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I am a year ahead of my physics curriculum, but I plan to stay as an undergrad for the 4th year to increase my chances at top graduate schools in physics. In this 4th year, I will take all the graduate courses in physics a typical 1st/2nd year PhD student would take: two semesters of quantum mechanics and a semester each of statistical physics and electrodynamics.

My question is: is it worth it taking all of these graduate courses as an undergrad? From what I know, most universities don't accept transfers in graduate courses and I would have to take them again.

I would still like to take them because I am eager to learn them, and also achieving good grades in them would help me demonstrate my readiness for graduate school.

Other option would be taking courses in other disciplines that would benefit me, such as math or electrical engineering.

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    Instead of taking those classes, you could aso consider taking a seminar or a self-guided research project/capstone. – Compass Jun 11 '15 at 15:18
  • One would hope that wherever you go for a PhD the only classes they make you take are ones where your knowledge is deficient (i.e. you won't pass the qualifying exams without more study). If you really know the material and they make you retake classes anyway, you should worry about whether they have your best interests in mind. Note many physics PhD students do retake undergrad classes, but at the same time most undergrad physics curricula are extremely lacking in the fundamentals, and this may not be the case for you. – user4512 Jun 11 '15 at 19:07
  • What country? It will make a difference... – Lightness Races in Orbit Jun 11 '15 at 20:26
  • Research projects look much better than classes. Although graduate classes will increase your understanding greatly. I'd say go for some classes, but make room for research as well. – Joe Moeller Jun 12 '15 at 8:03
  • You might want to talk over your financial situation with your family. The big advantage of getting out the door quickly and starting the graduate studies is that you would hopefully get support in grad school -- free tuition + stipend. – aparente001 Jun 14 '15 at 22:51
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Research experience is almost always better than additional classes, even graduate classes. Either graduating early so that you can work/volunteer full time in a research lab or taking the minimum number of credits to maintain your status as a student and work/volunteer part time in a research lab is likely going to increase your chances of admissions to a top graduate school much more than taking a full load of classes.

If you go with taking classes, classes that fulfil general graduate requirements are going to be less valuable than classes that will help prepare you for your research.

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    Perhaps your first sentence is true for experimental physics, but is it true for theoretical physics? It's certainly not true for math. – Kimball Jun 11 '15 at 17:32
  • @Kimball I'd say it's probably true for many flavors of theoretical physics as well. Even good graduate classes aren't as good as starting to do real work. – WaterMolecule Feb 21 at 19:22
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In the US system, it's important to distinguish between transfering academic credits from one university to another versus simply having required courses waived on the basis of work that you did at another university.

Most graduate programs significantly limit transfer of credits from other institutions. A common rule is that you can't transfer more than 12 credit hours from another institution. Furthermore, you typically can't transfer credits that you used to earn a previous degree. If these courses that you'll be taking next year appear on your undergraduate transcript, then its unlikely that they would be transferable. The more common situation in which graduate credits would be transferred is when a student switches from one graduate program to a graduate program at another university.

However, it is also possible that the graduate program that you go to might be willing to recognize that you had previously taken these graduate courses by waiving the requirement that you take the courses again, and instead let you take other more advanced or elective courses instead of repeating the same material. You can always ask for this consideration, but I wouldn't count on getting it.

In my experience, it's quite common for students to end up retaking graduate courses that they took as advanced undergraduate students at another university. In other cases, the student may have taken a very good undergraduate course that basically covers the same material as the graduate course. Some students find this very boring, while other students find that it makes for an easy first couple of semesters of graduate school.

I don't think that there's anything wrong with taking these graduate courses, but you should be aware that there's a good chance that you'll end up having to retake the same courses in your graduate program. If your math background isn't very strong, then taking some additional math courses (particularly mathematical physics, PDE's, and analysis courses) could help and likely wouldn't overlap with required course work in your graduate program.

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    As an example, I had a really good undergrad quantum course, taught by Will Happer. In graduate school, I got to take quantum again, taught by Ed Salpeter. The great benefit of 'knowing' the basics of the material the second time was that I could concentrate more on the corner cases, off-the-cuff comments (very illuminating), and the 'philosophy' of quantum mechanics. Much depends on how you personally choose to approach 'retaking' a course in grad school. – Jon Custer Jun 11 '15 at 16:27
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Taking the graduate classes will indeed help prepare you for graduate school, and consequently will also help you get into a top graduate program, particularly if you are not coming from a top undergrad school.

At least in math, it's not uncommon to test out of standard graduate classes when you start a grad program. And if you go to a grad program that is considerably better than your current school, the grad classes will probably be at a more advanced level, so it will probably not be a waste to take (at least some of) them over. At the least, if you retake these courses, they will be easier next time and you will have extra time then that you can use to learn things more deeply.

I don't think it makes sense to take classes in other areas just because you are worried about retaking the material in graduate school, but if you want to take a class in a related area because you're interested or you want to shore up some deficiency, that's a different story. But you should be studying at least some physics next year, if that's your passion.

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I was in your same position myself as an undergrad rushing to grad school. My interests evolved as I found out more about other fields. I had thought physics might get me what I wanted, and followed it through as fast as I could, only to learn that what I really wanted to do matched up better with other fields.

I would recommend taking the opportunity to plug some gaps in your knowledge that can come in handy in graduate school.

If you're interested in theory, make sure you brush up in mathematics. Typically you only need to take the basic calculus sequence in physics, so maybe take a higher-level analysis class to supplement your understanding. Linear algebra is indispensable, take an upper level version if you can.

If you think you might be doing a lot of computational work, take some computer science as well: take software engineering and learn a language well (I suggest python). If you can program pretty well already, then I'd suggest taking an algorithms class. You're never taught to program well, and yet, you need to! I learned this first-hand when my computational code for research would get stuck forever and never return an answer. With the correct understanding and algorithms, that code can be written to give an answer in 5 seconds.

If you're interested in a more experimental route, take some chemistry and electrical engineering courses. Chemistry will get you some hands-on experience with some equipment that you will often touch as a graduate student when testing your samples, as well as different perspective on the theory. You may need to fabricate your own devices to gather data (or repair them...) so it can't hurt to be familiar with circuits, so take a good EE class. Signal processing (typically also an EE class) will really come in handy.

There's many options, so just take what seems interesting and useful and go with the flow. It's certainly not a bad idea to get a preview of grad school and take more physics, but I would definitely take your time and explore other areas too before you go to grad school, it will absolutely pay off.

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(Making @Kimball's points perhaps even more forcefully...) If you are interested in experimental physics, I have no real advice, but if you are interested in theoretical physics, I will assume for the sake of discussion that the situation resembles that of mathematics. In that case, in fact the question as posed involves implicit hypotheses that (I think) far over-shadow the literal question asked. That is, to get to the best grad program one can, letters of recommendation (from people in the field, who've had contact with you at the highest level you can manage) are critical. So making an excellent impression in graduate-level courses would be a great thing, apart from "taking the class" per se.

For that matter, witnessing how (presumably) seasoned experts talk about more-sophisticated (grad-level rather than undergrad, anyway) material ought to be educational and inspirational in itself, beyond the literal content (which should be accessible in written sources).

For that matter, I think it misses the mark to think of a "program" as essentially following a schedule of classes and perhaps only doing what is commanded by the coursework, homework, exams. It is permitted to read other books, papers, and to think about math (or physics...) as much as one wants. A reason to "take classes" is for easy documentation (and meeting faculty). Private study is hard to document.

Finally, the psychological element of familiarity/comfort matters hugely, in my observation. That is, the longer one has been aware of a thing, the more comfortable one is (even without "mastery"), and often the comfort/discomfort issue is a large cognitive load feature. New/scary things are harder to think about. So looking around and being exposed to things as far in advance as possible is a very good thing.

Finally, at least for "theoretical" subjects such as parts of mathematics and physics, the popular attempted distinction between "study" and "research" is crazily misleading, in my opinion. True, if "study" means some stultifying on-command busywork, that's not so good, but "research" might also mean blundering about in a fog of ignorance, so that could be bad too. The good versions of both, that is, spending one's time thinking about math/whatever, are fundamentally indistinguishable from each other.

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