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I am currently an undergraduate student majoring in Applied Math. I have been reading recent papers published by two of my professors who I admire and I'm wondering what it would be like to conduct research with them. In what ways can an undergraduate student contribute to mathematical research? In what ways could I prepare myself to conduct mathematical research?

To be more specific, my academic background is in History and Social Sciences which I studied intensely from High School through my first two years in college. I conducted research at University of Arizona my junior year of high school analyzing a large set of longitudinal data on a group of high schools in NYC. My interest in math, specifically applied math, started when I took a Computer Science class because I was curious. Since then, I've taken calculus courses, applied combinatorics, probability courses, and I'm currently enrolled in a computational geometry course and an operations research course. The reason I'm interested in pursuing undergraduate mathematical research is because I enjoyed the experience a lot when I was studying social sciences. My concern is that I don't have a strong enough background to contribute to the research my professors currently conduct. I get good grades in my classes, but I'm concerned with my lack of background for a Junior in an applied math major. Recent publications from my professors are difficult for me to understand, so I'm questioning whether I'm ready to conduct research with them. I'm hoping you may be able to offer insight into whether my background is sufficient for conducting research and how I may be able to strengthen my skills. I take my school work seriously and think I have a good understanding of the material I'm taught. Thank you for your time.

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    You don't really prepare yourself to do research - you just do it. It helps to find a professor who is interested in working with you. But, about your question: it might be a duplicate of the one here: academia.stackexchange.com/questions/44695/… . Could you edit the question, if that one does not answer it, to explain what else in particular you'd like to know? – Oswald Veblen Oct 23 '15 at 1:23
  • Go ask them directly if they have some (easy) problems you can try your hand on, look around for journals publishing undergraduate's papers where you might publish results, ,,, – vonbrand Oct 23 '15 at 1:24
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    @OswaldVeblen, thank you for your response. I'm new to Stack Exchange so I'll be sure to look out for duplicate questions before posting in the future. The question you linked has some good general advice, but I see the question was specific, so I'm hoping adding more details to my question could result in more personally tailored advice. Thanks again! – Adam Pollack Oct 23 '15 at 1:41
  • @vonbrand, that's a good idea. I've been to my professor's office hours before and I think he would be willing to introduce me to extra curricular problems. Maybe that will show him I'm a good candidate for research. – Adam Pollack Oct 23 '15 at 1:43
  • @AdamPollack "Personally tailored" is one of the red flags here--we typically want questions to appeal to more than just the person asking them. Oswald's link contains three answers, one of which address the specific/tailored Number Theory aspect of the original post, but the other two are fairly generic. Do those answers fail to address what you want to know? – zibadawa timmy Oct 23 '15 at 21:28
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It's very reasonable to wonder how you, an absolute novice, could "help" experienced experts. Some people are fond of claiming that somehow "just trying hard" or "being smart" can make this possible in some way, but those are needless (and doubtful) claims that miss the mark about what the real question could be.

That is, many or most faculty are happy to mentor beginners and introduce them to the subject(s) the faculty know and like. It need not be the case that they "need help", and, if they did, sure, recruiting novices is not the best gamble. But that's not the point! The point is that experts may enjoy (and find stimulating) introducing beginners to their subject. So you help them by allowing them to do so.

It's not at all surprising that you have trouble reading their recent papers, and, again, that's essentially irrelevant. (The internet mythology about young people becoming world experts in a few weeks or months is invidious... In particular, no, you should not expect to "read those papers and then go talk to them about them.", contrary to much advice given on-line.)

An astute expert can find interesting "starter" projects for novices. It may happen that such a project produces something interesting to the expert. Or, it may be that the expert can so well foresee the outcome that the element of surprise evaporates. But that doesn't matter. Little kids don't have to immediately play sports (or whatever) with world-class professionals. But they can be coached by such professionals, if both parties are interested. I do think that's the correct analogy, though many other people on these sites are adamant otherwise.

  • Not only should you not expect to understand current research papers when just starting out, but you may already have tenure when you finally feel confident that you'll understand the introduction to a paper in your area of expertise more often than not. It's not unusual for the introduction to be the most confusing part of a paper, even when well-written. Introductions are full of sweeping statements, off-hand summaries of complex results, terms from other fields (a pure math paper may invoke a lot of physics terminology you weren't expecting), and references to a large number of papers. – zibadawa timmy Oct 23 '15 at 23:38
  • Thanks for your comment. Combined with some of the links posted, this was the kind of advice I was hoping to get. I'm just trying to gauge how I could participate in research with my professors, and I think your answer has some good recommendations. I definitely get the sense that they would be interested in motivating me with "starter" projects and this is the initial experience I'm looking for. – Adam Pollack Oct 24 '15 at 2:14

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