I don't have ArcGIS and won't buy a license for it for this. Math is fine, though. I'm interested in what other people use to do this but for my own purposes I'd rather write the projection conversions myself rather than use prebuilt software to do it.
So I suppose I'm looking more for the math behind it than a program that does it in a black box sort of way. (and ideally a mathematica, matlab or maple notebook)