Mathematica as a basic calculator:

3 + 2

4*5

4/5

N[(4/5)]

N[4/5]

3^4

4*3 + 12

4(3+12)

Most if not all common mathematical functions are built in to Mathematica. All functions have names that start with a capital letter, and take arguments in square brackets:

Sqrt[25]

Sin[Pi]

Cos[Pi]

Calculate the length of the hypotenuse of a triangle with legs of length 3 and 4:

Sqrt[ 3^2 + 4^2 ]

Try to come up on your own with a Mathematica expression that calculates the distance from (2,1) to (5,-1). Here’s what you found:

Sqrt[ (2-5)^2 + (1 - -1)^2 ]

N[(Sqrt[13])]

N[(Sqrt[13])]

There’s also a EuclideanDistance function built in, which does this calculation in one command (most calculations anyone would even remotely want to do seem to be built in to Mathematica -- if you think one might be, Google it and see):

EuclideanDistance[ {2,1},{5,-1}]

Plotting 3D implicit surfaces:

ContourPlot3D[ x^2 + y^2 + z^2  == 4, {x,-3,3},{y,-3,3},{z,-3,3} ]

ContourPlot3D[ (x-2)(y-3)==0, {x,-5,5},{y,-5,5},{z,-5,5}]

Beware that error messages from Mathematica (and any other computer language) are likely to be hard to understand, especially for novices:

ContourPlot3D[x==2,y==3, {x,-5,5},{y,-5,5},{z,-5,5}]