Dr. Sarah's 3110 Page on the Solution of the Quadratic, Cubic, Quartic and Quintic by Radicals

Read the first section on Galois Theory from this web page, which contains a good historical introduction to the subject

Briefly skim through some of the numeric computation involved in solving a quartic

Briefly skim through this history of quadratic, cubic and quartic equations

Read Through this page on the progression of solutions of polynomials by radicals to the begining of Modern Algebra via fields

Work in groups of two on Dr. Sarah's Maple Demo on the Insolvability of Quintics by Radicals