Algebra II

This course aims to broaden and deepen the student's knowledge and understanding of abstract algebra by building on the material of MATH3020.06 (or a comparable course which the student may have taken).

The algebraic structures to be discussed in some detail are groups, rings, fields and (possibly) boolean algebras. Topics will be chosen from the following:

Group theory: finitely generated abelian groups, permutation groups, simple groups, symmetry groups, Sylow's theorems. Ring theory: divisibility in integral domains with applications to diophantine equations, elements of algebraic number theory, rings with chain conditions. Field theory: field extensions with applications to constructions with straightedge and compass, finite fields, elements of Galois theory. Boolean algebra: boolean algebras with application to circuitry and logic, boolean rings, finite boolean algebras, lattices.

The text will be announced later.

The grade breakdown has not yet been decided.