Defining field extensions and analysing field extension types, Defining field automorphisms and splitting field, Introducting to Galois 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
-
Office Hour(s)
-
Teaching Methods and Techniques
Lecture, practice, homeworks, discussions
Principle Sources
John B. Faraleigh, A first Course in Abstract Algebra , Addison-Wesley Publishing Company, 1969
I. N. Herstein, Topics in Algebra , Xerox College Publishing, 1964
Nathan Jacobson, Lectures on Abstact Algebra III , Springer-Verlag, 1975
Serge Lange, Algebra , Addison-Wesley Publishing Company, 1974
Ian Stewart, Galois Theory , Chapman and Hall, 1973
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Prime field, Algebraic and transcendental numbers
Lectures and applications
2. Week
Minimal polynomials, Problems
Lectures and applications
3. Week
Conjugate elements and Equivalent fields
Lectures and applications
4. Week
Finite and algebraic extensions
Lectures and applications
5. Week
Algebraic closure
Lectures and applications
6. Week
Field automorphisms
Lectures and applications
7. Week
Automorphism group of a field
Lectures and applications
8. Week
Midterm
9. Week
Splitting field of a polynomial
Lectures and applications
10. Week
Primitif root, Euler phi fuction, Mobius function
Lectures and applications
11. Week
Finite fields
Lectures and applications
12. Week
Folded root and differential of a polynomial
Lectures and applications
13. Week
Absolute field, Primitive Element Theorem
Lectures and applications
14. Week
Normal extension, Galois group
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
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
Understanding the notion of extending number systems
LO-2
Defining some notions to use for extending fields
LO-3
Defining field extension types and analysing them in details
LO-4
Constructing the group of automorphisms of a field
