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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
SELECTIVE TOPICS OF NUMBER THEORY MAT 519 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
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

Number theory is one of the most studied area of mathematics. Especially, number theory has an active part in exploring Diophantine equations. Our aim is to search some topics of number theory that is related to Diophantine equations.

Dersin İçeriği

Farey sequences and rational approximations, simple continued fractions, infinite continued fractions, approximation to irrationel numbers, Pell equations, algebraic numbers, Quadratic fields, algebraic integers, Diophantine equations, appyling algebraic integers to some Diophantine equations, Quadratic forms, arithmetic functions.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - He/she recognizes Farey sequences. 1 - 4 - 15 - A - C -
2 - He/she understands continued fractions and application areas. 1 - 4 - 15 - A - C -
3 - He/she recalls algebraic numbers and algebraic integers. 1 - 4 - 15 - A - C -
4 - He/she recognizes Pell´s equations and Diophantine equations. 1 - 4 - 15 - A - C -
5 - He/she investigates the relations of Pell´s and Diophantine equations. 1 - 4 - 15 - A - C -
6 - He/she applies algebraic integers to some Diophantine equations. 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 Farey sequences and rational approximations
2 Simple continued fractions
3 Infinite continued fractions
4 Infinite continued fractions
5 Irrational numbers
6 Approximation to irrationel numbers
7 Pell equations
8 Quadratic fields
9 Algebraic numbers
10 Diophantine equations
11 Appyling algebraic integers to some Diophantine equations
12 Quadratic forms
13 Arithmetic functions
14 Arithmetic functions

Kaynaklar

Ders Notu
Ders Kaynakları

1- I. Niven, H. S. Zuckerman, H. L. Montgomery, An ıntroduction to the theory of numbers, fifth ed., John Wiley, 1991,
2- K. H. Rosen, Elementary Number theory and its applications, Addison Wesley, 1999.


Döküman Paylaşımı


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 20 20
Assignment 1 15 15
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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