a ** b ** c is a general associative, but non-commutative, form of multiplication.
SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.
RevolutionPlot3D and SphericalPlot3D have been added to the built-in Mathematica kernel. RevolutionPlot3D includes the functionality of CylindricalPlot3D.
Level
(Built-in Mathematica Symbol) Level[expr, levelspec] gives a list of all subexpressions of expr on levels specified by levelspec. Level[expr, levelspec, f] applies f to the sequence of subexpressions.
PairedBarChart[{y_1, y_2, ...}, {z_1, z_2, ...}] makes a paired bar chart with bar lengths y_1, y_2, ... and z_1, z_2, ..., respectively.PairedBarChart[{..., w_i[y_i, ...], ...
Characters["string"] gives a list of the characters in a string.
One significant advantage Mathematica provides is that it can symbolically compute derivatives. This means that when you specify Method->"Newton" and the function is ...
If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...
DiscreteIndicator[x, x_1, {u_1, u_2, ...}] yields the discrete indicator function, equal to 1 if x = x_1 and 0 if x = u_i for any i.
DiagramPlot[{{x_1, y_1}, {x_2, y_2}, ...}] plots the Voronoi diagram of the points {{x_1, y_1}, ...}. DiagramPlot[{{x_1, y_1}, {x_2, y_2}, ...}, {q_1, q_2, ...}, val] plots ...