Finite Fields (MATH332) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Finite Fields MATH332 3 0 0 3 6
Pre-requisite Course(s)
Math 331
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives This course is designed to introduce the basic theory of field extensions and finite fields which have various applications in both cryptography and coding theory.
Course Learning Outcomes The students who succeeded in this course;
  • gain knowledge about field extensions,
  • be able to compute in a finite field,
  • gain knowledge about polynomials over finite fields
  • understand and use traces and norms in finite fields,
  • learn how to factorize polynomials over finite fields.
Course Content Characterization of finite fields, roots of irreducible polynomials, trace, norm, roots of unity and cyclotomic polynomials, order of polynomials and primitive polynomials, irreducible polynomials, construction of irreducible polynomials, factorization of polynomials

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Algebraic Foundations: Groups, Rings (review) pp. 1-11
2 Algebraic Foundations: Fields, Polynomials pp. 11-30
3 Field Extensions pp. 30-37
4 Characterization of Finite Fields, Roots of Irreducible Polynomials pp. 45-51
5 Traces, Norms and Bases pp. 51-59
6 Roots of Unity and Cyclotomic Polynomials, Representation of Elements of Finite Fields pp. 60-66
7 Midterm Exam
8 Order of Polynomials and Primitive Polynomials pp. 76-84
9 Irreducible Polynomials, Construction of Irreducible Polynomials pp. 84-95
10 Examples of determining minimal polynomials pp. 96-100
11 Factorization over Small Finite Fields pp. 132-142
12 Factorization over Small Finite Fields (continued) pp. 132-142
13 Factorization over Large Finite Fields pp. 142-153
14 Calculation of Roots of Polynomials pp. 153-162
15 Review
16 Final Exam


Course Book 1. Introduction to Finite Fields and their Applications, R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
Other Sources 2. Applications of Finite Fields , Alfred J. Menezes, Ian F. Blake, Xuhong Gao, Ronald C. Mullin, Kluwer, 1993.

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses
Major Area Courses X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
Homework Assignments 5 8 40
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 12 24
Prepration of Final Exams/Final Jury 1 18 18
Total Workload 130