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I'm unemployed but I like to learn graduate studies in mathematics just for fun and to get a non-academic work. Thus far I have managed to fill details of the lecture notes and learn theorems completely from axioms. But now, when I read advanced books or articles, I feel like I can't do every step of proofs. Are there some advice how deeply one should learn things? I think it is fine to skip hard theorems like the classification of finite simple groups but if there is for example some hard exercises on books, should I spend weeks or months to works the details?

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    As long as you reasonably follow along the exposition and most exercises (consider using math SE for questions that fit there too), don't obsess about doing every exercise. It's good to dig in thoroughly, but after some time your effort becomes unproductive. Instead, if you keep reading and working like this, you'll often find that, some time later, an exercise that stunned you earlier will now seem quite clear. Feb 26, 2016 at 16:16
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    Side note: if you are unemployed and enjoy graduate level mathematics, perhaps you should consider a PhD.
    – Cliff AB
    Feb 27, 2016 at 5:15
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    If you're doing this for fun, I think the answer is going to be "learn at whatever level of detail you find most fun." (The answers to "what should I do" questions on this site tend to directly follow from "what is your objective.")
    – ff524
    Mar 18, 2016 at 20:14
  • Perhaps this is more appropriate for Math.SE?
    – Kimball
    Mar 19, 2016 at 2:34
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    I'm voting to close this question as off-topic because it is about learning a specficf academic subject and not about academia in general. It may be on-topic on Mathematics or Mathematics Educators though.
    – Wrzlprmft
    Mar 19, 2016 at 15:59

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