1  Course Title:  NUMBER THEORY I 
2  Course Code:  MAT5203 
3  Type of Course:  Optional 
4  Level of Course:  Second Cycle 
5  Year of Study:  1 
6  Semester:  1 
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. İSMAİL NACİ CANGÜL 
16  Course Lecturers: 
Prof.Dr.İsmail Naci CANGÜL Prof.Dr.Osman BİZİM 
17  Contactinformation of the Course Coordinator: 
Uludağ Üniversitesi, FenEdebiyat Fakültesi Matematik Bölümü, 16059 Görükle BursaTÜRKİYE 0 224 294 17 51 tekcan@uludag.edu.tr 
18  Website:  
19  Objective of the Course:  The aim of the course is to make the students gain the some algebraic properties on number theory 
20  Contribution of the Course to Professional Development 
21  Learning Outcomes: 

22  Course Content: 
Week  Theoretical  Practical 
1  Overview of basic concepts on lessons  
2  Algebraic numbers, algebraic groups and reduction theorems  
3  Finite fields and algebraic operations on them  
4  Prime numbers and the number of prime numbers  
5  Legendre symbol and the relationship between quadratic congruencies and Legendre symbol  
6  Ring of Gauss integers  
7  Gauss primes, Galois groups and sums  
8  Rings and units of rings  
9  The relationship between units of rings and the integer solutions of Pell equations  
10  Farey sequences  
11  Quadratic forms and their relationship between the groups GL(2,Z) and SL(2,Z)  
12  Positive definite and indefinite quadratic forms  
13  Minkowski theorem and its application  
14  The ring Z[exp(2pi/ n)] 
23  Textbooks, References and/or Other Materials: 
[1] J. Buchmann and U. Vollmer. Binary Quadratic Forms: An Algorithmic Approach. SpringerVerlag, Berlin, Heidelberg, 2007. [2] D.A. Buell. Binary Quadratic Forms, Clasical Theory and Modern Computations. SpringerVerlag, New York, 1989. [3] H.M. Edward. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics, vol. 50, SpringerVerlag, 1977. [4] D.E. Flath. Introduction to Number Theory. Wiley, 1989. [5] R.A. Mollin. Quadratics. CRS Press, Boca Raton, New York, London, Tokyo, 1996. [6] R.A. Mollin. Fundamental Number Theory with Applications. Chapman&Hall/ CRC, 2008 
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  7  98 
Homeworks, Performances  0  0  0 
Projects  14  5  70 
Field Studies  0  0  0 
Midtermexams  0  0  0 
Others  0  0  0 
Final Exams  1  15  15 
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 