Galois theory is rightly regarded as the peak of undergraduate algebra, and the modern algebra syllabus is designed to lead to its summit, usually taken to be the unsolvability of the general quintic equation. I fully agree with this goal, but I would like to point out that most of the equipment supplied-in particular normal extensions, irreducible polynomials, splitting fields and a lot of group theory-is unnecessary. The biggest encumbrance is the so-called "fundamental theorem of Galois… Expand

Department of Mathematics Monash University Clayton 3168 Australia PICTURE PUZZLE (from the collection of Paul Halmos) This famous topologist was usually considered more scary than scared