Goal: Acquirement of basic algebraic and number theoretic notions and theorems, their
application in exercises.
Course description: Operations, algebraic structures, basics of group theory, permutation
groups, Cayley theorem, Lagrange theorem, normal subgroups, factor groups, homomorphisms,
Isomorphism theorems, Sylow theorems, simple groups, soluble groups, nilpotent groups,
Abelian groups, composition series, direct products, fundamental theorem of finite Abelian
groups; free groups, basics of ring theory, commutative rings, ideals, factor rings, principal ideal
domains, Noetherian rings, integral domains, fields, construction of fields, finite fields, field
extensions, modules, algebras, basics of number theory, fundamental theorem of arithmetic,
Euclidean algorithm, congruence, linear congruences, Euler’s totient functions, quadratic
congruences