| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Theory of Rings | MAT510 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Neşe ÖMÜR
Associate Prof. Dr. Selda ÇALKAVUR
Associate Prof. Dr. Evrim GÜVEN
Associate Prof. Dr. Yücel TÜRKER ULUTAŞ
Learning Outcomes of the Course Unit
1) Explain the concepts of rings, ideals and homomorphism.
2) Recall the Polynomial and Formal power series ring and factorization in polynomial rings.
3) Explain the concept of module, exact sequences, free module and tensor product.
4) He/she establishes a graduate study schedule related to ring theory by understanding the scientific research process.
5) Classify the structural features of a given ring by analyzing them.
6) .
7) .
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | Middle | No relation | Middle | No relation | Middle | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | Middle | No relation | No relation | |
| 3 | No relation | Middle | No relation | Middle | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 7 | Low | Low | Low | Low | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Selected Topics in Algebra
Course Contents
This course provides candidates with profound knowledge on rings and homomorphisms, ideals, factorization in commutative rings, rings of fractions, polynomial rings, formal power series ring, factorization in polynomial rings, modules, homomorphism of modules, exact sequences, free modules, projective and injective modules, dualite, tensor product, algebras
Weekly Schedule
1) Rings and Homomorphisms2) Ideals
3) Factorization in Commutative Rings
4) Rings of Fractions and Localization
5) Polynomial and Formal Power Series Rings
6) Factorization in Polynomial Rings
7) Modules
8) Midterm examination/Assessment
9) Homomorphism of Modules
10) Exact Sequences
11) Free Modules and Vector Spaces
12) Projective and Injective Modules
13) Hom ve Duality
14) Tensor Product
15) Modules in Principal Ideal Domain
16) Final examination
Recommended or Required Reading
1- J. B. Fraleigh, A first course in abstract algebra, New York, 2003.
2- T. W. Hungerford, Algebra, Springer-Verlag New York, 1974.
3- N. Aydın, H. Kandamar, Soyut Cebir.
4- I. N. Herstein, Topics in Algebra, 1976.
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Group Study
5) Self Study
6) Problem Solving
Assessment Methods and Criteria
Contribution of Semester Studies to Course Grade |
40% |
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Contribution of Final Examination to Course Grade |
60% |
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Total | 100% | |||||||||||
Language of Instruction
Turkish
Work Placement(s)
Not Required