School of Mathemagics

You search for the logical concepts behind the arcane in mathematics and numbers and use this knowledge to manipulate the spells you cast from the most basic building blocks up.

Runic Deriviation

While studying the casting of spells you created a theorem to siphon off the energy needed to create the spell and use it for additional damage. Whenever you cast a spell you can use your Bonus action to make a ranged spell attack to deal damage equal to the number of damage dice and the damage type(s) of the spell to a target in 30 ft. of you.

At 11th level. You can add your proficiency bonus to the damage.

Arcane Algebra

When you transcribe a spell, you can choose to either double the time spent transcribing and half the cost or double the cost to half the transcription time.

Commutative Magic

While you are concentrating on a Spell, you can use your action to move the effect to another point or target within 30 ft. of it. The new point or target must be legal for the Spell. Any spell effects end immediately on targets and places that are no longer targeted by the Spell. You can use this feature a number of times equal to your Intelligence modifier (a minimum of once). You regain all expended uses when you finish a long rest.

Advanced Geomagical Theorems

Starting at 6th level, you have spent years solving complex mathematical equations, allowing you to shape your spells with precision and create pockets of safety for allies. When you cast a spell that affects other creatures that you can see, you may choose a number of them equal to your Intelligence modifier. The chosen creatures automatically succeed on their saving throws against the spell, and they take no damage if they would normally take half damage on a successful save. Additionally, when you cast a spell that has an area of effect radius, you may choose to manipulate it in the following ways:

Line	You can bend the spell once by 90° at any point
Cone	Creatures at the thin end of the cone have advantage on the saving throw but take the spells level * 2 dice extra damage, that are the same die and damage type as the ones the spell uses. If the Spell deals no damage,  creatures on the broad end of the cone have disadvantage on their saving throw against the spell.
Cube	After you cast the spell a magical cube of force remains, no creature can cross these walls. The size of the cube is equal to the size of the spell. The AC of the cube is equal to 8 + your proficiency modifier, its HP are 5 * spell level. It remains until the end of your next turn, but after that you can concentrate on it as if it was a concentration spell.
Sphere	Any Creature must succeed on a Strength saving throw or be sucked as far vertically into the center of the spell as possible.
Cylinder	Until your next turn, allied creatures only must spend 2,5 ft of movement every 5 ft while moving through the area the spell was cast.

Universal Theory

You are able to use your intellect and knowledge of the basic working of the world to succeed in most of your tasks, when ever you make a roll that uses Wisdom or Charisma you can use Intelligence instead.

Whenever you succeed on a saving throw on a magical effect that charms or frightens you can use your reaction to explain the logical workings of the effect to your allies to immediately let them reroll the save if they failed it.