Back when I was an undergraduate, taking a course like calculus, I had so many available resources at my disposal: suppose I wanted to learn more deeply about the mean value theorem, which was just introduced in a lecture. I could find very detailed descriptions on Wikipedia and some calculus books like Rudin's, Spivak's etc...

Now, going beyond the scope of undergrad, suppose I want to learn about the "connection problem" in the field of differential equations. Googling the term doesn't result in a nice Wikipedia article anymore (in fact it gives results discussing internet problems). Using Google Scholar results only in particular cases of connection problems.

Basically my questions/requests are:

  1. How can one learn about a new (for the reader) mathematical term in the postgraduate setting, when it doesn't appear on Google, or in some classical book.

  2. My understanding is that mathematical articles help with the reduced access to books and Wikipedia/MathWorld pages available for postgraduate topics. How does one orient themselves in the setting of mathematical papers? I know that the paper itself has references to earlier works, and that on Google Scholar you can see which papers have cited the current paper later on. This allows one to think of mathematical papers as a graph, where citation between papers corresponds to an edge between the two. Hence, studying a new topic/term is like a walk on this graph. Is this the typical way to get around?

  3. If there are any other popular methods that help with studying postgraduate mathematics in particular, please let me know.

Thank you!

  • 7
    $\begingroup$ Welcome to Graph Walking of mathematical research! Where proven results (even important ones) may fall into obscurity because nobody walked the "edges" that it happened to be connected to. $\endgroup$ – user123641 Feb 1 '18 at 14:40
  • $\begingroup$ You may want to take a look at this list, which is compiled mostly by the experts. I found some of them to be really helpful. $\endgroup$ – polfosol Feb 25 '18 at 14:27
  • $\begingroup$ apart from google scholar you may use mathscinet mathscinet.ams.org/mathscinet and zblatt zbmath.org These require subscription, but: 1) even if you are not in academia you may be able to get access to a library in a nearby college or university, and the computers may have access to mathscinet and/or zblatt, and 2) zblatt would show you 3 papers for free, you need to learn (by trials) what to put in your search fields to get 3 relevant and close results. Also, when using google, try to rephrase/restate your search different ways, sometimes that evades the shadowing problem $\endgroup$ – Mirko Feb 25 '18 at 18:12
  • $\begingroup$ Don't blindly trust the various monographs that are out there. Work through the proofs in detail (even though, they did it in some 10-15 lines) and end up constructing a counter-example why the claim doesn't hold :D $\endgroup$ – Alvin Lepik Feb 27 '18 at 7:32

I have discussed this topic a few times with my colleagues and we always arrive at sad/unsatisfactory conclusions.

I can give you a few tips that may expedite your quest:

1) When looking for something, always prefer sources in this order: textbook, lecture notes, survey papers, other papers.

2) In case you don't find a good source in a reasonable time window, you should definitely ask your fellow students. It is likely that someone knows and, even if they can't help you, this can encourage you to the next step.

3) Go and knock on professors' doors. In my experience, everybody would welcome a good question. It is highly likely that, even if they don't know, they will be intrigued by your question and think about it. Otherwise, they may redirect you to some other guy who "should know".

It is a jungle out there, you will have this problem over and over. It is not so easy to get pointers.


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