Note: You are looking at a static copy of the former PineWiki site, used for class notes by James Aspnes from 2003 to 2012. Many mathematical formulas are broken, and there are likely to be other bugs as well. These will most likely not be fixed. You may be able to find more up-to-date versions of some of these notes at http://www.cs.yale.edu/homes/aspnes/#classes.

Suppose you want to write down some mathematics. How do you do it?

# 1. Option 1: by hand

This method is recommended for CS202 assignments.

Don't need to learn any special formatting tools: any symbol you can see you can copy. Very hard to make typographical errors.
Not so good for publishing. Results may be ugly if you have bad handwriting. Results may be even worse if you copy somebody else's bad handwriting.
Example

# 2. Option 2: LaTeX

This is what I use for writing papers.

Very nice formatting. De facto standard for mathematics publishing. Free.
You have to install it and learn it. Can't tell what something looks like until you run it through a program. Cryptic and uniformative 1970's-era error messages.
Example

The text above was generated by this source code:

$\sum_{i=1}^n i = \frac{n(n+1)}{2}$

although a real LaTeX document would also include some boilerplate around it.

You can find many introductions to LaTeX at http://www.latex-project.org/guides/. LaTeX runs on the computers in the Zoo, and can be made to run on just about anything.

There are front-ends to LaTeX like LyX that try to make it WYSIWYG. I don't use any of them personally.

# 3. Option 3: Microsoft Word equation editor

This is probably a bad habit to get into.

There's a good chance you already type things up in Word.
Ugly formatting.

I don't use Word much, so no example.

# 4. Option 4: ASCII and/or Unicode art

This is the method used on most of the pages on this wiki.

Everybody can read ASCII and most people can read Unicode. No special formatting required. Results are mostly machine-readable (e.g., trying copying the ∑ symbol to the search box above and see what pages contain it).

Very ugly formatting. Writing Unicode on a computer is a bit like writing Chinese—you need to learn how to input each possible character using whatever system you've got. May render strangely on some browsers.
Example
sum[i=1 to n] i = n(n+1)/2 (ASCII) or ∑[i=1‥n] i = n(n+1)/2 (Unicode).

Or a fancy version:

 n     n(n+1)
∑ i = ——————
i=1       2

Amazingly enough, many mathematics papers from the typewriter era (pre-1980 or thereabouts) were written like this, often with the more obscure symbols inked in by hand. Fortunately (for readers at least), we don't have to do this any more.

2014-06-17 11:58