Continuation
of Algebra I, with applications: groups (finitely generated
Abelian groups, solvable groups, simplicity of alternating groups, group
actions, Sylow's theorems, generators and relations); fields (splitting
fields, finite fields, Galois theory, solvability of equations); additional
topics (lattices, Boolean algebras, modules).
[Ed. note: In the absence of any information from Trojan, we
give Professor Burns's supplementary course description from
1998/99.]
This course aims to broaden and deepen the student's knowledge
and understanding of abstract algebra by building on the material
of MATH 3020 6.0 (or a comparable course which students may
have taken). Further possible topics:
Group theory: permutation
groups, simple groups, symmetry groups.
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.
Boolean algebra (time permitting): applications to circuitry
and logic, boolean rings, finite boolean algebras.
Prerequisite:AS/SC/AK/MATH 3020 6.0 or permission of the course
coordinator.
ExclusionAS/SC/MATH 4241 3.0.
Coordinator: A. Trojan
