Your First Mathematica Calculations

Type and then press Shift+Enter (hold down the Shift key and press Enter) to tell Mathematica to evaluate your input.

Note that labels are added automatically, and output is placed below the input.
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Your first calculation will take longer than subsequent calculations because the Mathematica kernel has to start up.

You can use Mathematica just like a calculator. Type the input and press Shift+Enter. Here is the result.

A basic numerical calculation.
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Here is an example from algebra. Type the input Factor[x^25-1] and note that as you type, the first bracket after the function name Factor has a special color until the closing bracket is typed.

A basic algebraic calculation.
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You can use Greek letters or letters from other alphabets as variables.
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You can recall your most recent input (or output) in your next evaluation by pressing "Ctrl"+L (or Shift+"Ctrl"+L).

Mathematica uses syntax coloring to help you compose expressions that are complicated. As part of that, function names and variables that are known to the Mathematica kernel are colored black. New symbol names are by default colored blue, but turn black after being evaluated for the first time.

You can configure the syntax coloring system using the Syntax Coloring dialog box. To open the dialog box, choose Edit ► Preferences, click the Appearance tab, and then the Syntax Coloring tab.

Here are some more examples.

Integrate is just one of over a thousand built-in Mathematica functions.

Note that the variable of integration is specially colored in the input.
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Plot3D produces a three-dimensional plot. The graphic appears directly in your notebook, and can be interactively rotated and zoomed in or out.

Note that the plotting variables are also specially colored.
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You can get instant information about a built-in function. Type ?, the function name, and then press Shift+Enter.

In a notebook interface, ?function also gives a link to the documentation for function.

To complete a partially typed command name, press "Ctrl"+K. This is equivalent to Edit ► Complete Selection. To see a function template for a given function, press Shift+"Ctrl"+K. This is equivalent to Edit ► Make Template.

To abort a calculation, press DynamicBox[ToBoxes[Which[$OperatingSystem === MacOSX, Cmd, $OperatingSystem === Windows, Alt, True, Mod1], StandardForm], ImageSizeCache -> {16., {0., 10.}}]+. More options for controlling evaluation can be found under the Evaluation menu.

Some Mathematica Conventions

Here are some basic things to remember when working with Mathematica:

Built-in functions are capitalized. Arguments to functions are wrapped with square brackets. Sin[x]
Each of these represents multiplication. means .
These are standard arithmetic operations.
Uppercase and lowercase letters are recognized as different characters. Lists are wrapped with curly brackets.
Built-in symbols are capitalized. Commas are used to separate arguments. A semicolon suppresses output, but the command is still evaluated. N[Pi, 50];
Variables are usually lowercase. Entire words can be used.
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