The aim of this lesson is to improve the abstract thinking ability of students and give a background for an advanced degree in mathematics and related areas.
Lecture, practice, homeworks, quizess, and discussions
Principle Sources
- John B. Fraleigh, Soyut Cebire Giriş, Palme yayıncılık, 7. Baskıdan Çeviri, Prof. Dr. Mehmet Terziler, Yrd. Doç. Dr. Tahsin Öner.
-H. İbrahim Karakaş, Soyut Cebire Giriş, https://acikders.tuba.gov.tr/ -F. Çallıalp, Örneklerle Soyut Cebir , Birsen Yayınevi, İstanbul, 2009
Other Sources
-H. Şenkon, Soyut Cebir Dersleri Cilt I ve Cilt II, İ.Ü. Fen Fakültesi Basımevi 1998
-G. Birkhoff , S. Mac lane, A Survey of Modern Algebra, Macmillan, New York , 1965
-I. N. Goldstein, Abstract Algebra, Prentice Hall, New York, 1973
-S. Lange, Algebra, Addiso-Wesley, Reading-Massachusetts 1965
Course Schedules
Week
Contents
Learning Methods
1. Week
Rings and basic properties
Lecture and practice
2. Week
Integral Domains
Lecture and practice
3. Week
Characteristic of a ring, Fields.
Lecture and practice
4. Week
Subrings and Ideals.
Lecture and practice
5. Week
Quotient Rings
Lecture and practice
6. Week
Ring homomorphisms, Isomorphisms and Isomorphisms Theorems
Lecture and practice
7. Week
The Field of Quotients
Lecture and practice
8. Week
Polynomial Rings
Lecture and practice
9. Week
Midterm Exam
10. Week
Arithmetics in Rings, Principal Ideal Domain.
Lecture and practice
11. Week
Factorization of Polynomials.
Lecture and practice
12. Week
Reducibility Tests, Irreducibility Tests.
Lecture and practice
13. Week
Divisibility in Integral Domain.
Lecture and practice
14. Week
Unique Factorization Domains.
Lecture and practice
15. Week
Final Exam Week
16. Week
Final Exam Week
17. Week
Final Exam Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Quizzes
4
20
Final Exam
1
40
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Defining the algebraic structures with two operations and understanding their properties
LO-2
Defining the characteristic and ideal in the ring theory and operating this terms for solving problems
LO-3
Distinguish the rings with respect to their structures and relate between them
LO-4
Defining the field of quotients of an integral domain and interpreting some properties of integers to integral domains
LO-5
Defining the Euclidean domains and understanding some properties of them
LO-6
Defining the polynomial rings and solving some problems
