Undergraduate Seminar in Discrete Mathematics
18.204, Spring 2016
Term paper
The term paper is an expository article on a theorem in discrete math written for your
peers, specifically the other students in the class. The paper should draw primarily
from 1-3 research papers on your theorem as source material. No original research
is required (nor recommended!) for your term paper. However, you should write as
much as possible in your own words and cite your sources. Some specific requirements
for the paper are listed below.
• Formatting: The paper must be written in LATEX, and should be about 7-10
pages single-spaced with references.
• Sections: Your paper must have at least three sections: Introduction, Preliminaries, and Main theorem. Optionally, you may have other sections for
applications or complex examples.
• Introduction: In the introduction, you should briefly state the main theorem,
give a small example, and describe some application or external value of the
result. This section should be 1-2 pages in length.
• Preliminaries: In the preliminaries section, you should provide definitions and
basic examples that you will revisit in later sections. Its length will depend on
the number of definitions you require.
• Main theorem: In this section, you should carefully state the main theorem
and give some explanation for how to prove the theorem. Part of your explanation should include any supporting lemmas used in the proof. The theorem
should be illustrated by an example of appropriate complexity.
• Proofs: If the proof of the theorem (or any supporting lemmas) is sufficiently
interesting and accessible, then you should include it as well. However, the
proof must be written in your own words as much as possible! If you are unsure
of which proofs to include, please ask me.
• Bibliography: The bibliography should be written in BibTex. You should
never need to write an actual bibliographic entry to any of your sources. If you
run a search for your paper (say on MathSciNet), you should find BibTex data,
which you can copy into a “.bib” file. To include this data in your paper, write
\bibliographystyle{plain}
\bibliography{bib file}