$Assumptions is the default setting for the Assumptions option used in such functions as Simplify, Refine, and Integrate.

$ProcessorCount gives the number of processor cores available on the computer system on which Mathematica is being run.

When you write a program in Mathematica, you should always try to set it up so that its parts are as independent as possible. In this way, the program will be easier for you ...

Converting between strings and lists of characters. This gives a list of the characters in the string. You can apply standard list manipulation operations to this list.

Steps in the operation of Mathematica. When you type something like x^2 what Mathematica at first sees is just the string of characters x, ^, 2. But with the usual way that ...

"Redrawing and Combining Plots" describes how you can make regular arrays of plots using GraphicsGrid. Using the Inset graphics primitive, however, you can combine and ...

In many kinds of calculations, you need to set up "arrays" that contain sequences of expressions, each specified by a certain index. One way to implement arrays in ...

Many of the most powerful list manipulation operations in Mathematica treat whole lists as single objects. Sometimes, however, you need to pick out or set individual elements ...

Manipulating global options in the front end. Just like cells and notebooks, the complete Mathematica front end has various options, which you can look at and manipulate from ...

It is often useful to carry out a numerical integration using fixed step sizes. For example, certain methods such as "DoubleStep" and "Extrapolation" carry out a sequence of ...