10

I think the purpose of (funded) research by undergraduates is to give the participants a taste of what real research mathematicians do: think in good company about interesting questions that no one yet knows how to answer. If a high quality paper (or any paper at all) comes out of this work, that's a big plus. But it's not how to measure the success of the ...


5

In my experience, most projects led by undergraduate students do not result in high-quality research papers, or even a paper at all. Undergraduate students can often work well under the frequent supervision of a graduate student, and I have seen many undergraduate students earn a second-author spot on a good paper. Some graduate students will be able to ...


5

It's not rude. It quite probably is futile. Many faculty are not in their offices very often normally. Many faculty are in their offices less in the summer - in particular, they are unlikely to have scheduled office hours. During a pandemic, you might not be able to go into the building anyway. If the professor does not feel safe meeting in person during ...


3

In the CV, you can mention it under 'Working Papers', and yes, attach the document as a separate file to the application.


2

No, it isn't reasonable to expect undergraduates to do high quality research on their own. They are too inexperienced and need to learn a lot about process as well as the topic of the research as they do. I think that funders recognize this and treat the funding as a kind of training, not a way to get the highest quality results. But, to manage the students ...


2

Many (but not all) PhD applications specifically ask for a writing sample. The exact requirements can vary, but in my experience unpublished drafts are typically acceptable. That would be an ideal approach to share your work with them. Otherwise, if they don't ask for a writing sample or allow attaching additional documents, do not try to use a trojan horse. ...


1

You can definitely mention these manuscripts in your resume or online portfolio. To do that, you give the manuscript title and full author list as it appears in the submission, and mention the word submitted either in a section heading or with the reference itself. If you want to explain more about your contribution to these manuscripts, you can write a ...


1

Given that there was a tacit agreement to have a meeting sometime in the summer, an unannounced drop-in wouldn't be unusual. But the real issue is that you don't even know if they will be in their office during the summer. COVID is still forcing several campuses to stay remote and have less than full attendance. Several professors are still conducting all ...


1

A person with a bachelors degree entering into doctoral studies directly in the US has a long road ahead. First there will be (mostly or entirely) coursework in advanced topics that will give you the background necessary to pass comprehensive exams and assure you have a broad knowledge. Specialization and research only comes later in most programs. Given ...


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