# Finite Fields (MATH332) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Finite Fields MATH332 Area Elective 3 0 0 3 6
Pre-requisite Course(s)
Math 331
Course Language English Elective Courses Natural & Applied Sciences Master's Degree Face To Face Lecture, Question and Answer. 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. 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. 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

### Sources

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

### Evaluation System

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 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to apply knowledge of mathematics, science, and engineering.
2 An ability to design and conduct experiments, as well as to analyse and interpret data.
3 An ability to design a system, component, or process to meet desired needs.
4 An ability to function on multi-disciplinary domains.
5 An ability to identify, formulate, and solve engineering problems.
6 An understanding of professional and ethical responsibility.
7 An ability to communicate effectively.
8 Recognition of the need for, and an ability to engage in life-long learning.
9 A knowledge of contemporary issues.
10 An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
11 Skills in project management and recognition of international standards and methodologies
12 An ability to produce engineering products or prototypes that solve real-life problems.
13 Skills that contribute to professional knowledge.
14 An ability to make methodological scientific research.
15 An ability to produce, report and present an original or known scientific body of knowledge.
16 An ability to defend an originally produced idea.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
Project
Report
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