ECTS - Finite Fields
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 Lecturer(s) |
|
| 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;
|
| 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 | An ability to apply knowledge of mathematics, science, and engineering. | X | ||||
| 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. | X | ||||
| 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. | |||||
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 | ||