Syllabus
1) Number theory: prime factorization, congruences, Euler's theorem and RSA, the Chinese remainder theorem 2) Polynomials: rings and integral domains, polynomial rings, irreducibility, GCD, the Chinese remainder theorem and interpolation, the construction of finite fields and applications (error-correcting codes, secret sharing,...) 3) Group theory: permutation groups, subgroups, Lagrange's theorem, group actions and Burnsides's theorem, cyclic groups, discrete logarithm and applications in cryptography see also: https://www.logic.at/staff/kompatscher/algebra1.html
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.