Algebrical theory of numbers |
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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 |
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. Dedekind rings. Units in algebraic number fields. Some diophantine equations. Pell's equation. Continued fractions. On the Fermat-Wiles theorem. |
References |
1.K. Ireland, M. Roseu - A Classical Introduction to Number Theory, Springer-Verlag 1990
2. T. Albu, I. D. Ion - Capitole de teoria algebrică a numerelor, Ed. Academiei, Bucuresti 1981 3. I Niven, H. Zuckerman - Bevezetés a Számelméletbe, Müszaki Könyvkiadó, Budapest 1978 4. P. Erdos, J. Suranyi, Valogatott fejezetek a szamelmeletbol, Polygon Kiado, Szeged, 1996. 5. E. Gyarmati, Szamelmelet, Tankonyvkiado, Budapest, 1980. 6. G.H. Hardy, E.M. Wright, An introduction to the theory of numbers, Clarendon Press, Oxford, 1938. 7. W. Sierpinski, Elementary theory of numbers, Warszawa, 1964. 8. Megyesi L. - Bevezetés a Számelméletbe, Polygon, Szeged 1997. |
Assessment |
Exam. |