Math 101 Final Essay Guidelines
Mary Radcliffe
due 29 Feb 2015
First steps
1. Choose a topic or concept that we have discussed during the course that
you enjoyed or found interesting.
2. Do some independent reading/research about this topic. If you need help
getting started, come see me and I’ll give you some appropriate references.
3. Find some other theorems that relate to the topic in question. Read
them, and their proofs, to get an idea of how the topic you are interested
in relates to other kinds of mathematics. Come see me if you’re confused
or need help with this, I’m so happy to help you understand more math!
The essay. Your essay should include the following features.
1. Start with a full mathematical explanation of the topic you have chosen.
This should include definitions of main terminology, and an explanation
of why this topic is important.
2. Find a theorem you like that involves your topic. State the theorem and
prove it YOURSELF. Please don’t copy word for word a proof you found
somewhere. I have been reading student proofs for years. I promise, I’ll
know. You can use existing proofs as resources for developing your proof,
but once you understand what the proof looks like, close your laptop and
your books and write it yourself. Discuss why this theorem matters (to
you, or to Math, or to someone).
3. Talk about why this topic appeals to you. What ab out it is interesting?
How do you think this concept has improved mathematics? This is squishy.
It doesn’t have to be as mathematically precise as the previous items.
Presentation.
1. Your essay should be typeset using a standard mathematical typesetter.
Most mathematicians prefer L
A
T
E
X, but in other fields (some applied math,
statistics, mathematically adjacent fields), Microsoft Word’s mathematical
typesetting is also an accepted standard. If you have other preferred
typesetting programs, ask me about them. See here for a nice intro to
L
A
T
E
X. You are more than welcome to copy my preamble if you wish,
although many nice templates are out there for the taking.
2. I believe it will be virtually impossible to complete the assigned tasks in
less than 3 pages. I also believe it will be entirely unnecessary to write
more than 6 pages. Officially, there is no required length.
1
