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.