Subject matter:
Selected topics from:

    Divisibility into rings (especially Z- and polynomial rings); residual classes and congruencies; modules and ideals
    Euclidean, principal ideal and factorial rings
    The quadratic law of reciprocity     Primality tests and cryptography     The structure of abel groups (or modules about main ideal rings)     Symmetric function set     Body extensions, Galois correspondence; constructions with compasses and rulers     Non-Label groups (set of Lagrange, normal dividers, dissolvability, sylow groups)