Advice on finding math specialization

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Graduating with a B.S. in mathematics raises concerns about choosing a specialization for graduate school. Many students feel uncertain about their specific area of interest after completing foundational coursework. It's common for undergraduates to lack exposure to advanced topics that could inform their future focus. Recommendations for navigating this uncertainty include reading Steven Krantz's "A Mathematician's Survival Guide" for general guidance on graduate school, though it may not directly address specialization. There is a debate on whether students should apply to programs aligned with their interests or choose schools with diverse offerings, as many discover their specialization only after starting graduate studies.
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I'll be graduating in the fall with my b.s. in math and I'd like to continue on to graduate school. I would feel better about it though if I had a clue what particular area of mathematics I wanted to specialize in. So far, in my undergraduate career, I've gotten a good working overview of the fundamentals, but I've been exposed to very little motivation for 'what comes after' the basics.

I'd love to hear from someone who dealt with this issue himself/herself. Any book recommendations concerning the scope of some of these subfields might also be useful.

Also- I'm not aware of the usual sequence of events. Is it the case that most people know what their area of study will be before graduate school, or is it entirely possible to get a graduate degree just studying general mathematics as one does as an undergraduate, albeit at a higher level?
 
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I can recommend Steven Krantz's "A Mathematician's Survival Guide," for good general advice about grad school. However, I'm afraid that it doesn't really answer your question. In fact, I have not encountered a very clear answer to your question anywhere. On the one hand, it has been commonly suggested that one apply to schools that have strong programs in the area you'd like to specialize in. On the other hand, I've read that you won't really know what you want to specialize in until after you've been in graduate school for a while, so you should apply to a school with wide variety of subfields represented, and don't go in married to one particular area.

Perhaps Mathwonk will come along and educate the pair of us. :)
 
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