Course Name Code Semester T+U Hours Credit ECTS
Finite Fields and Finite Rings MAT 614 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. MEHMET ÖZEN
Course Lecturers Prof.Dr. MEHMET ÖZEN,
Course Assistants
Course Category
Course Objective This lecture provides an introduction to the mathematics and protocols needed to make data transmission and electronic systems secure, along with finite algebraic structures.
Course Content Finite algebraic structures, Ring, Field, Subrings and Ideals, Integral Domains, Polynomial Rings, Prime and maximal ideals, Finite Fields, Quotient Rings, Quotient Fields, Hensel’s Lemma and Lift, Galois Rings.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will able to learn the significance and properties of the minimal polynomial. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 Students will able to learn the concept of field extensions and properties of the algebraic element. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 Students will able to learn how to estabish and use the concept of the degree of an extension. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 Students will able to learn to construct splitting fields, normal extensions and algebraic closed fields. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 Students will able to learn fundamental theorems of Galois rings. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 Students will able to how to construct finite fields. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Basic Definitions
2 Ring, Field, Subrings and Ideals
3 Integral Domains
4 Polinomial Rings
5 Prime and maximal ideals
6 Quotient Rings and Quotient Fields
7 Strucures of Finite Fields
8 Strucures of Finite Fields
9 Advanced Properties on Finite Fields
10 Factorization of Polynomial on Finite Fields
11 Irreducible Polynomials on Finite Fields
12 Hensel’s Lemma and Lift
13 Galois Rings
14 Galois Rings
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application.
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result.
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches.
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters.
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
1. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 2 1 2
Assignment 1 15 15
Final examination 1 25 25
Total Workload 158
Total Workload / 25 (Hours) 6.32
dersAKTSKredisi 6