Guessing at what each of the classes means. Blanks are left when I'm uncertain. If you have advice/corrections post it.
Findamancy- Life+Erf. Summoning, probably more.
Predictamancy- Life+Fate. Let's you see the likely outcomes for battles between two stacks.
Mathamancy- Life+Numbers. Let's you adjust the stats of your/the enemies units.
Turnamancy- Motion+Erf. Let's you extend your turn, speed up unit production, move farther, etc.
Dollamancy- Motion+Fate. Voodoo-style attacks!
Weirdomancy- Motion+Numbers. Uncertain. Sounds like Wyrdomancy, but that would be fate.
Dirtamancy- Matter+Erf. Crap Golems and other units can be made with this magic.
Changemancy- Matter+Fate. Transmutation, certainly. What exactly it transmutes is uncertain.
Dittomancy- Matter+Numbers. Copying objects.
Lookamancy- Life+Motion+Erf. Let's you see into the "Fog of War" present in games like Civ.
Thinkamancy- Life+Motion+Fate.
Foolamancy- Life+Motion+Numbers. Illusions.
Flower Power- Life+Matter+Erf. Probably uses Mother Nature for various stat boosting effects.
Signamancy- Life+Matter+Fate.
Date-a-mancy- Life+Matter+Numbers. Maybe love spells, but that doesn't seem number-y
Shockmancy- Matter+Motion+Erf. Either electrical or emotional, or shock waves.
Croakamancy- Matter+Motion+Fate. Resurrects dead units, allows them to be used again. However, they decay after awhile, and presumably cannot be used again.
Deletionism- Matter+Motion+Numbers. Not sure. I'd suggest outright killing, but that's unbalanced and has to do with life.
Hat Magic- Life+Matter+Motion+Erf. Creates hats for various purposes, including boosting stats and communication between units.
Carnamancy- Life+Matter+Motion+Fate.
Rhyme-a-mancy- Life+Matter+Motion+Numbers.
Luckmancy- Erf. Perhaps this just shifts battles and the like into someone's slight favor. The odds are shifted, but probably not significantly, and probably for only limited periods of time.
Healomancy- Fate. Heal units.
Moneymancy- Numbers. Adjusts upkeep costs.
So, any thoughts on the rest?
EDIT: Skipped Thinka/Foola. Too tired right now to bother...