Tutorial 2A:  Keystrokes

by R. Dover, IMSA

Note:  This notebook is optional.  It may be done at any point after Tutorial 2. Or you may wish to skip it entirely.  This shows another way of entering mathematical notation and symbols.  You are still welcome to use the palettes or simply enter expressions using the English terms and "longhand," such as one would use on a graphing calculator.  For some, it will be much easier to continue with the other tutorials and become more familiar with the program before adding another layer of choices at this point.

Special letters

First, find the "escape" key,  Esc, on the keyboard.  This will become very familiar.  Mathematica denotes this by  when showing keystrokes for symbols.  For example, in order to create the symbol π, the keystokes are  Esc p Esc .  This will also be shown as   p .  Try it.

For e, shown as e, the coding is  ee .  Similarly for i = (Sqrt[-1]), use  i i .  Now evaluate (e^(2  iπ)).  (Use the palette or simply ^ to get the exponent.)

For Greek letters, the approach is similar.  For α, type  a .  The first letter will work for many (but there are often choices and options).  For θ, use  q .  ( q is also used in symbol font to obtain θ.  Unfortunately, t  is already taken by τ.)  Type:  Sin[α + β] / / TrigExpand.  Then try that for a couple of other variables and some other trig functions.

To create the ∞ symbol, type  inf .  Alternatively, Mathematica does understand the word "Infinity."  An arrow, used for options when plotting and for limits, may be created by "->", a dash and the greater than symbol.  Using  before and after these will make it look like a real arrow.  Execute the following cell.

Limit[(1  +  1/n)^n,  n  ->  ∞]

Now try a couple of your own expressions.

Notation

For this section, find the "control" key, Ctrl.  Many notational forms use it. To obtain  (3^125), enter the following below:  3 Ctrl-^ 125. (Hold the control key down as you type ^.)  Then use either the right cursor or Ctrl-␣ to move out of the exponent.  (Note that you may also enter 3 Ctrl-6  125, since the 6 and the ^ are on the same key.  This is actually a bit simpler.)

For a fraction, the approach is similar.  To write (1/2), enter  1 Ctrl-/  2.  Again, use the right cursor or Ctrl-␣ to move out of the denominator.  In other words, use the Ctrl with the symbol on the key you would normally use.  Add a couple of fractions together.  Then find a numerical approximation.

Creating a fraction with something a bit more complicated in the numerator requires a slightly different approach.  For example, to obtain ((x + 3)/4), type x + 3, select this expression, and then type Ctrl - / to continue with the denominator.  Try this.

A square root is obtained by using Ctrl-2.  Do it.

Harder?

Execute the following.

Sum[1/k^2,  {k,  1 ,  Infinity}]

Let's enter the same expression in 2-dimensional form (rather than the 1-dimensional form above).  Begin a new cell and type the following: 
	  sum   Ctrl-= k = 1 Ctrl-%   inf   Ctrl-␣ 1 Ctrl-/ k Ctrl-6  2 Ctrl-␣

Was that fun?  It does look nice, but sometimes it is much easier (and quicker) to simply use the palettes.  Or to type in one-dimension.  For many, once you are accustomed to the Esc key and the Ctrl key, many letters and symbols actually do come quite quickly.  But it will take a bit of practice.
	In reality, many experienced Mathematica users switch forms and freely combine palettes, keystrokes, and longhand, depending upon the expression.  It will also depend on the mood they are in at that moment.