Just to save some time, here is list I just made up. I also abuse Staff WS's to save Stratagems. Happy Scholaring!
Fire
*Stone > Fire = Liquefaction
*Thunder > Fire = Liquefaction
Fire > Thunder = Fusion
Full Swing > Thunder = Fusion
**Rock Crusher > Fire = Liquefaction
Ice
*Water > Blizzard = Induration
Water > Shattersoul = Induration
Luminohelix > Stone = Distortion
Retribution > Blizzard = Induration
**Omniscience > Stone = Distortion
**Starburst > Blizzard = Induration
Wind
*Stone > Aero = Detonation
*Thunder > Aero = Detonation
Noctohelix > Aero = Detonation
Blizzard > Water = Fragmentation
Shattersoul > Water = Fragmentation
**Rock Crusher > Aero = Detonation
Earth
*Fire > Stone = Scission
*Aero > Stone = Scission
Aero > Noctohelix = Gravitation
Shell Crusher > Stone = Scission
Thunder
*Water > Thunder = Impaction
*Blizzard > Thunder = Impaction
Blizzard > Water = Fragmentation
Retribution > Thunder = Impaction
Shattersoul > Water = Fragmentation
*Shattersoul > Thunder = Impaction
**Starburst > Thunder = Impaction
Water
*Stone > Water = Reverberation
Luminohelix > Stone = Distortion
Luminohelix > Water = Reverberation
**Omniscience > Water = Reverberation
Light
*Fire > Thunder = Fusion
Full Swing > Thunder = Fusion
Dark
*Aero > Noctohelix = Gravitation
Blizzard > Noctohelix = Compression
Shattersoul > Noctohelix = Compression
Basic Scholar Light and Dark Skillchains
* Indicates which skillchains I personally use the most
** Skillchains I use the most with magical weapon skills to never miss