Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
FİNİTE FİELDS AND FİNİTE RİNGS MAT 614 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. MEHMET ÖZEN Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı This lecture provides an introduction to the mathematics and protocols needed to make data transmission and electronic systems secure, along with finite algebraic structures. Dersin İçeriği 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.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students will able to learn the significance and properties of the minimal polynomial. 1 - 4 - 15 - A - C - 2 - Students will able to learn the concept of field extensions and properties of the algebraic element. 1 - 4 - 15 - A - C - 3 - Students will able to learn how to estabish and use the concept of the degree of an extension. 1 - 4 - 15 - A - C - 4 - Students will able to learn to construct splitting fields, normal extensions and algebraic closed fields. 1 - 4 - 15 - A - C - 5 - Students will able to learn fundamental theorems of Galois rings. 1 - 4 - 15 - A - C - 6 - Students will able to how to construct finite fields. 1 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
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

Ders Notu
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
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. 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. 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. 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. 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. 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
12 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.
13 Student completes the missing or limited knowledge by using the scientific methods. X
14 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result.
15 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
16 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches.
17 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
18 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.
19 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
20 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
21 Student follows the necessary technological developments in his/her field, and s/he uses them. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
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
Toplam İş Yükü 158
Toplam İş Yükü /25(s) 6.32
Dersin AKTS Kredisi 6.32
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