Week
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Topics
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Study Metarials
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1
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Rings and ring homomorphisms
|
|
2
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Ideals
|
|
3
|
Factorization in commutative rings
|
|
4
|
Rings of quotients and localization
|
|
5
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Rings of polynomials and formal power series
|
|
6
|
Factorization in polynomial rings
|
|
7
|
Modules, module homomorphisms, and exact sequences
|
|
8
|
Free modules and vector spaces
|
|
9
|
Projective and injective modules
|
|
10
|
Hornomorphisms and Duality
|
|
11
|
Simple rings and primitive rings
|
|
12
|
The Jacobson radical
|
|
13
|
Semisimple rings
|
|
14
|
The prime radical, prime and semiprime rings
|
|
Prerequisites
|
-
|
Language of Instruction
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English
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Responsible
|
Assist. Prof. Dr. Celalettin KAYA
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Instructors
|
-
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Assistants
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Assoc. Prof. Dr. Faruk Karaaslan
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Resources
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1.) Thomas W. Hungerford, (2003), Algebra (Graduate Texts in Mathematics, Vol. 73) 8th Edition, Springer.
2.) Serge Lang, (2005), Algebra (Graduate Texts in Mathematics, Vol. 211) 3rd Edition, Springer.
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Supplementary Book
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I. N. Herstein, (1975), Topics in Algebra, 2nd Edition, John Wiley & Sons.
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Goals
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To study the basic notions and theorems of ring theory, and to examine the structure of rings.
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Content
|
Rings and ring homomorphisms, ideals, factorization in commutative rings, rings of quotients and localization, rings of polynomials and formal power series, factorization in polynomial rings, modules, projective and injective modules, homomorphisims and duality, chain conditions, simple and primitive rings, the Jacobson prime radicals, prime and semiprime rings.
|
|
Program Learning Outcomes |
Level of Contribution |
1
|
Improve and deepen the gained knowledge in Mathematics in the speciality level
|
5
|
2
|
Use gained speciality level theoretical and applied knowledge in mathematics
|
5
|
3
|
Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
|
2
|
4
|
Analyze mathematical problems by using the gained research methods
|
4
|
5
|
Conduct independently a study requiring speciliaty in Mathematics
|
5
|
6
|
Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
|
5
|
7
|
Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
|
3
|
8
|
Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
|
5
|
9
|
Communicate with colleagues written and verbally by mastering a foreign language at least European Language Portfolio B2 General Level
|
5
|
10
|
Make use of the necessary computer softwares and information technologies related to Mathematics
|
-
|
11
|
Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
|
4
|