Short paper, first draft

Due: Sep 18th, 2020

In this assignment you will write a first draft for your short paper.

As a reminder, from the syllabus, this paper is:

A short paper about an open question, unsolved problem, or currently studied research area within algebra, algebraic geometry, or computational algebra, or an application of one of those areas.

You should already have a topic chosen, and already identified one or more sources. Now it’s time to write it up!

Assignment

In this assignment, write as much of your short paper as possible.

  • Include section headings for all the sections you will have. (Being a short paper, you might not have very many sections.)
  • Include at least one fully written section, specifically the section that contains the main result or main conjecture.
  • At this first-draft stage it is acceptable to have a partial or empty introduction.
  • Include a bibliography. See How To Bibliography (pdf). (You might only have one or two sources. That’s okay. Part of the purpose is to learn how to write a bibliography.)
  • Give your paper an appropriate title.
  • Be aware of your audience. Typically you should write to an audience of your peers, i.e., graduate students still learning algebra and algebraic geometry.

Math Details

For this short paper, you will have to leave out details and technical parts. Your task is to decide which parts of your topic are interesting, and how to explain them; and which parts are technical, and can be skipped. Will you skip some things without mentioning them? Will you mention briefly, with phrases like “and now using advanced methods of cohomology, one can prove that…”? Will you summarize, with phrases like “this upper bound comes from looking at the codimension of the kernel”? The decision is up to you.

This is a big part of the purpose of this writing assignment: an opportunity for you to think about these issues. What will you include? What will you leave out? Think about what makes the topic interesting to you. Share your excitement with your reader!

Structuring your paper

With a target length of 2-4 pages you should plan to have a limited number of short sections. Some possible sections are:

  • Introduction
  • History
  • Background
  • Main result / main conjecture
  • Other results
  • Further questions These are only suggestions. Other sections are possible; you don’t need to include all these things, only the ones that make sense for your paper.

Math papers almost never have “Conclusions” or “Methods” sections. The conclusions of a math paper are the main result (or main conjecture). The methods are proofs.

Formatting

Please write your responses in a PDF file created using LaTeX. Make it have a filename like 584-ShortPaper-FirstDraft-YourLastName.pdf, for example 584-ShortPaper-FirstDraft-Teitler.pdf. Upload the PDF to BlackBoard.