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I am living in a poor country but I have managed to get admission for a PhD program in Western Europe. This was a daunting task for me due to my family background and also social conditions. ( I don't feel like elaborating on this) . Also , I never had much guidance in mathematics and motivation was intristic. What motivated me was that I always liked studying mathematics and wanted to study it more, try problems and work on some problem and do research. I am working on an area of Pure mathematics.

Can you please share with me resources ( books/ blogs/ websites/ videos) about what I should need to know and what will definitely help me to do good research in mathematics ( for PhD and beyond)?

There might be no best answer for this but it will be best for me ( and hopefully future visitors, there might be more people like me with less guidance and fortune) as many resources are mentioned in comments and answers.

I shall be thankful for any guidance/advice received.

Thank you!

Arnold
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    Sara Billey has a few nice bits of advice collected on her website here: https://sites.math.washington.edu/~billey/advice/ – Sam Hopkins Aug 28 '22 at 16:19
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    The following MO question possibly is of interest to you: https://mathoverflow.net/questions/27299/on-starting-graduate-school-and-common-pitfalls – Max Muller Aug 28 '22 at 17:18
  • Can you be more precise about the subject you intend to study? Pure mathematics is too broad to give you useful indications. – Romain Gicquaud Aug 28 '22 at 19:26
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    @RomainGicquaud Number Theory . To be more precise, number theory with analytic flavour. – Arnold Aug 29 '22 at 08:27
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    https://blogs.ams.org/mathgradblog/ – Stopple Aug 29 '22 at 19:10
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    I am by no means an expert in this area. I read the book "A course in arithmetic" by Serre which gives a short introduction to the subject and watched the YouTube channel of Richard Borcherds. He has an amazing series of videos on modular forms. I cannot help much more, sorry. However, you should make precise the area you are interested in in the main body of your question so that experts can give you more appropriate answers. – Romain Gicquaud Aug 30 '22 at 09:16

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