Recalling the notions of normal subgroup and quotient group, Repeating izomorphism theorems, Describing the notions normalizator, komutator and center in details, Illustrating the group of all automorphisms of a group, Describing Sylow subgroups, Analysing Abelian groups, Relating field extentions and group theory.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Professor Songül Esin
Course Assistant(s)
Ress. Assist. Mehmet Selçuk TÜRER
Schedule
Will be announced in the forthcoming term
Office Hour(s)
Prof. Dr. Erhan GÜZEL - 3-A-07 - Will be announced in the forthcoming termRess. Assist. Mehmet Selçuk TÜRER - 3-A-13 - Will be announced in the forthcoming term
Teaching Methods and Techniques
Lecture, practice, homeworks, discussions
Principle Sources
B. Baumslag , B. Chandler, Group Theory, Schaum’s Outline Series, McGraw-Hill Book Company, 1968
G. Birkhoff , S. Mac lane, A Survey of Modern Algebra, Macmillan, New York , 1965
F. Çallıalp, Örneklerle Soyut Cebir , Birsen Yayınevi, İstanbul, 2009
J.F. Fraleigh, A First Course in Abstract Algebra, Addiso-Wesley, London 1970
I. N. Goldstein, Abstract Algebra, Prentice Hall, New York, 1973
S. Lange, Algebra, Addiso-Wesley, Reading-Massachusetts 1965
W. Ledermann, Theory of Groups, Edinburg, London, New York Interscience Publishers İnc. 1953
H. Şenkon, Soyut Cebir Dersleri Cilt I ve Cilt II, İ.Ü. Fen Fakültesi Basımevi 1998
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Normal Subgroups
Lecture and applications
2. Week
Quotient Group
Lecture and applications
3. Week
Homomorphisms, Izomorphisms and Kernel
Lecture and applications
4. Week
Izomorphism Theorems
Lecture and applications
5. Week
Group of Outomorphisms
Lecture and applications
6. Week
Cayley Theorem
Lecture and applications
7. Week
Normalizator, Komutator and Center
Lecture and applications
8. Week
Midterm
9. Week
Sylow Subgroups
Lecture and applications
10. Week
Sylow Subgroups
Lecture and applications
11. Week
Abelian Groups
Lecture and applications
12. Week
Abelian Groups
Lecture and applications
13. Week
Relation Between Field Extensions and Group Theory
Lecture and applications
14. Week
Relation Between Field Extensions and Group Theory
Lecture and applications
15. Week
Final Exam Week
16. Week
Final Exam Week
17. Week
Final Exam Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Homework / Term Projects / Presentations
2
10
Final Exam
1
50
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
Recalling the notions of normal subgroup and quotient group
LO-2
Repeating izomorphism theorems
LO-3
Describing the notions normalizator, komutator and center in details
LO-4
Illustrating the group of all automorphisms of a group
LO-5
Describing Sylow subgroups and analysing Abelian groups
