35314 Pure Mathematics 3B

Requisite(s): 35111 Discrete Mathematics

Topics in this subject include a selection of:

• number theory: the division algorithm and unique factorisation in Z, number-theoretic functions, congruences, Fermat's theorem, Euler's theorem, linear diophantine equations, continued fractions
• groups: basic definitions, symmetry groups, cyclic groups, generators, relations and presentations of a group, subgroups and cosets, conjugacy and normal subgroups, quotient groups, solvable groups, prime power groups, Sylow theorems
• group homomorphisms and isomorphism theorems, and
• introduction to rings: homomorphisms, subrings, ideals, quotient rings.

Typical availability

Autumn semester, City campus