lhs :> rhs or lhs :> rhs represents a rule that transforms lhs to rhs, evaluating rhs only after the rule is used.

SetOptions[s, name_1 -> value_1, name_2 -> value_2, ...] sets the specified default options for a symbol s. SetOptions[stream, ...] or SetOptions["name", ...] sets options ...

Combinatorial functions. The factorial function n! gives the number of ways of ordering n objects. For non-integer n, the numerical value of n! is obtained from the gamma ...

Functions relating real numbers and integers. Extracting integer and fractional parts. IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left ...

Much of what Mathematica does revolves around manipulating structured expressions. But you can also use Mathematica as a system for handling unstructured strings of text. ...

Repeated patterns. Multiple blanks such as x__ allow you to give patterns in which sequences of arbitrary expressions can occur. The Mathematica pattern repetition operators ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.

BarChart3D[{y_1, y_2, ...}] makes a 3D bar chart with bar lengths y_1, y_2, ....BarChart3D[{..., w_i[y_i, ...], ..., w_j[y_j, ...], ...}] makes a 3D bar chart with bar ...

Locator[{x, y}] represents a locator object at position {x, y} in a graphic. Locator[Dynamic[pos]] takes the position to be the dynamically updated current value of pos, with ...

Text[expr] displays with expr in plain text format. Text[expr, coords] is a graphics primitive that displays the textual form of expr centered at the point specified by ...