[Note this post is somewhat under construction]

Applying to a PhD is a difficult process, and a complete source of good advice is hard to come by. I've decided to compile and share all the advice and resources that I have found helpful when I worked on my applications. This content will most strongly apply for physics applicants, but can likely be generalized to other STEM fields.

• Letters of Recommendation (LOR)
  • Three letters, ideally from faculty members or equivalent (i.e. national lab research scientists) attesting to your potential as a Ph.D. candidate.
• Statement of Purpose (SOP)
  • ~2 page essay, with prompts slightly varying per school. The main goal is to sell why your experiences prepare you to succeed in a Ph.D. program, and why you are applying. This must be somewhat customized per school.
• Personal Statement (PS)
  • Some schools allow you to submit a ~1 page paper separate from the SOP discussing more personal aspects to your application.
• CV
  • Curriculum Vitae, a 2-3 page document outlining, more or less, everything you've done in your academic career.
• GRE/PGRE Scores
  • GRE is mostly phased out, while PGRE depends on schools and subfields.

The earliest deadlines tend to be around December 15th (if you're also applying for engineering for CS, it may be earlier). For many of us, this is right during finals, and you do not want to save major parts of your application for the last day or two. I would say the absolute minimum amount of time you can get away with to compile a good application is one month, but you want to avoid that. Below I will suggest a closer to optimal timeline, and the rest of the post will elaborate on each of those points.

TLDR:

• Should you take the GRE?
  • No, unless a school you're very interested in explicitly requires it
• Should you take the Physics GRE (PGRE)?
  • Maybe...

The PGRE, prior to 2020, was required of nearly all physics applicants. It was a 3 hour (now shortened to 2), multiple-choice question test spanning all courses in a typical physics degree, and then some. During COVID-19, this was phased out. Since then, many schools now accept it optionally (or "recommend it"), with only a small number requiring it for consideration.

Studying to do well is not a small time commitment. It is expected that you will be able to quickly recall many specific results from various points in your program. Can you recall the magnetic field in a solenoid? Or the $n$ the energy level of a 3D quantum harmonic oscillator? I sure can't. So, is it worth committing the time?

The mindset many schools tend to have now is, if you feel your GPA does not reflect your physics knowledge, the PGRE is another way to demonstrate your abilities. If your GPA is not ideal, say 3.5-3.7, this could help you avoid getting filtered out at a top school (although a 3.5 is not generally a barrier). If your GPA might be more of a concern point in your application, say <3.5, or you have nonideal grades in core classes, the PGRE may be an important step to help alleviate this concern to the committees.

Most of this is speculative, as no one outside of the committees really knows how they view PGRE scores in the modern day. If I had to go with my best guess, I would suggest:

For experimental applicants:

• GPA $\in$ [3.7, 4.0): Take it if you have time
• GPA $\in$ [3.5, 3.7): Should take it if you want to improve odds at top schools
• GPA $<$ 3.5: Take it

For theory applicants:
GPA is much more emphasized, so unfortunately it is often more important to take.

• GPA $\in$ [3.8, 4.0): Consider taking it, some schools will require it
• GPA $<$ 3.8: Take it

The best resource for preparing is the book listed above. This is based on the old version, which generally was harder; If you are well-prepared for that one, you will do well on the new one. There is only one practice test available in the new format, which is in the official practice book (linked above). I suggest saving this to use in test conditions relatively close to the date. If you can, take it twice. They are a month apart, so if you don't do as well as you'd like, you have some more time to prepare for the last one.

Choosing which schools you will apply to is a difficult decision, and there's no one process that's right for everybody. There are many factors to consider, and only you can decide what's most important for you. Here are the main ones I could think of, and my thoughts:

• Faculty close to your area of research
  • Generally regarded as the most important. Ideally, you'll have multiple faculty in your area (in case you don't like one or two of them), and more graduate students in your field provides a better support network. For jobs in academia, the reputation of the faculty member you work with is more important than the reputation of the school.
• Reputation
  • You may want to consider the overall reputation, especially if you feel likely to change fields in industry later, but subfield reputation is generally a better indicator. For example, for nuclear or accelerator physics Michigan State University is considered a top (and competitive) spot due to housing the FRIB, although you might be hard-pressed to find someone outside of that subfield that regards MSU as a top program.
• Location
  • You'll be there for six years, or more. Pick somewhere you'll be happy living.
• Student Life
  • How closely does the department value student life/well-being? Talk to current grad students if you can.
• Stipend (although this can be difficult to know reliably before applying)
  • Does the program offer guaranteed funding for the full duration? How long do students often have to TA? How much is the pay relative to cost of living?
• "Vibe" of the department
  • Some departments are known for not having great social environments
• Closeness to other institutions
  • The more you can build your network, the better
• Connections with your LOR writers
  • If members on the committee know your LOR writers, this may boost your chances of admission (perhaps significantly). Looking at where your writer's collaborators are located, or their former postdoc/PhD institutions, is a good way to build an initial list

I recommend building a spreadsheet listing all your interested schools and their deadlines. This is important to send to your LOR writers as soon as you have it close to ready, and good for keeping track of notes you may want to use when crafting your SOPs.

Another big question here is how many to apply to. This can depend on your finances, how strong of an applicant you are, how many programs fit your needs, or time constraints. To get a sense of an average, in my experience experimental applicants applied for 10-15, while theory applicants did 15-25. There are never any safety schools at this level, but there are schools you're far more likely to get into than, say, Harvard or Caltech. What schools might be 'in-range' is a good question for your advisors.

There is around a $60-120 fee associated with each application. This is often a factor in limiting how many you can apply for. Fee waivers are available, but not many are offered. Apply for these early (I did not get any, so I will refrain from giving advice on those).

And lastly, don't apply to any schools you don't think you would actually attend, if you got into nowhere else. It wastes time, money, and can take away a spot from another student.

Your LORs are perhaps the most important part of your application. You will need to find three faculty members to agree to write them for you, ideally who know you well and can attest to your skills and potential. Note that while many schools may allow you to submit more than three, most have a clause that they are only guaranteed to read three. For that reason, I would only do three, and pick your strongest.

Who to Ask?

At a minimum, you should have one writer who can discuss your research ability. Most frequently, this is an REU advisor or someone from your institution you did research a research project with. The longer you know them and the better the work you did, the 'stronger' the letter is. It is challenging to get three research based letters, especially if you get involved in research later, or work with the same faculty for a longer period of time. Generally this is fine.

Other good candidates are:

• Your undergraduate advisor
• Faculty you were a TA for
• Supervisor if you did some form of mentoring or tutoring

None of these would be particularly strong, but that's ok - it is not common for all letters to be strong, research-based letters, but the more you can, the better. You should avoid asking faculty who you only had as an instructor. If all they can say about you is you performed well in-class, that is not illuminating as they have your transcripts. This may be a better option for a small graduate level course, or if you had the same faculty for several high level classes, but in general should be avoided.

In my case, I was fortunate that I was able to, for one faculty member:

• Complete an independent study research project
• TA twice, both for an undergraduate and graduate-level course
• Have as an instructor for the same two courses, and get an A in both cases

'double-dipping' in this way is ideal, if you're able to make it work. Doing well in classes or just TAing isn't amazing, but they are great to have included along research related content.

How to Ask?

Many people find asking to be one of the most intimidating parts, as they feel that they are being a bother or an annoyance. While it's true that no one enjoys writing a LOR, it's part of their job as an advisor/mentor. They had to ask for many to get where they are now, and most view writing them as their way of paying it forward.

You do want to take care to make the process as easy as possible for your writers. To do this:

Ask in advance. 2-3 months is ideal. Most would not find 1 month to be a problem. To be respectful of their time, 1 month is the shortest in advance I would recommend asking unless there is some kind of extenuating circumstances. If you wait for one or two weeks before, you run the risk of them feeling disrespected or not having the time.

Send your application materials. The most important thing they need to know is your list of schools and their deadlines. Provide them with this list (perhaps in a google sheet or something similar) 1 month before the deadline at the latest. This list need not be final, but should be as close to final as you can, and you should avoid adding any earlier deadlines after. Later is usually fine. For them to provide a properly customized letter, especially if they may not know you as well as you'd like, you should provide a draft of your SOP/PS and CV. This is a good time to ask for feedback on these.

I recommend first compiling a shared Google Drive folder with the mentioned spreadsheet, SOP/PS drafts, CV, and optionally your transcript. Here is an example of an email I may write:

SUBJECT: Ph.D. Program Letters of Recommendation

Dear Prof. XXXX,

I hope all is well. I am applying this cycle for Physics Ph.D. programs, and I wanted to see if you would be comfortable writing me a strong letter of recommendation. [1-2 sentences describing why your experience with them will add to your application]. The first deadline is [insert date]

I have linked below a folder with all of my application materials, should you find those useful. Any feedback you may have on those would also be welcome.

[Drive link to your folder]

Thank you for your time,
[Your Name]

For the 1-2 sentences, you should provide some context on why you're asking them specifically. If you did a research project for example, you may want to mention if you're applying to programs working on similar things or things with transferrable skills. If you were a TA, you may mention how you think discussing your teaching skills would be relevant.

You can of course tweak the formality of this message based on your relationship with the faculty member. For an advisor I had been with for two years and was still working with, I simply sent a message on Slack. Use your best judgement here, but it generally isn't a problem to be 'too' formal.

Make sure you check the deadline times of all your schools, and report any that are not midnight. Harvard is typically 5pm, and people miss this every year.

Did They Forget?

Probably not. Despite months of notice, most faculty members will not submit the letters until the day they're due (hey, don't pretend you don't procrastinate either). I had many cases of them not submitting until around an hour before the deadline. It's good to send occasional reminders, I would suggest around one week and one day before the first deadline. If they said they would write one, it's highly unlikely they will fail to submit, just keep in mind it may be finals season and they are also quite busy.

In the event that they don't submit on time, there's still no need to stress. The deadlines for LOR's are always more flexible, as committees understand it is outside the students control. I had a writer submit a letter 12 days late (for a January 15th deadline, no less) and I was still admitted with a fellowship. No reasonable committee will reject or penalize a strong student due to a late letter. Despite this, you should make strong attempts after the deadline to ensure it is put in as soon as you are able, and mind if any schools specifically cite having a hard deadline for letters.

The statement of purpose is a key part of your application. Its function is to tie together every other part of your application, and highlight why this collection of letters, grades, awards, etc means you're ready to be a grad student, and why you want to be a grad student at that institution. Typically, there is either a two page or 1000-word limit. To make customizing it easier, I would keep to both of these.

General Tips

Be concise. You have a lot of content to convey in two pages. Every word in your statement should be contributing to your overall goal.

You will likely, on your first draft, write far too much. That's okay. Write three pages, then work through, and do your best to follow the above rule. If it does not actively contribute to your ability as a Ph.D. student, delete it or work it into another sentence.

Start with an outline. Look over a couple schools prompts (MIT's is a good one) and come up with an outline that addresses it, more customized to you. I outline below the three main 'blocks', but it's easier to make a finer outline based on your profile. ChatGPT or similar are good at this (but don't use for actual writing, it's very obvious, and committees will know)

Formatting

I suggest using LaTeX or Typst rather than Docs or Word. A small touch, but looks more professional. Use 12 point font. After customizing my statement to each school, I would adjust the line spacing slightly to make the content fill the two pages completely. Empty space at the bottom may look like you ran out of things to say.

I used section headers for each paragraph. This was slightly controversial, as some faculty members I asked didn't like it very much. But those who did, really did, as it aided skimming quite a bit. I would encourage it, I think it is more likely to help than hurt in my opinion.

I also used bolding for important sentences, particularly when describing the outcomes of my work, or awards I received. This is especially important towards the end of a paragraph. This makes sure that anyone who's skimming would catch it. Be careful not to over do this, I would suggest no more than once per paragraph.

Introduction

Keep this brief. Write 3-5 sentences answering who you are, what you're doing, and why. Practically, you're a passionate, motivated student, successful in some area of research, and applying to some school to continue to do research, to achieve some career goal. You will elaborate on all of this, so keep it as concise as possible. Do not talk about your childhood. Every applicant has been fascinated with physics or the universe since childhood, this does not add anything for you.

Academic Background & Research Experience

This will be the bulk of your paper. You will have to sell, in a couple paragraphs, what experience you have and why that makes you prepared for a PhD. I wrote these in a very formulaic way:

[1-2 sentences on what I was working on, and with who]. [2-3 sentences with more detail on my specific contributions, what tools I used, or what I had to learn]. [1-2 sentences on the outcome of this work]

For your intro sentence, include the collaboration (if applicable), the faculty member you worked with (name dropping is great if they're well known), and what the overall goal in the lab is.

Most likely, you could write a whole paper just on your specific contributions. Unfortunately, you will not have that space available. You'll have to choose carefully what to include. I would try to include the use of any tools are skills that would generalize to the position you're applying for. Foe example, many groups like experience CAD, Geant4, electronics, etc. Even better if you used some tools very specific to a subfield.

For the outcome, this need not be a publication. One of my projects had a poster presentation at an APS meeting, which was great to mention. But even more importantly, talk about how the work you did is benefiting the lab. Is the code you wrote currently in use, performing analysis or saving people time? Did you put together an electronics system currently powering the experiment? How will these things benefit the lab after you leave? Faculty understand publications, especially in HEP-ex or nuclear physics, are not in your control, so talk about the local impacts of your work instead.

Why are you applying for a Ph.D.?

Finally, you will want to talk about your goals, both during and after your Ph.D. This is the part you will want to customize for each school.

The more important part, is you will want to discuss your motivations for applying to a specific program. Say UMass, why there out of any other program in the US? This shows you've done your research, and for top-level schools, shows you aren't just chasing a name. You should describe some things that may make the school unique (does it provide access to a national lab, or accelerator facility?), and mention 3-4 faculty that you would like to work with. The last part is important, as they will likely have influence on your application's success, or possibly be on the committee. Briefly say who stands out to you, why, and if you can, why you would be successful in their lab.

Then, you will want to mention why you want to do a Ph.D. at all. Keep this fairly short, as I'm not sure this as has much influence as the rest, but it should be present. Do you want to do research full-time after? Where in academia or industry? Almost any answer that actually requires a Ph.D. is fine. I believe this is mostly to weed out people who are just applying because they don't know what else to do, and focus on people driven to enter the research community permanently.

Getting Feedback

Your SOP should go through several revisions and drafts. If you can, get personal feedback from several faculty members after you already feel it's in good shape. Do ask several, as advice may conflict, and as many perspectives as possible is good. If you can, set up a couple meetings with different faculty, and sit down and read it live with them, and note down any thoughts they have.

The purpose here is to provide a more personal touch to your application. This is most often optional, but generally in your best interest to submit. Many schools prompts are different, so check each one and tailor accordingly. Here are some topic ideas to discuss:

• Did you have any extenuating circumstances that impacted your application?
  • Illness, death in the family, homelessness, etc may be all reasons for a period of poor grades. This is important for them to know.
• Do you have any oddities on your transcript to discuss?
  • If anything looks unusual, they may assume the worst. I had gaps from COVID and community college credits to discuss.
• How will you contribute towards a strong, positive community at your new institution?
  • I very much enjoy teaching, so I highlighted my teaching experience and how I plan to utilize that
  • Mentoring, club work (especially any diversity-related clubs), or volunteering are also great topics

In addition to a great researcher, they want someone who will be a pleasure to work with, and who will be a positive impact on their community. Any work you've done to support that is a great supplement.

An academic CV, if you don't have one, is a document that summarizes your entire academic career. Think of a resume, but with unlimited pages. You may find many faculty members with 10-20 pages, or more. I would recommend keeping to 2, or 3 if you must. You should have the following sections:

• Education
• Research Experience
• Publications (if applicable)
• Posters and Presentations (if applicable)
• Honors & Awards (if applicable)
• Teaching Experience (if applicable)
• Mentoring Experience (if applicable)
• Extra Circular Activities (if applicable and relevant)
• Additional Skills (software, programming languages, hardware, etc)

These are not sorted in any particular way. Prioritize based on your profile where things should be, with more important things first. You can see in my example how I chose to order mine.

Use a professional template, ideally in LateX or Typst. Many are available online. Do not include a headshot.

Keep in mind your deadlines. Avoid having to do any significant work on the day of your deadline. In the weeks leading up to it, I would spend downtime (or time I was bored in lecture) filling out the tedious online forms. Your SOP/PS drafts should already be done prior to the deadline. Personally, I waited until the day of to actually submit, in case I discovered any typos I wanted to correct. But, do not wait until close to midnight. Very few programs are forgiving for late submissions.