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Course Information
Course Unit Title : Applications of Finite Fields
Course Unit Code : 01MAT5189
Type of Course Unit : Optional
Level of Course Unit : Second Cycle
Year of Study : Preb
Semester : 255.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Structure of finite fields, Irreducible and primitive polynomials over finite fields, Construction of irreducible polynomials.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Characterization of Finite fields, Roots of irreducible polynomials, Roots of unity and cyclotomic polynomials, Order of polynomials and primitive polynomials, Constructions of irreducible polynomials.
Languages of Instruction : Turkish-English
Course Goals : The aim of this course is to learn the theory of finite fields and the structure of polynomials over finite fields.
Course Aims : The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are needed in Cryptography.
WorkPlacement   Not used.
Recommended or Required Reading
Textbook : -
Additional Resources : 1) R. Lidl and H. Niederreither, Introduction to Finite Fields and Their Applications, Cambridge Univ. Press, 1986.
2) A. J. Menezes, Editor: Applications of Finite Fields, Kluwer Academic Publisher, Boston, 1993.
3) R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer Academic Publisher, Boston, 1987.
4) Z.-X. Wan, Lectures on Finite Fields and Galois Rings, World Scientific Pub Co Inc, 2003.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
14 3 42  
Homeworks :
5 15 75  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 30 30  
Finals :
1 30 30  
Workload Hour (30) :
30  
Total Work Charge / Hour :
0  
Course's ECTS Credit :
0      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 25
Quiz :
0 0
Homework :
5 75
Attendance :
14 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
70
The ratio of final to success :
30
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 Groups
 
2 Rings
 
3 Fields
 
4 Polynomials
 
5 Field Extensions
 
6 Characterization of finite fields
 
7 Roots of irreducible polynomials
 
8 Traces, norms and bases
 
9 Roots of unity and cyclotomic polynomials
 
10 Representation of elements of finite fields
 
11 Wedderburn's theorem
 
12 Order of polynomials and primitive polynomials
 
13 Irreducible polynomials
 
14 Constructions of irreducible polynomials
 
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