Introduction to Mathematica at UMBC

Contents

1. Getting To Mathematica at UMBC
2. General Use of Mathematica
   • The Basics
   • Help on Mathematica Commands
   • Editing Command Lines
3. Linear Algebra Commands
4. Number Theory Commands
5. Statistics Commands

Mathematica is a commercial symbolic algebra system which allows computations in many fields of mathematics and engineering. Packages can be used to extend the Mathematica language in areas where the basic language is weak.

Getting To Mathematica at UMBC

UMBC appears to have a site license for Mathematica (OIT pages [1] [2]). As a result Mathematica is available in computer labs, on remotely accessible servers and for use on home machines by faculty, staff and students.

Mathematica is also available on UMBC servers which are accessible across the internet. Any UMBC employee or student has access using the account name and password they normally use for UMBC e-mail.

• Computer Labs: computer labs in the ENGR and ACIV buildings and the basement of the library [OIT labs page].
• UMBC Servers: If you are a UMBC student or staff with an @umbc.edu email account you have access to Mathematica on the server gl.umbc.edu. Details of logging into this server are here. Once you have logged in you can run Mathematica by typing the command math followed by pressing the return key. (If you have set up an X-Windows (remote graphics) display the appropriate version of Mathematica is run with the command mathematica.)
• Home Computers: If you are UMBC faculty, student or staff the site license should allow you to install a copy of Mathematica on your home machine. The current [OIT instructions] direct you to the "Services" tab on http://my.umbc.edu, where there should be a link to both download the program and a (yearly updated) license key.

2. General Use of Mathematica

The Basics

At the Mathematica command prompt (which usually looks something like In[1]:=) type the command to be run, and then press the Return key to have Mathematica evaluate the command. As a simple example, if you want to add two integers type:

3 + 12

Intermediate values can be saved by giving them a name and assigning them a value with the "=" operator. If the following two commands are run the second output will be 1:

thesum = 3 + 12
thesum - 14

Mathematica uses square brackets for functions and reserves the usual round brackets for grouping operations. Thus, to take the sin of 3, add it to 5, and divide the result by 2 we would write (Sin[3] + 5)/2.

Mathematica is very careful about exact values. Exact values are things like symbols and integers. Thus Sin[3] is an exact value and when you evaluate Sin[3] you get Sin[3] back as an answer. Contrast this with the fact that 3.0 is an approximate value and thus Sin[3.0] evaluates to the approximate value 0.14122. The N[] operator will force a numerical evaluation.

In[1]:= Sin[3]
Out[1]= Sin[3]

In[2]:= Sin[3.0]
Out[2]= 0.14112

In[13]:= N[Sin[3]]
Out[13]= 0.14112

When you are done with Mathematica, type the command Quit (remembering the capitalization) and press the return key.

Help on Mathematica Commands

There are several ways to find help in Mathematica. You can search by the specific Mathematica command (if you know it). The basic help request is
?cmd.
This only works if cmd is a correctly spelled (and capitalized) Mathematica command. A slight improvement can be gained with the use of the wildcard * (any string of characters).

In[9]:= ?Plus
x + y + z represents a sum of terms.

In[12]:= ?Add*
AddOnHelpPath AddTo

More detailed information (although generally not more helpful) can be gotten with the double question mark operator.

In[17]:= ??Plus
x + y + z represents a sum of terms.

Attributes[Plus] = {Flat, Listable, NumericFunction, OneIdentity, Orderless, 
   Protected}
 
Default[Plus] := 0

A more common situation is when you know your topic but don't know the name of the appropriate command. Currently, the best solution for this is to refer to the Mathematica Book, either in hard copy or the web-based version freely available at [http://reference.wolfram.com].

Editing Command Lines

When working with Mathematica on the Windows/Mac interface you can edit a command using the usual mouse, click and type method. If you are working across a network connection Mathematica is clumsier to work with than say, Maple, as there is no way to edit a line short of backspacing to the error and retyping the end of the command. Arrow keys are not recognized and there isn't a simply accessible command history.

Mathematica does have a fairly complete way of referring to previous expressions. Each line is numbered. A command may be referred to by it's number or by how far back it was. Thus, command -1 is the previous command. The various mechanisms are:

• In[n] - Re-execute the input from command n.
• InString[n] - The input from command n, exactly as typed, in the form of a string.
• Out[n] - The output from command n. A shorthand for this is %n. % is the previous command, equivalent to Out[-1].

Note that re-executing a command with In[n] may not give the same result as simply recalling its original output with Out[n].

In[1]:= x=2
Out[1]= 2

In[2]:= x+y
Out[2]= 2 + y

In[3]:= x=3
Out[3]= 3

In[4]:= x+y
Out[4]= 3 + y

In[5]:= In[2]
Out[5]= 3 + y

In[6]:= Out[2]
Out[6]= 2 + y

In[7]:= InString[2]
Out[7]= x+y