The purpose of the course is to teach students the fundamental concepts, theorems and methods of abstract algebra.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
Yok
Instructor(s)
Assoc. Prof. Neşe Yelkenkaya
Course Assistant(s)
Schedule
Thursday, 15:00-18:00, 3B 08-10
Office Hour(s)
Neşe Yelkenkaya, Wednesday 13:00-17:00, 3A-11.
Teaching Methods and Techniques
-Oral and written presentation
Principle Sources
-D. S. Dummit, R. M. Foote, Abstract Algebra, Wiley, Third Edition, 2003.
Other Sources
I._N._Herstein-Abstract_algebra-Wiley, 1996
I.M. Isaacs Algebra: A Graduate Course, 1994.
J.J. Rotman An Introduction to the Theory of Groups, Springer-Verlag 1999
E. B. Vinberg, A Course in Algebra, AMS, 2017.
Course Schedules
Week
Contents
Learning Methods
1. Week
Groups and Homomorphisms
Oral and written presentation
2. Week
Lagrange’s Theorem, Isomorphism Theorems
Oral and written presentation
3. Week
Group Actions and Examples\Types of Groups
Oral and written presentation
4. Week
Sylow Theorems
Oral and written presentation
5. Week
Classification of Finite Abelian Groups
Oral and written presentation
6. Week
Composition Series and Composition factors
Oral and written presentation
7. Week
Midterm
Midterm
8. Week
Rings, Ideals, Homomorphisms
Oral and written presentation
9. Week
Isomorphism Theorems
Oral and written presentation
10. Week
Prime Ideals, Maximal Ideals
Oral and written presentation
11. Week
Irreducible Elements, Prime Elements, Units
Oral and written presentation
12. Week
Integral Domains, Euclidean Domains
Oral and written presentation
13. Week
PIDs, UFDs
Oral and written presentation
14. Week
Polynomial Rings, Factorization of Polynomials
Oral and written presentation
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Homework / Term Projects / Presentations
4
15
Final Exam
1
45
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Develop a deeper understanding of the concepts concepts (such as groups, rings, their homomorphisms, etc.) and methods of abstract algebra
LO-2
Knows fundamental theorems of the subject.
LO-3
Outlines basic ideas and technics of their proofs of fundamental theorems.
LO-4
Applies these theorems and methods to solve related problems.
