Abstract Algebra I  (MSU - Fall 2006 - Meierfrankenfeld)

 

Homework 1: pregroups, semigroups, and groups

 

Homework 2: quotient groups and automorphisms

 

Homework 3: normal subgroups and the second isomorphism thm

 

Homework 4: cosets, third isomorphism thm, and finite presentations

 

Homework 5: group actions and Sylow p-subgroups

 

Homework 6: semigroup rings, division rings, and ideals

 

Homework 7: prime ideals and principal ideals

 

 

 

Abstract Algebra II (MSU - Spring 2007 - Meierfrankenfeld)

 

Homework 1: modules

 

Homework 2: polynomial rings and fields of fractions

 

Homework 3: field extensions

 

Homework 4: algebraic field extensions and Galois theory

 

Homework 5: algebraically closed extensions and Frobenius

 

Homework 6: R-linear actions and dual spaces

 

Homework 7: unique factorization domains and varieties

 

 

 

 

Complex Analysis  (MSU - Summer 2008 - Kurtz)

 

Homework 1: sets in the complex plane, harmonic and analytic functions

 

Examination 1: roots, harmonic and analytic functions, and elementary integrals

 

Homework 2: residue theorem, heat equation boundary value problem