AS/SC/AK/ MATH 4020 6.0

Algebra II

      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.