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 Mathematica Tutorial

# Getting Used to Mathematica

 • Arguments of functions are given in square brackets. • Names of built-in functions have their first letters capitalized. • Multiplication can be represented by a space. • Powers are denoted by ^. • Numbers in scientific notation are entered, for example, as 2.5*^-4 or 2.510^-4.

Important points to remember in Mathematica.

If you have used other computer systems before, you will probably notice some similarities and some differences. Often you will find the differences the most difficult parts to remember. It may help you, however, to understand a little about why Mathematica is set up the way it is, and why such differences exist.
One important feature of Mathematica that differs from other computer languages, and from conventional mathematical notation, is that function arguments are enclosed in square brackets, not parentheses. Parentheses in Mathematica are reserved specifically for indicating the grouping of terms. There is obviously a conceptual distinction between giving arguments to a function and grouping terms together; the fact that the same notation has often been used for both is largely a consequence of typography and of early computer keyboards. In Mathematica, the concepts are distinguished by different notation.
This distinction has several advantages. In parenthesis notation, it is not clear whether c (1+x) means c[1+x] or c*(1+x). Using square brackets for function arguments removes this ambiguity. It also allows multiplication to be indicated without an explicit * or other character. As a result, Mathematica can handle expressions like 2x and ax or a (1+x), treating them just as in standard mathematical notation.
You can see from "Some Mathematical Functions" that built-in Mathematica functions often have quite long names. You may wonder why, for example, the pseudorandom number function for generating reals is called RandomReal, rather than, say, Rand. The answer, which pervades much of the design of Mathematica, is consistency. There is a general convention in Mathematica that all function names are spelled out as full English words, unless there is a standard mathematical abbreviation for them. The great advantage of this scheme is that it is predictable. Once you know what a function does, you will usually be able to guess exactly what its name is. If the names were abbreviated, you would always have to remember which shortening of the standard English words was used.
Another feature of built-in Mathematica names is that they all start with capital letters. "Defining Variables" and "Defining Functions" discuss how to define variables and functions of your own. The capital letter convention makes it easy to distinguish built-in objects. If Mathematica used max instead of Max to represent the operation of finding a maximum, then you would never be able to use max as the name of one of your variables. In addition, when you read programs written in Mathematica, the capitalization of built-in names makes them easier to pick out.

## Some Mathematica Conventions

Built-in functions are capitalized. Arguments to functions are wrapped with square brackets. Sin[x]
Each of these represents multiplication. a*b a b a(b+1) 2x means 2*x.
These are standard arithmetic operations. 2+3 2-3 2/3 2^3
Uppercase and lowercase letters are recognized as different characters. Lists are wrapped with curly brackets. {a, b, B}
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. x=5 xvalue=3