<p>What would PhD graduate admissions like to see more: depth of study, including graduate classes in a subfield; or breadth of study, many different classes? I ask this question specifically for physics and math. Basically, should I take very high-level classes even though I'm not sure what I want to do yet, or do I take several different classes?</p>
<p>I assume the answer is depth, but I would like to run it by you guys first.</p>
<p>Just throwing this out there, but if you’re not sure what you want to do, why do you want to get a PhD?</p>
<p>I think he means he doesn’t know what subfield he wants to do, which is not something you need to know upon entering a PhD program in your general field.</p>
<p>As for the OP question, I think the answer is neither. I think graduate schools care less about what classes you took in your field and more about whether you did well in the classes you did take. You should guide your course selections on where your interests lie. If you really like the subfield in which there are graduate courses available to you, then take them. If you have varied interests that are represented by many non-graduate-level courses, then explore those.</p>
<p>I don’t know much about physics, so I will restrict my answer to mathematics: depth.</p>
<p>Reasoning in graduate-level courses is much more complex than in undergraduate courses, and the concepts become more abstract and involved. Graduate courses are a much better indicator of your talent, motivation and work ethics than undergraduate courses. The graduate courses will help you mature academically, give you a better idea if you really want to pursue the grad school option, and give graduate schools a better idea of your merits as an applicant. </p>
<p>Of course there are a few foundational math courses that you should take as an undergraduate before you get to graduate school: real and complex analysis, abstract algebra, PDEs, point-set topology and some sort of discrete math. After that I would highly encourage you to focus on some area in depth.</p>
<p>I am unable to communicate just how much I gained from my graduate courses. They really opened up a whole new world for me! I gained a better appreciation for just <em>how much</em> math is out there, what sort of problems current mathematicians are working on and how they approach them; I was able to attend research seminars and colloquia and understand at least some of the talks, and I generally had way more opportunities to interact with professors than when I was taking undergraduate courses. (-> letters of recommendation!) Undergraduate courses are artificially self-contained and may convey a false impression about the field as a whole.</p>
<p>Don’t worry about accidentally choosing the “wrong” focus as an undergraduate. You don’t need to declare a specialty when you apply to graduate programs in math. First-year graduate students typically take courses in algebra, analysis and geometry/topology before they are expected to choose a field and go advisor-shopping.</p>
<p>Thank you all for your responses. I’m actually a freshman, so I’m not sure yet what I want to do. I am trying to get a rough idea of my schedule though, so I can plan it correctly. I would very much like to take graduate classes as far as I can in my subfield (when I discover it), but I just wanted to make sure I wouldn’t hurt myself for graduate admission.</p>
<p>Going a little on what b@r!um said, my grad classes really showed me how many questions out there are unanswered even in fields you took in undergrad and felt were considered done. Classes weren’t taught as much with “This is the absolute answer.” as with “Here’s where the boundaries of our understandings are, and these are the tools we have to probe further.”</p>