1. Eğitim Bilgi Sistemi
  2. Matematik Pr. (Yl)
  3. Algebraıc Number Theory II (2020 - 2021)
Ders Adı Kodu Yarıyıl T+U Saat Kredi AKTS
Algebraıc Number Theory II MAT 568 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi YUKSEK_LISANS
Dersin Türü Seçmeli
Dersin Koordinatörü Prof.Dr. REFİK KESKİN
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi Diğer
Dersin Amacı

The topic given in Algebraic number theory I will be continued and the applications of algebraic numbers will be examined by considering Bachet-Mordell Diophantine equation.
Dersin İçeriği

Algebraic integers, Number fields, Norms and discriminants, Modules, Ideals and ideals as Z-modules, Residue class, Cancellation laws, Divisibility of ideals, Decompositions of primes, Principal ideal test, Class group, Finitiness of class number, Computation of class groups, Bachet-Mordell equation.
# Ders Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 He/ she learns to decomposite the ideals to prime ideals in algebraic number ring. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
2 After learning decompositions of ideals to prime ideals, he/ she applies this in solving Pell equations. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
3 He/ she calculates the class number and uses this in solving Pell eqautions. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
Hafta Ders Konuları Ön Hazırlık
1 Algebraic integers
2 Number fields
3 Norms and discriminants
4 Modules
5 Ideals and ideals as Z-modules
6 Residue class
7 Residue class
8 Cancellation laws
9 Divisibility of ideals
10 Decompositions of primes
11 Principal ideal test
12 Class group, Finitiness of class number
13 Computation of class groups
14 Bachet-Mordell equation
Kaynaklar
Ders Notu
Ders Kaynakları

1. Ian Stewart and David Tall, Algebraic Number Theory and Fermats Last Theorem, A K Peters, Ltd., 2002.
2. Şaban Alaca and Kenneth S. Williams, Introductory Algebraic Number Theory, Cambridge University Press, 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
Sıra Program Çıktıları Katkı Düzeyi
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. 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
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
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
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
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
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.
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
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
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
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
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
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
# Ders Öğrenme Çıktılarının Program Çıktılarına Katkısı PÇ 2 PÇ 2 PÇ 3 PÇ 3 PÇ 4 PÇ 4 PÇ 5 PÇ 5 PÇ 6 PÇ 6 PÇ 7 PÇ 7 PÇ 8 PÇ 8 PÇ 9 PÇ 9 PÇ 10 PÇ 10 PÇ 10 PÇ 11
1 He/ she learns to decomposite the ideals to prime ideals in algebraic number ring.
2 After learning decompositions of ideals to prime ideals, he/ she applies this in solving Pell equations.
3 He/ she calculates the class number and uses this in solving Pell eqautions.
Değerlendirme Sistemi
Yarıyıl Çalışmaları Katkı Oranı
1. Ara Sınav 100
Toplam 100
1. Yıl İçinin Başarıya 40
1. Final 60
Toplam 100
AKTS - İş Yükü Etkinlik Sayı Süre (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
Final examination 1 30 30
Toplam İş Yükü 126
Toplam İş Yükü / 25 (Saat) 5,04
dersAKTSKredisi 6