Algebra (3rd Edition). Prentice-Hall, Inc, New Jersey.
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Goals
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Learning of the fundamental concepts of the ring and field theories
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Content
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Rings, subrings, ideals, ring homomorphism and isomorphism, polynomial rings.
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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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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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2
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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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