Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MA025	Algebraic Number Theory	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	8	2+2+0		optional	
Mathematics-Computer Science - in Hungarian	8	2+2+0		optional	

Teaching Staff in Charge	Prof. MARCUS Andrei, Ph.D., marcus@math.ubbcluj.ro	
Aims	Deepening the knowledge in arithmetics and number theory studied in previous semesters. Presentation of notions and results which are useful for a future teacher and mathematician.	
Content	Integral domains. Divisibility. Euclidean and factorial rings.
The structure of the group of units of Z/nZ. Primitive roots and indices. 
Congruences of higher degree. Quadratic residues and quadratic reciprocity. Algebraic number fields. Integral extensions of commutative rings. Quadratic fields. The ring of Gauss  and Euler integers. Diophantine ecuations.	
Bibliography	1. K. IRELAND, M. ROSEN: A Classical Introduction to Number Theory, Springer-Verlag 1990. 
2. T. ALBU, I. D. ION: Capitole de teoria algebrica a numerelor, Ed. Academiei, Bucuresti 1984. 
3. I. NIVEN, H. ZUCKERMAN : Bevezetes a szamelmeletbe, Muszaki Konyvkiado, Budapest, 1978. 
4. P. ERDOS, J. SURANYI: Valogatott fejezetek a szamelmeletbol,  Polygon, Szeged, 1996.
5. A. SARKOZI, J. SURANYI: Szamelmelet-feladatgyujtemeny, Tankonyvkiado, Budapest, 1979.
	
Assessment	Homework. Essays. Exam.