Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MA025 | Algebraic Number Theory |
| 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. |
| 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. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |