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.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Professor Songül ESİN
Course Assistant(s)
Schedule
Tuesday, 09:00-10:45 , Friday, 09:00-10:45
Office Hour(s)
Monday, 13:00-14:00
Teaching Methods and Techniques
Lecture, practice, homeworks, discussions
Principle Sources
-H. İbrahim Karakaş, Soyut Cebire Giriş, https://acikders.tuba.gov.tr/
-F. Çallıalp, Örneklerle Soyut Cebir , Birsen Yayınevi, İstanbul, 2009
-H. Şenkon, Soyut Cebir Dersleri Cilt I ve Cilt II, İ.Ü. Fen Fakültesi Basımevi 1998
-J.F. Fraleigh, A First Course in Abstract Algebra, Addiso-Wesley, London 1970
-W. Ledermann, Theory of Groups, Edinburg, London, New York Interscience Publishers İnc. 1953
Course Schedules
Week
Contents
Learning Methods
1. Week
Review: Set Theory, Functions, Relations.
Lectures and applications
2. Week
Modular Arithmetic.
Lectures and applications
3. Week
Binary Operations and Operation Tables.
Lectures and applications
4. Week
Algebraic Structures. Groups.
Lectures and applications
5. Week
Subgroups.
Lectures and applications
6. Week
Permutation Groups.
Lectures and applications
7. Week
Symmetric groups.
Lectures and applications
8. Week
Midterm
9. Week
Generators, Cyclic Groups.
Lectures and applications
10. Week
Cosets and Lagrange’s Theorem.
Lectures and applications
11. Week
Normal Subgroup
Lectures and applications
12. Week
Factor Groups
Lectures and applications
13. Week
Group Homomorphisms
Lectures and applications
14. Week
Group Isomorphisms.
Lectures 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
Quizzes
2
8
Homework / Term Projects / Presentations
3
12
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
Have the basic knowledge on divisibility theory in integers. Solve the problems related the linear congruences and use them for the solution of various problems.
LO-2
Know the definitions of binary operations, associative, commutative,
identity element, inverses, cancellation. Prove the uniqueness of unit element and inverse of an element.
LO-3
Group, order of a group, subgroups and cyclic subgroups, order of an element.
LO-4
Analyze some special groups in detail.
LO-5
Determine right cosets and left cosets of a group and state Lagrange’s Theorem. Explain normal subgroup, group homomorphism, kernel and image.
LO-6
Applies homomorphic and isomorphic structures to groups.
