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 | Bachelor’s Degree (First Cycle) |
| 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 | |
|---|---|
| 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) | |||
| 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 | ||