All assignments are to be done in LaTeX and be neat and professional (I suggest using Overleaf). Here is an Overleaf template (go to "Menu">"Copy Project") with examples of LaTeX code for everything from lists, to figures, to tables, to graphs. Good writing, grammar, punctuation, etc. are important and can affect your grade.
Choose a proof from the literature in your field of study that you would like to master and show it to me to make sure it is appropriate. (You will write a short paper deconstructing/analyzing this proof for a non-specialist audience -- see more details in the next section.) Please send me your proof via a direct message on discord by midnight on the date this assignment is listed on the schedule.
Write a short paper (probably 2-5 pages) in LaTeX that teaches your chosen theorem to a non-specialist audience. You will need to provide (numbered) definitions for every concept in the theorem statement (and possibly some second-level definitions to support these first-level ones). You will also need to provide at least one figure and one simple example to help the reader (and you) understand the theorem/proof. You should provide a "plain English" translation of the theorem. You should provide some explanation of why the theorem is interesting/important and to what situations it applies (sometimes this can be tied to the example). Finally, you must provide a logic-and-proof-strategies analysis of the theorem's proof. Remember, the big picture goal of all of these pieces is a cogent document that effectively teaches, so try to write accordingly. Email me a PDF version of your paper by midnight on the date this assignment is listed on the schedule. I and another student will subsequently critique this submission.
Here is an example of a proof paper.
Here is another example of a proof paper.
Read and critique a classmate's Proof Paper #1 (you will be assigned one). You should treat this like you are reviewing a submission to a conference or journal. That is, you should read critically and write a brief (1/2-1 page in LateX) review of the paper. Your review should point out both strengths and weaknesses, provide suggestions for improvement and do so in a diplomatic manner -- your aim should be to teach not to criticize. You will be graded on how well your review accomplishes these tasks. Additional tips on reviewer best practices can be found here. Reply all on the same email thread by which you received your classmate's rough draft with a PDF version of your critique by midnight on the date this assignment is listed on the schedule.
Here is an example of a proof paper critique that was written in response to the second proof paper example above.
Write a concise, formal and accurate statement of your theorem (to be proved). Include with this a set of brief definitions (formal, if possible, informal when necessary for brevity) that will allow a reader to understand the content and significance of your statement. Again, do this in LaTeX and, again, email me a PDF version of your paper by midnight on the date this assignment is listed on the schedule. I will be providing feedback to you on this submission.
Construct an outline of your proof strategy. Fill in as much of the outline with actual logic (that is write the proof) as possible. For those parts for which you cannot (yet) do so, sketch what you need to accomplish to fill in the gaps and discuss how you will proceed. This should read as much like a proof as possible, and should be at least semi-polished in its construction and writing. Please submit this to me via email by responding to the same email thread that contained your Proof Paper #2 theorem statement submission by midnight on the date this assignment is listed on the schedule. I and another student will subsequently critique this submission.
Here is an example of a proof paper #2 rough draft (which also contains a theorem statement).
Read and critique a classmate's Proof Paper #2 rough draft (you will be assigned one). You should treat this like you are reviewing a submission to a conference or journal. That is, you should read critically and write a brief (1/2-1 page in LateX) review of the paper. Your review should point out both strengths and weaknesses, provide suggestions for improvement and do so in a diplomatic manner -- your aim should be to teach not to criticize. You will be graded on how well your review accomplishes these tasks. Additional tips on reviewer best practices can be found here. Reply all on the same email thread by which you received your classmate's rough draft with a PDF version of your critique by midnight on the date this assignment is listed on the schedule.
Write a final, polished version of your proof, including advances you've made since your rough draft, and taking into account feedback you received on that draft. Please submit this to me via email by responding to the same email thread that contained your other Proof Paper #2 submissions by midnight on the date this assignment is listed on the schedule.
