I'm an undergrad majoring in mathematics. Being in first year I'm still exploring new branches of mathematics and till now, It is analysis and Number theory that I've come to have a great interest in, and now I'm currently exploring both fields as much as possible on my own and it is number theory that I'm finding hard to explore( on my own).
I have done everything , I came across including moderate level of problem solving related to elementary number theory and as I wish to study it further at a more advanced level, I searched on net, asked to people for advice on how can I proceed to do that, but till now have come to know only the basic stuff like: At advanced level it is divided into 2 parts: algebraic and analytic and to study analytic you should have knowledge of complex analysis and basic abstract algebra about algebraic NT.
At this point , I do not have much knowledge in abstract Algebra and know even less in complex analysis, so here goes my first question: Am I right in first clearing my concepts in basic complex analysis ( for analytic) and algebra( for algebraic). If yes, then exactly what or how much should I know in both of these subjects to study these two branches, at advanced level. and, which books I can follow for them that are not too hard for a beginner for me?
Next, I looked into the classic text of analytic Number theory by Tom Apostol, often recommended to study Analytic number theory and found the first few chapters appropriate for a beginner, requiring no pre requisites of analysis. So, my next question is: at what point while I'm doing this or any other book in ANT would I require knowledge in analysis( complex).
Last question: The method I'm following in studying and exploring new fields of interest in Mathematics
( i.e., of studying in detail both these fields at the same time, until I reach a point when I have found out which of these two interest me most, and study that one further). Is it right? If not, then how should I study instead?
Right now, I can't think of more questions that I had to ask, so I'll just stop here. Thanks to all who had patience in reading my query and made an attempt to answer it, in advance.