School of Magical Math

The School of Magical Math focuses on the application of common education in the arcane arts. Many wizards who specialize in this school typically spend there time studying and educating, rather than adventuring or fighting. Some however, use these principles in their travels to assist those in need. The core principles of applying mathematics to spellcasting involves using universal truths to rationalize these magical feats, and in doing so, the wzards who practice this can manipulate the very essence of spells.

Derivative Spellcasting

At 2nd level, you can derive the basic essence of spells that you have learned. By deriving a spell, one learns the basics of that spells formula, and can cast it without a spell slot, however, in doing so the spell is converted to its cantrip equivalent. All spells produce the same effect, simply at a lower level, for example, a derived fireball has it's sphere range halved and it's damage drastically reduced. See the list for spell effects after having been derived.

• If the spell deals damage, you roll a single damage die for its damage. Whenever you reach a cantrip scaling level, you can roll one additional damage die up to the spell's original amount of dice.
• If the spell deals a fixed amount of damage, it deals one-forth (1/4) of the damage. Whenever you reach a cantrip scaling level, this fixed amount of damage gains another part of its original damage like so: two-forths (2/4) at 5th level, three-forths (3/4) at 11th level, and original damage at 17th level.
• If the spell has a area effect, the size of the area is halved.
• If the spell has a effect duration, it becomes 1 minute. Whenever you reach a cantrip scaling level, the duration effect increase like so: 10 minute at 5th level, half-hour at 11th level, and 1 hour at 17th level.
• If the spell targets more than one creature or object (Bless, for example), it will target just a single one instead. Whenever you reach a cantrip scaling level, you can target one additional target up to the spell's original amount of targets.
• If the spell has a casting time of bonus action or reaction, or it summons or conjure something, it can't be derived.

You can only derive spells you have registered in your spellbook and you can derive a number of spells equal to your Intelligence modifier plus half of your Proficiency Bonus (rounded down).

Potent Derivatives

Starting at 6th level, your cantrips and derivative spells gain increased strength. You can now add your Intelligence modifier to the damage rolls of your cantrips and derivative spells.

Arcane Middle

Starting at 10th level, you can mold the spell equations for your damage dealing spells to guarantee a certain outcome. Whenever you cast a damage dealing spell, you can choose to deal the average amount of damage that spell would normally deal instead of rolling. You can do this a number of times equal to your Proficiency Bonus and regain expended uses after a Long Rest.

You can use this ability even if you spent all uses, however, the magic of your spell becomes unstable and dangerous. When you use this ability after you spend all uses, you gain one level of the variant exhaustion (the new one in the UA) per use.

Formulaic Recall

Starting at 14th level, you can attempt to cast spells from your memory. After studying arcane formulas for so long, you have begun to memorize them, because of that, you can attempt to cast a spell from your spellbook that you do not have prepared. To do this, you must succed on an pure Intelligence check with a DC equal to 13 + the spell's level that you are trying to cast, spending the spell slot as normal. The outcome of the casting may vary:

• If you succeed the check, the spell is casted successfully as normal. In addition, if you succeed the check by 5 or more, you roll 1 additional damage die, if the spell deals damage.
• If you fail the check, the casting fails consuming your spell slot. In addition, if you fail the check by 5 or more, you take damage equals a number of d6 equal your Intelligence modifier plus your Proficiency Bonus ([INT mod]d6 + PB) force damage.