Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ALGEBRAİC NUMBER THEORY I MAT 567 0 3 + 0 3 6
Ön Koşul Dersleri Algebra I and Algebra II
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. REFİK KESKİN Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Diğer Dersin Amacı To find the integer solutions of the Diophantine equations is an area of interest of many mathematicians. Here, our aim is to investigate solutions of some Diophantine equations by using the theorems of algebraic number theory. Therefore studying algebraic number theory becomes important. Dersin İçeriği Rings and ideals, Quotient Rings, Prime and maximal ideals, Unique factorization domains and principal ideal domain, Algebraic numbers and albgebraic integers, Number fields, Rings of algebraic integers, Determinants and discriminants, Euclid domains, Norms and traces, Integral bases, Pell equations, Solvability of the Pell equations, The Ramanujan- Nagell equation
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she uses undergraduate algebra knowledge in order to conceive the algebraic number theory. 1 - 4 - 8 - 14 - 15 - A - C - 2 - He/ she learns solutions of the Diophantine equations by using algebraic number theory. 1 - 4 - 8 - 14 - 15 - A - C - 3 - He/ she understands how to use theory and application. 1 - 4 - 8 - 14 - 15 - A - C - 4 - He/ she constitutes necessary background in order to understand Algebraic Number Theory II. 1 - 4 - 8 - 14 - 15 - A - C - 5 - He/she learns investigating concerning with algebraic number theory from different sources. 1 - 4 - 8 - 14 - 15 - A - C - 6 - He/she learns literature search and reading and understanding the articles concerning with the subject. 1 - 4 - 8 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 8:Group Study 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Rings and ideals
2 Quotient Rings
3 Prime and maximal ideals
4 Unique factorization domains and principal ideal domain
5 Algebraic numbers and albgebraic integers
6 Number fields
7 Rings of algebraic integers
8 Determinants and discriminants
9 Euclid domains
10 Norms and traces
11 Integral bases
12 Pell equations
13 Solvability of the Pell equations
14 The Ramanujan- Nagell equation

#### Kaynaklar

Ders Notu
Ders Kaynakları

1) Ian Stewart and David Tall, Algebraic Number Theory and Fermat´s Last Theorem, A K Peters, Ltd., 2002.
2) Şaban Alaca and Kennet S. Williams, Inductory Algebraic Number Theory, Cambridge University ress, 2004.
3) Algebraic Number Theory, Franz Lemmermeyer, http://www.fen.bilkent.edu.tr/~franz/ant-st.pdf
4) Algebraic Number Theory, Samir Siksek, http://www.warwick.ac.uk/~maseap/teaching/ant/antnotes.pdf

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 100
Toplam 100
Yıliçinin Başarıya Oranı 40
Finalin Başarıya Oranı 60
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 25 25
Quiz 1 10 10
Performance Task (Laboratory) 1 30 30
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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