1	Course Title:	NUMBER THEORY II
2	Course Code:	MAT5204
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. AHMET TEKCAN
16	Course Lecturers:	Prof.Dr.İsmail Naci CANGÜL Prof.Dr.Osman BİZİM
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, 16059 Görükle Bursa-TÜRKİYE 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:

1 Learn the some fundamental concepts on number theory.; 2 Learn the finite fields and algebra on these fields.; 3 Learn the Legendre, Jacobi and Kronecker symbols. ; 4 Learn the cycle and proper cycle of indefinite forms. Also compute the right and left neighbors of them and compute the simple finite continued fraction expansion of the base points of indefinite forms.; 5 Modules of indefinite quadratic forms, automorphisms of indefinite forms and their roles on finding the integer solutions of Pell equations.; 6 Learn the ambiguous classes and some properties of them.;

22	Course Content:

Week	Theoretical	Practical
1	Overview of basic concepts on lessons
2	Algebraic numbers, groups and reduction theorems
3	Finite fields and the units of them
4	Gauss sums
5	Farey sequences
6	Legendre symbol and the role of it on quadratic congruence
7	Jacobi and Kronecker symbols
8	Cycle and proper cycle of indefinite forms
9	Right and left neighbors of indefinite forms
10	Simple finite continued fraction expansion of base points of indefinite forms
11	Quadratic ideals and the relationship between quadratic ideals and indefinite forms, cycles of quadratic ideals
12	Pell forms and modules of indefinite forms
13	Automorphisms of indefinite forms and the role of them on finding the integer solutions of Pell equations
14	Ambiguous classes, class group and genera

23	Textbooks, References and/or Other Materials:	[1] J. Buchmann and U. Vollmer. Binary Quadratic Forms: An Algorithmic Approach. Springer-Verlag, Berlin, Heidelberg, 2007. [2] D.A. Buell. Binary Quadratic Forms, Clasical Theory and Modern Computations. Springer-Verlag, New York, 1989. [3] H.M. Edward. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics, vol. 50, Springer-Verlag, 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
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 4 2 4 3 3 5 5 5 3 LO2 4 3 2 4 3 2 5 5 4 4 LO3 5 4 2 4 4 4 4 5 5 4 LO4 4 3 2 4 3 2 5 5 4 3 LO5 5 3 2 4 3 5 4 5 5 3 LO6 5 3 2 4 5 2 5 5 4 3

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High