PhD Mathematics Admission Advice
Although some people might reasonably think that &quot;pure math&quot; courses are irrelevant to your larger goals, I would claim that the popular distinction between &quot;pure&quot; and &quot;applied&quot; math is both scientifically meaningless, and potentially hazardous to people trying to get started.
Having fluency with basic ideas of abstract mathematics (&quot;algebra&quot;, &quot;topology&quot;, and such) is inestimably useful. Illiteracy in these things makes it impossible to really know what the substance of many &quot;applied&quot; conversations may be.
The ideas in &quot;pure/abstract&quot; math are not at all disjoint from &quot;the real world&quot;. They were all motivated by the desire to understand things. Yes, some self-styled &quot;applied math&quot; people pretend that all they need is computer time, and some self-styled &quot;pure math&quot; people pretend that whatever they do is disconnected from reality, and is practically useless. This is all silly, in my opinion.
In particular, having a basic grounding in &quot;abstract&quot; math will make you a far better candidate for any reasonable math program, whether eventually aiming at something &quot;applied&quot; or &quot;not&quot;.