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This topic includes: Basic concepts of mathematical logic and set theory. Axiomatic definition of integers. Divisibility, primes, Euclidean algorithm, co-primes, Euclid's lemma, prime factorisation. Congruence classes and modular arithmetic. Groups, subgroups, cyclic groups, Euler's function. Permutations, even and odd, definition of determinant. Homomorphisms and isomorphisms of groups, Cayley's theorem. Cosets, Lagrange's theorem. Normal subgroups, quotient groups, first isomorphism theorem. Cartesian product of groups. RSA public key cryptography. Classification of finitely generated abelian groups. Sylow theorems. Rings, subrings, units, zero-divisors, integral domains and fields. Polynomial rings over fields, remainder and factor theorems. Irreducible and coprime polynomials. Euclid's lemma and prime factorisation for polynomials. Roots of polynomials, criteria of irreducibility. Homomorphism and isomorphisms of rings. Ideals, principal ideals, quotient rings. Prime and maximal ideals. Ideals of polynomial rings, finite fields and their construction.
This topic aims to provide:
Timetable details for 2021 are no longer published.
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