1  Course Title:  ALGEBRAIC NUMBER THEORY II 
2  Course Code:  MAT5208 
3  Type of Course:  Optional 
4  Level of Course:  Second Cycle 
5  Year of Study:  1 
6  Semester:  2 
7  ECTS Credits Allocated:  6 
8  Theoretical (hour/week):  3 
9  Practice (hour/week) :  0 
10  Laboratory (hour/week) :  0 
11  Prerequisites:  none 
12  Recommended optional programme components:  None 
13  Language:  Turkish 
14  Mode of Delivery:  Face to face 
15  Course Coordinator:  Prof. Dr. OSMAN BİZİM 
16  Course Lecturers:  Prof. Dr. Osman BİZİM 
17  Contactinformation of the Course Coordinator: 
Uludağ Üniversitesi, FenEdebiyat Fakültesi Matematik Bölümü, Görükle BursaTÜRKİYE 0 224 294 17 57 / obizim@uludag.edu.tr 
18  Website:  
19  Objective of the Course:  The aim of this lecture is to illustrate how basic notions from the theory of algebraic numbers may be used to solve problems in number theory. The main focus is to extend properties of the integer numbers to more general number structures: algebraic number fields and their rings of algebraic integers. So students can So students have the ability conduct original research and independent publication. 
20  Contribution of the Course to Professional Development 
21  Learning Outcomes: 

22  Course Content: 
Week  Theoretical  Practical 
1  Integral domains, unique factorization domains, ideals.  
2  Noetherian domains,principal ideal domains, algebraic numbers and number fields, quadratic fields.  
3  Field extensions, automorphisms, Galois groups.  
4  Norms and traces, integral bases and discriminants, norms of ideals.  
5  Class groups, binary quadratic forms, ideal class group.  
6  Prime power representation, Bachet’s equation, The Fermat equation, factoring.  
7  Ideal decomposition in number fields, ramification.  
8  Splitting of prime ideals, Galois theory and decomposition.  
9  The ramification of prime ideals in Galois extensions.  
10  The fundamental theorem of abelian extensions and nuerical examples.  
11  Kummer extensions and classfield theory.  
12  The ideal class group, Minkowski theorem, determining the ideal class group.  
13  Dirichlet’s unit theorem, valuations and properties of valuations.  
14  Roots of unity, fundamental units in cubic fields, regulator. 
23  Textbooks, References and/or Other Materials: 
[1]Algebraic Number Theory and Fermat’s Last Theorem, Ian Stewart, David Tall. [2] Algebraic Number Theory, J. Neukirch. [3]Introductory Algebraic Number Theory, Ş. Alaca, K.S. Williams. [4]Algebraic Numbers, Paulo Ribenboim. 
24  Assesment 
TERM LEARNING ACTIVITIES  NUMBER  PERCENT 
Midterm Exam  0  0 
Quiz  0  0 
Homeworks, Performances  0  0 
Final Exam  1  100 
Total  1  100 
Contribution of Term (Year) Learning Activities to Success Grade  0  
Contribution of Final Exam to Success Grade  100  
Total  100  
Measurement and Evaluation Techniques Used in the Course  
Information 
25  ECTS / WORK LOAD TABLE 
Activites  NUMBER  TIME [Hour]  Total WorkLoad [Hour] 
Theoretical  14  3  42 
Practicals/Labs  0  0  0 
Self Study and Preparation  14  5  70 
Homeworks, Performances  0  0  0 
Projects  0  0  0 
Field Studies  0  0  0 
Midtermexams  0  0  0 
Others  14  5  70 
Final Exams  1  43  43 
Total WorkLoad  225  
Total workload/ 30 hr  7,5  
ECTS Credit of the Course  7,5 
26  CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS  

LO: Learning Objectives  PQ: Program Qualifications 
Contribution Level:  1 Very Low  2 Low  3 Medium  4 High  5 Very High 