Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, Görükle Bursa-TÜRKİYE 0 224 294 17 70 / firstname.lastname@example.org
Objective of the Course:
The algebraic number theory brings two important areas of mathematics such as algebra and numbery theory. Our first aim is to introduce fundamental ideas of algebraic numbers and the second is to illustrate how basic notions from the theory of algebraic numbers may be used to solve problems in number theory. The main focus is to extend properties of the integer numbers to more general number structures: algebraic number fields and their rings of algebraic integers. Then give an introduction to Fermat’s last theorem. So students can see how basic ideas are used to solve problems in number theory.
Contribution of the Course to Professional Development
Learns basic concepts on symetric polynomials, modules, free abelian groups.;
Learns algebraic numbers, algebraic integers, integral bases, norms and traces. ;
Learns factorization into irreducibles, trivial factorizations and Euclidean domains.;
Learns ideals, the decomposition of ideals, the norm and classes of ideals, factorization in cyclotomic fields and lattices.;
Learns Minkowski theorem, two and four square theorem.;
Learns class groups, finiteness of the class groups and number-theoric applications and some class number calculations.;
Learns elliptic curves and the group structure on elliptic curves, Fermat’s last theorem.;
Basic concepts on groups, ring and fields and some elementary theorems.