School of Calculus

Some wizards are able to understand mathematical truths, and weave them into their spellcasting. By observing the very monads which all things are made of, they can see the world as one big parametric function, and manipulate it as such. They excel at battlefield control and integration by parts, which are basically the same thing when you think about it.

Mathematical Savant

Beginning when you select this school at 2nd level, the time and gold it takes to copy any spell into your spellbook is raised to the power of 9/10.

Range Calculation

Starting at 2nd level, whenever you cast an area of effect spell, instead of using the normal range, roll 5d6. Define a function f(x) such that f(0)=0 and assign the die results to the value of the first through fourth derivatives of f(x) at x=0 (One die result will be neglected). Then, graph the fourth-degree Taylor polynomial of f(x) at x=0. Place the graph on the battlemap with yourself at the origin and the graph in whatever orientation you choose. The range of the original spell is replaced with every square this graph goes through. The domain of f is [-150,150] (Don’t worry, your party will be perfectly fine with the amount of time it takes to determine the optimal curve to hit as many enemies as possible)

 

Constant of Integration

Starting at 6th level, twice each long rest, you can realize that you forgot the constant of integration and hastily add it in as an action. You and all creatures within 150 feet of you are transported up to c∈[-25,25] feet in any direction. All creatures must be moved the same way. Any creature that would be transported into a solid object takes 2d6 force damage and is moved to the nearest available space. At 10th level, you may use this ability as a bonus action.

 

Greater Range Calculation

Starting at 10th level, whenever you activate your Range Calculation, you may expend a spell slot of first level or higher. If you do, 1d6 damage is added to the damage dealt by the spell to each enemy per level of the spell slot. Additionally, you may replace f(x) with g(x), defined in one of the following ways: g(x)=xf(x), g(x)=f(x)/x, g(x)=(d/dx)f(x), or (d/dx)g(x)=f(x), with initial condition g(0)=0.

 

Polar Integration

Starting at 14th level, once each long rest, you can take a polar integral. Any number of creatures you can see within 60 feet must make a dexterity saving throw. On a failure, they take ½(r^2)d4 psychic damage, where r is their distance from you, in battlemap square. On a success, they take rd4 damage instead.