The aim of the Course is to teach students basic theory of Finite Fields
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)
Professor Erol BALKANAY, Assoc. Prof. Neşe YELKENKAYA
Course Assistant(s)
None.
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Prof. Dr. Erol BALKANAY, AK/3-A-15.
Teaching Methods and Techniques
-
Principle Sources
-Rudolf Lidl & Harald Niederreiter,Finite Fields,Vol.I, Cambridge University Press
Rudolf Lidl & Harald Niederreiter, Finite Fields,Vol.II, Cambridge University Press.
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Field Extensions
Oral and Written presentation
2. Week
Field Extensions
Oral and Written presentation
3. Week
Characterization of Finite Fields
Oral and Written presentation
4. Week
Characterization of Finite Fields
Oral and Written presentation
5. Week
Roots of Irreducible Polynomials over a Finite Field
Oral and Written presentation
6. Week
Roots of Irreducible Polynomials over a Finite Field
Oral and Written presentation
7. Week
Traces, Norms and Basis
Oral and Written presentation
8. Week
Midterm exam
Midterm Exam
9. Week
Traces, Norms and Basis
Oral and Written presentation
10. Week
Roots of Unity
Oral and Written presentation
11. Week
Representation of Elements of Finite Fields
Oral and Written presentation
12. Week
Representation of Elements of Finite Fields
Oral and Written presentation
13. Week
Wedderburn's Theorem
Oral and Written presentation
14. Week
Applications
Oral and Written presentation
15. Week
Final exams
Final Exam
16. Week
Final Exams
Final Exam
17. Week
Final Exams
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Have the necessary knowledge about the field extensions to understand theory of finite fields.
LO-2
Know the general theory of finite fields.
LO-3
Learn basic knowledge about Traces, Norms and Basis.
LO-4
Know how to represent the elements of finite fields
