Guide for working on the chosen research project

General Overview. The class will split into collaboration teams based on the chosen Research Projects. I have suggested a few in the OneNote notebook, but feel free to suggest a problem that comes from your interests.

NOTE: You need to be registered for the course with a @unm.edu email. Any other email will disable features of Microsoft Teams. I have sent you by email a link to join the MATH311 team. Please follow it in order to request access. Soon after you join the class MS Team I will also give you access to Overleaf. The latter will be used to collaborate on writing the findings of your respective research projects.

You will work on the chosen problem with your respective research team memebers throughout the semester. Each team will have their own “space” in the class notebook of Microsoft Teams. Only the respective team members and I will be able to see and edit this space. Each team should set-up an hour long meeting every week throughout the semester. The meeting could be in Microsoft Teams or in-person or a combination of both, alternating each week for example.

There are several elements of your work that you should keep in mind.

1. Each collaboration group will have their own overleaf project where you will write your findings. You will use latex (help and guidance areprovided in the class OneNote notebook). Overleaf has automatic version control so that all of you can work on the file at the same time.

2. The format of your writing will be the standard format for a scientific article (samples will be provided, but the references you already looked through were in this format and can serve as examples). What and how you going to write?

3. Your paper will go through several revisions. There are some standard parts of the paper, like the introduction and the background, but ultimately you want to make the paper precise, as short as possible and easy to follow. The following “schedule” will be followed.

   • The introduction is the last section to be written despite its title.

   • You will begin with a section stating the problem and some of the most important known results.

   • The next section will be a background section containing necessary facts and definitions for understanding the problem.

   • The next section will contain the proofs or sketches of the proofs of some of the known results.

     
     

     The above parts will be mainly based on the provided references and other references and literature found through MathSciNet, the arxiv of papers, and the resources of the UNM library.

     
     

   • The next section will contain your contribution. As with any problem there is no guarantee that we will be able to make a new contribution, especially in the limited amount of time we have, in which case the paper will become a review paper. Keep in mind that some problems take months, years, a century or more to be solved. Simplifying known solutions or finding alternative proofs is a valuable and a legitimate contribution. In addition, suggestions of “new” variants or problems inspired by your readings and thoughts are also contributions.

     
     

   • Once we have all of the above parts, a new draft will be made where some parts can be revised, shortened and improved while new sections and/or sub-sections can be added and an introduction will be included. A final draft will be made. It will be due at the end of the semester.