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How to do mathematics research as undergraduate?

  1. May 2, 2015 #1
    Dear Physics Forum friends,

    I am a college sophomore in US with double majors in mathematics and microbiology. My algorithmic biology research got me passionate about the number theory and analysis, and I have been pursuing a mathematics major starting on this Spring semester. I have been independently self-studying the number theory textbooks written by Niven/Zuckerman/Montgomery, Apostol, and Ireland/Rosen on this semester. As this semester progressed, I discovered that I am more interested in the pure mathematics than applied aspects (computational biology, cryptography, etc.). I want to pursue a career as analytic number theorist and prove the Collatz conjecture and Erdos-Straus conjecture.

    I have been thinking about doing the number-theory research on my university (research university; huge mathematics department). I have been self-studying the NT by myself and also regularly attending the professional and graduate seminars on number theory but I did not do any pure mathematics research as an undergraduate. Should I visit NT professors in my university and ask them about if I can do undergraduate research under them? If research is not possible (perhaps due to my lacking maturity), should I request of doing independent reading under them and later proceed with the research? How should I ask them? What should I address? If even independent reading is not desirable to them, what should I ask to them or do in my own?

    As for my mathematical background, I have been taking Calculus II (computational) and discrete mathematics. I will be taking calculus III (vector calc.) on Summer, followed by Analysis I, Probability, Theoretical Linear Algebra on Fall 2015. As for my self-studying on this semester, I have been studying NT textbooks (mentioned above), proof methodologies, and basic linear algebra.

    Thank you very much for your time, and I look forward to your advice!


  2. jcsd
  3. May 2, 2015 #2


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    Talking to your professors would be a good start, have you broached the topic with your current calculus 2 professor? He may be able to point you in the right direction, or at least introduce you to the appropriate faculty who have may have some work for you.
  4. May 3, 2015 #3
    Thanks for the suggestion. I did not discuss with my Calculus II or discrete mathematics professors since I am quite familiar with my university's NT professors through the NT seminars for both professionals and graduate students. I am going to basically walk up to their offices during their office hours and requesting for the undergraduate research/independent reading. My questions are what should I address and if I should propose to do a semester of independent reading course under him and start the research under him after completing such course. What can I do independently?
  5. May 3, 2015 #4


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    If I were in your position, I would approach a number of professors and ask for their advice. If you are sincere and enthusiastic and clear about your ambition then I think you'll find they have some good ideas for you. Some of those ideas might involve research....
  6. May 3, 2015 #5
    Right. Just approach the professors and tell them you're interested in number theory and would like to do some (undergrad) research. They will then start giving advice. That advice might consist of doing some reading or might consist of doing research immediately (unlikely).
  7. May 4, 2015 #6
    Thank you all for very helpful advice! I am actually going to visit couple of NT professors on tomorrow during their office hours. I am planning to address the issue as independent reading (if it is needed) first and then proceed with the research under one of them.
  8. May 4, 2015 #7
    How do you find problems that will be suitable for an undergrad though? Like say I'm interested in an area how do I go about looking for problems that would even be possible for an undergrad? I'd rather see a taste of various problems that I could tackle and then bring it to an adviser that I'm interested in this problem and ask for advice on how to go about investigating it.

    I'm curious if their is like a database of certain problems that people haven't had a chance to figure out yet(but more then likely could be solved given enough time) that would be suitable for an undergrad.

    It seems doing undergrad research in math is much harder then in the sciences where you can get work in a lab pretty easily.
  9. May 4, 2015 #8
    You go to your advisor and (s)he will present some problem that you might be able to tackle. You're not supposed to find problems on your own at this stage. You don't have the experience or the knowledge.
  10. May 4, 2015 #9
    What is special about these problems to you? I used to want to be the guy who came up with a theory of quantum gravity, but then I realized that there was nothing really special about this problem except that it was famous.
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