There are two ways to enter mathematical symbols. The first is, to use the panel with mathematical symbols on the right side of the screen. The second is, to use shortcuts which often is a more efficient way once you get familiar with the names of the commands. The shortcuts are specifically chosen to be intuitive. Also pointing the mouse at a symbol in the panel will give you a hint for the specific keyword.
Here are a few of the useful shortcuts:
Here are some useful shortcuts.
^ -- raise to a power.
sqrt -- create a root symbol which by default is a square root when nothing is entered for the degree of the root.
integrals- int for an indefinite integral
- cint for a contour integral
- dint for a definite integral
- union/intersection
- cup for a union
- cap for an intersection
pi -- create the Greek letter for pi
arcsin, arccos, arctan -- inverse trigonometric functions. Please also note that (-1) power notation is never used for inverse trig functions in Gradarius. 
po -- create (,) notation for a point
(,) -- create notation for an interval
vectors
- vec + symbol for an arrow notation of a vector named symbol
- vec + < or <> for an angle brackets notation
- vi or vx, vj or vy, vk or vz for unit vectors (<1,0,0>, <0,1,0>, <0,0,1> respectively)