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)
N/A
Course Language English
Course Type Elective Courses
Course Level Natural & Applied Sciences Master's Degree
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

Sources

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 X
Major Area Courses
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 Applies knowledge of mathematics, science, and engineering. X
2 Designs and conducts experiments, analyzes and interprets experimental results.
3 Designs a system, component, or process to meet specified requirements.
4 Works effectively in interdisciplinary fields.
5 Identifies, formulates, and solves engineering problems. X
6 Has awareness of professional and ethical responsibility.
7 Communicates effectively.
8 Recognizes the need for lifelong learning and engages in it.
9 Has knowledge of contemporary issues.
10 Uses modern tools, techniques, and skills necessary for engineering applications.
11 Has knowledge of project management skills and international standards and methodologies.
12 Develops engineering products and prototypes for real-life problems.
13 Contributes to professional knowledge.
14 Conducts methodological and scientific research.
15 Produces, reports, and presents a scientific work based on original or existing knowledge.
16 Defends the original idea generated.

ECTS/Workload Table

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
Total Workload 130