Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful constructs for doing this. Applying functions of one ...

Converting to and from character codes. Mathematica assigns every character that can appear in a string a unique character code. This code is used internally as a way to ...

Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

Within a standard interactive session, you can create "subsessions" or dialogs using the Mathematica command Dialog. Dialogs are often useful if you want to interact with ...

When you ask for the square root s of a number a, you are effectively asking for the solution to the equation s^2a. This equation, however, in general has two different ...

If you type in an expression like 0/0, Mathematica prints a message, and returns the result Indeterminate. An expression like 0/0 is an example of an indeterminate numerical ...

Options associated with the interactive entering of expressions. The option SingleLetterItalics is typically set whenever a cell uses TraditionalForm. Here is an expression ...

Pure functions. When you use functional operations such as Nest and Map, you always have to specify a function to apply. In all the examples above, we have used the "name" of ...

Mathematica always allows you to refer to special characters by using names such as ∖[Alpha] or explicit hexadecimal codes such as ∖:03b1. And when Mathematica writes out ...

Mathematica saves information about every plot you produce, so that you can later redraw it. When you redraw plots, you can change some of the options you use. Functions for ...