Subject: Algebraic Number Theory	Code: MA025	

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

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	
Selective References	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