Syllabus
1. Monoids, groups and subgroups. Factorization of groups and normal subgroups.
2. Cyclic groups and RSA.
3. Basic notions of universal algebra: algebra, homomorphism, congruence.
4. Lattices and Boolean algebras.
5. Rings and ideals. Fields of fractions. Construction of finite fields.
Annotation
The course in basic algebra is devoted to fundamental algebraic notions that are demonstrated on basic algebraic structures. Notions include closure systems, operations, algebras (as sets with operations), homomorphisms, congruences, orderings and the divisibility.
Lattices, monoids, groups, rings and fields are regarded as the basic structures. The course also pays attention to modular arithmetic and finite fields.