MTH2122

Algebra and number theory

(SCI)

Dr Tom Hall

6 points + Three 1-hour lectures and an average of one 1-hour support class per week + Clayton + Second semester + Prerequisites: MTH1020, or MTH1112, or MAT1830, or equivalent + Prohibitions: MAT3091, MTH2121, MTH3121, MTH3122.

Synopsis: Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the fundamental homomorphism theorem. The euclidean algorithm, prime factorisation, congruences, the Euler totient function; the theorems of Fermat, Euler and Wilson, and the RSA public key cryptosystem; Chinese remainder theorem; rings, fields and abelian groups in number theory.

Assessment: Examination (3 hours): 70% + Assignments and tests: 30%