<p>Hi,</p>
<p>First semester I took intro linear algebra, and theoretical multivariable. This semester, my 2nd, I'm taken advanced linear algebra, theoretical differential equations and advanced prob + stat. I've decided I want to go to grad school (highly ranked) for a PhD in applied math. To complete my degree in pure math, I need to take either applied or abstract algebra, or both. Also, topology is not required, either is multidimensional analysis. Instead, I can take applied real and applied complex. I'm planning on taking Real, applied real, and applied complex analysis classes. As well as a further class in probability, and a further class in stat/data analysis. I'm also going to take mathematical modeling/computational methods. I guess my main question is, should I take classes such as topology, abstract algebra, number theory, that are not required, and instead take graduate level/more applied courses?</p>
<p>Well, anyone going into any sort of Ph.D. in math should take some abstract algebra and topology. It's not necessary to go to more specialized topics like algebraic topology, though those are fun, but I would be careful of going to any math Ph.D. program knowing only applied stuff + analysis. I understand the most important things for an applied route may be measure theory + probability material relying on it, but still, the ideas in basic algebra are very foundational. </p>
<p>I'd try to manage as many applied courses as possible, but try topology and algebra for sure. number theory does not seem foundational, but you can take it if you like -- there are application to cryptography, for one thing. But don't be afraid of taking some pure math classes, because pure math is really foundational stuff for anyone dealing with math. If someone wanted a top PH.d. in pure math, he/she would actually go well, well beyond these standard pure math courses.</p>
<p>thanks, any other ideas?</p>