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For someone who has finished their M.S. degree in pure mathematics, what is a good way to keep learning mathematics within your specialization? Would you suggest reading research articles from particular journals, or to try to see what is submitted to conferences etc? Or something different?

Or maybe it is better not to go deeper at all, but to read broader, or to do applied math?

Caleb Stanford
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Student tea
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    Could you give some more information about your plans? For example, do you think you'll eventually want to get a Ph.D.? Do you teach mathematics (community college, high school, etc.)? Do you have a university library near you (less than a 1 hour drive)? Do you have certain specific areas of math you're very interested in? Do you know English and another language well? (There are many older papers in French, German, Italian, Russian, etc. that it would be a great service to have translated to English.) – Dave L. Renfro May 15 '14 at 15:33
  • Thank you @DaveL.Renfro for taking interst in the question! I don't expect to make a PhD, even though I would very much want to. And I do live close to a uni library, and speak a few languages. Please note that the question is not about good carreer paths or anything like that, but abut how to go deeper into a specialisation. – Student tea May 17 '14 at 03:39
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    I've been thinking about how to answer your question but don't know what to suggest other than what's worked for me, but that would involve getting into a lot of content specifics that may not be relevant to you. Perhaps you could say what you're interested in. In general, I suggest spending some of your free time browsing university library shelves for things that you might be interested in. As for subjects, you might consider a back-water area that not many people are currently working in, as this will make your efforts relatively more significant than if you tried working in (continued) – Dave L. Renfro May 20 '14 at 18:13
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    (continuation) an area that everyone and their brother is working in, especially areas where a lot of high level people are involved and areas that require a lot of background knowledge. You could pick a topic a little tangential to something you've studied (matrix summability theory, if you like infinite series and convergence topics) and do some "library research" like I suggest here (continued) – Dave L. Renfro May 20 '14 at 18:20
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    (continuation) and here. If you pick a narrow enough topic, or at least don't spend months and months on it, you'll have time to move to other topics, and after 4 or 5 such topics you should be well on your way to finding something you like and want to continue in. In the mid 1980s I learned cardinal and ordinal arithmetic very well by doing this, writing up nearly 200 pages of very carefully handwritten notes that I still (continued) – Dave L. Renfro May 20 '14 at 18:23
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    (continuation) refer to today. For several months I poured over many books (over 50) on set theory, real analysis, topology, functional analysis, etc. to get neat and interesting examples and results. I stayed away from hard-core axiomatic set theory (because it all seemed way too advanced for me then) but I did go heavy into the theory of linearly ordered sets (e.g. first half of Joseph Rosenstein's 1982 book Linear Orderings) and carefully went through much of Sierpinski's Cardinal and Ordinal Numbers. – Dave L. Renfro May 20 '14 at 18:28

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