Syllabus
Basic techniques and results from algebra applied in combinatorics and number theory.
For example, in extremal problems (combinatorics) or diophantine equations (number theory).
Annotation
If the field of fractions Q is replaced with its finite extension K, for example K=Q(i) or K=Q(2^{1/2}), the ring of integers Z extends in the ring of integers O_K of K. Algebraic number theory investigates arithmetic of O_K, especially unique factorization.
These results have important applications in the original ring Z, mainly for solving diophantine equations. In the course we shall present basic notions and results as well as some applications to diophantine equations.