Does one have to study algebra at a graduate level (master's degree) in order to do a Phd related to complex analysis and analytical number theory, or functional analysis and PDE? Is a master's degree in analysis and PDE sufficient?
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3I'm not convinced this question is on topic here (it may be more about mathematics than academia in general), but I don't think it's a duplicate. The proposed duplicate question deals with substantial changes of field, while moving between subfields can be rather different. In U.S. mathematics departments, it's common to end up specializing in a subfield you have never studied at all before entering the graduate program. Things may work differently in other countries, but this is in any case a very different situation from trying to get a Ph.D. in mathematics after studying, say, physics. – Anonymous Mathematician May 29 '16 at 19:57
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I agree it's not a duplicate, but I don't see any point in reopening it, just to close it as off-topic. – David Richerby May 07 '17 at 23:12