Guidelines for scribing lecture notes for mathematical classes
Here are some thoughts on how to go about the business of scribing
lecture notes for mathematical classes. Any comments, suggestions,
amendments are welcome. Please email them to me. My address is my last
name at cse.iitd.ernet.in.
- Accessibility. Make your notes intelligible to people who
don't know anything about what you are talking about.
The most important thing to keep in mind while scribing lecture notes
for any advanced class is that apart from the students currently
taking the class here, there will be others in other places, in the
future, who might want to use these notes as a resource to teach their
own classes or to study topics on their own. Of course there is a
limit to how much background you can provide, which leads us to our
- Completeness. If you are skipping some background material
or assuming knowledge, try to point to references where this might be
picked up from.
This also includes giving pointers to previous lectures in later
lectures. You may irritate people who have all the background needed,
but people who don't will thank you profusely and probably name their
first-born after you.
- Citation. Always provide a reference to the textbook or
paper that is being followed.
If the proof or the method is more or less verbatim from the original
source this should be made amply clear and credit given where due.
- New Material. Take extra care over examples or
arguments developed for this particular class.
New material should be elaborated fully and extra care should be made
to ensure that they are clear and written in an easy to understand
way. They also need to be checked carefully.
For the material taken from other sources, there are those sources to
fall back on for the reader who can't understand what you've
written. But for the material being generated for this class, this is
the only source. Also, by being extra careful about writing this kind
of material you are doing a favour to your professor who probably
wants to teach this class again and yet, being an old and
mathematically inclined person, is fairly likely to forget things.
- Presentation. Attempt to present the material the way you
would like to see mathematical material presented in a text book.
Every author has a different take on the way theorems and proofs are
written, the way arguments are developed. As a student you have
probably suffered through several badly written mathematical books,
and been pleasantly surprised by a few well written ones. Try to
emulate the well written ones. A few general rules of thumb:
- Definitions should be grouped together in one easy-to-find place.
- If a couple of steps in an argument or derivation are being
skipped, indicate this. It may be obvious to you but could waste a lot
of someone else's time.
- Don't use words like obvious. They show arrogance, not an
attractive quality in any context, especially not in the context of
- Space should be saved by reducing fonts and increasing margins,
not by eliminating explanations.
- Repetition is okay. You're not writing a novel, it's okay to
belabour the point. The people who get it the first time will simply
skip over the repetitions.
- Typesetting. Latex is your friend.
There are several great guides to latex available on the web. Googling
"latex guide" will bring them to you. If you're not so familiar with
latex, take some time to read them and figure out what Latex can do
for you. The AMS math
package is available for most standard Latex
distributions. Understand how that can help you. Nicely typeset notes
are easier to read and less likely to cause a headache.