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I hope this is an appropriate place to ask such question. I apologize in advance if it's not.

I'm currently an undergraduate student in mathematics, but still very blurry about the career path of mathematicians.

After undergraduate study, one proceeds to graduate school. Do they undergo the same style as undergraduate, i.e. lectures, exams, etc.? Or is there gonna be some kind of research?

Then what comes after completing PhD? What does it take to be a professor? And what do professors do on a daily basis?

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Maybe you can peruse this: maa.org/careers –  Amzoti Sep 17 '12 at 15:45
    
This question is related: math.stackexchange.com/questions/64992/… –  Julian Kuelshammer Sep 17 '12 at 15:47
    
This may also provide perspective: 1) toroidalsnark.net/mathcareers.html, 2) bls.gov/ooh/math/mathematicians.htm –  Amzoti Sep 17 '12 at 15:49
    
And another related question math.stackexchange.com/questions/148165/… –  Julian Kuelshammer Sep 17 '12 at 15:51
    
If you want to be a professor, you will likely have to be willing to move. –  rschwieb Sep 17 '12 at 18:38

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