Things you’ll need for an application:
In general, you’ll need: research/internship/fellowship experience, letters of recommendation (2-3), a CV, a gpa above a 3.0 out of 4.0 (for more competitive schools this may be higher), a statement of purpose/research statement/personal statement, and possibly a GRE exam score. I’ll go through each one in more detail below:
Research / Internships / Fellowships/ Experience
You’ll need to have some background in working on projects in a group setting and getting some sort of results if you’re going to pursue either a research-based Masters or a PhD program. The school is hiring you to do research, so they want to make sure that you have some sort of ground work on how things generally work. This is probably the most crucial piece of your application! Learn more about research here!
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You don’t need publications in order to call your work a “research experience”.
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Aim to have at least a year of experience before applying, so a good time to start your research career would be in your sophomore/junior year.
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If you haven’t done any research and you’re about to graduate but still want to go to graduate school, I recommend that you take a year off and apply to be a research assistant/fellow somewhere and get experience. Then, apply with a much stronger application.
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I can’t speak too much on fellowships/internships, as I mainly focused on research. However, just ask your professors and they’ll know for sure which to apply to.
Letters of Rec.
Remember those office hours that you went to? Now would be a great time to think back to the professors with whom you connected with the best, and ask them for a letter of recommendation. You don’t need to have a solid list of programs yet, just a “Hey, I’d like you to write my letter of recommendation for graduate school” type of email. A little bit more formal than that, but you get the idea. Once you start the applications, there will be a text box for you to type in your professor’s email. They’ll get a link, and submit their letter. Pretty simple. Trivial, if you will.
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If you think that a professor may have forgotten you over the years, all you have to do to refresh their memory is, when you write the email, include what class you had them for, possibly what you most enjoyed about their class, and attach a recent copy of your CV. This will help them put together a strong letter for you, even if it's been a while.
Your CV
Basically a culmination of everything you’ve done in your undergraduate career. Everything should be on it. Things that are related to your major/course of study, things that aren’t related, things that could be related with enough of a stretch…
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Make sure you have descriptions of what you did for each project/job/responsibility.
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Add who you worked with, and where. It’s that age old saying of “it’s not what you know, but who you know”. Sometimes, potential advisors will know professors that you’ve previously worked with, which can be a very good thing! It adds credibility to your application, and shows that you’re serious.
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Don’t add things from high school, unless you’ve won the Nobel Prize. Don’t add things just to “add fluff” to your CV. Nothing good comes from adding things just because you want your CV to be a certain number of pages.
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Formatting: it should be clear, clean, and without too much distraction. There are many great templates on LaTeX Overleaf that are excellent to use for this very purpose. I would recommend to stay away from Google Docs and Word, only because indentation alignment could get messy, and from personal experience, they’re less reliable. However, you do you. ​
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GPA
Your GPA isn’t everything. I speak from experience when I say this, as I didn’t have the greatest GPA, nor was it even close to a 4.0, which is what you would expect anyone to need to get accepted into a graduate physics program. If you don’t have an outstanding GPA, then the rest of your application better help to balance it out. Again, it’s not the most valuable thing, but you should aim to have higher than a 3.0 out of 4.0 to be considered. I don’t know how strictly this rule is enforced, but it’s what I’ve been told. However, a perfect GPA is not going to exclude you from needing research or good letters of recommendation. You still need those…
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One more note, if you started out your undergraduate career with a rough time getting a handle on exam grades, then as long as you show an upward GPA trend, you’ll be fine. And if this is the case, then you have the opportunity to explain your situation in your Statement of Purpose, if you feel comfortable doing so.
Statements
Whether it is a general “Statement of Purpose”, or a more specific “Personal Statement” or “Research Statement”, each one holds the purpose of adding something that the admissions committee can’t get straight from your CV or the rest of your application. This might be the perfect time to explain that one bad semester you had. Don’t make it your entire essay, but you can definitely work it in about how this made you persevere more as a student, etc.
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“Statement of Purpose”: Think of this as a past, present, and future type of essay. What in the past made you want to apply for a graduate degree in physics? What are you currently doing (in undergrad, or after you graduated undergrad) that makes you a qualified candidate for consideration? This is a good time to list some research experience (with specific professors)… And why is doing a Masters/PhD the next logical step in your path to accomplish whatever goal you have after you graduate with your Masters/PhD?
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“Research Statement”: Not as sentimental as a general statement, but in essence, this is what your current research is about, and what you can see yourself doing research-wise at whatever university. Here, and in the general “Statement of Purpose”, you can list professors at the university with which you’d like to work with, and give details about their research to show that you’ve actually done your part in finding a program that fits your needs as a scientist.
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“Personal Statement”: This is probably the most out-of-the-box essay, and only one school I applied to requested to have this as a separate document. Basically, what about you is interesting outside of your research/academic background? Note that here you can also mention any leadership opportunities you had, whether or not they were directly related to your field of study. Leadership can take the form of the "traditional" executive student club board member, but also the less talked about student mentor/tutor, head of a project, or anything else that required you to give direction to someone else.
GRE
I can’t speak from personal experience on this one, but I think the general trend is showing that the GRE is becoming less and less important, as with a PhD it’s not a “How well can you pass exams” job, it’s a “how well can you do research and think creatively” job... After you get through your classes, that is.​ However, if you have a lower GPA and the GRE is still required, you can somewhat compensate for a lower GPA with a high GRE score, along with having a strong rest-of-your-application. I say somewhat only because with PhD programs specifically, your main job is to conduct research, not take exams. So it's great that you can show subject mastery through something like the GRE, but it is not an indicator of graduate school success. Many programs now (at least for the time being) have made both the general and physics GRE as optional, so keep an eye out for updates on the websites for the universities you'll be applying to!
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I also can't speak on the international student process in terms of exams needed to take and score well on, as I am not an international student. However, it is important that you score well, as it proves to the admissions committee that your English is good enough to conduct research and take classes, all of which will be done in English.