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Without knowing more about your background, it seems like you have a pretty solid background and should have a good shot at many programs. Are you a domestic student? Will you have solid letters of recommendation? What other math courses have you taken? Someone with a solid GPA and rigorous coursework from a top 30 university will certainly be viewed favorably compared to someone with the same grades/coursework at an unknown university. The problem is that your list of schools is a bunch of very selective programs, which is always risky. The application cycle isn't over yet, so you can always apply to one or two more match/safety schools (places like Texas A&M, Iowa State, Ohio State, etc.). These programs are still very well-regarded, but won't have the same universal "prestige" as the schools on your list. It just depends on your goals for your PhD and afterward. Do you want to go into academia? What are your research interests?

I suggest you post this question somewhere on Reddit like r/statistics or r/PhD.

You've only listed stats classes here. What math classes have you taken, and how well did you do in those? Math courses matter more for PhD applications than stats classes.

Sure, my background and acceptance info is here. To summarize the schools I applied to (with ranking): I got accepted to (in order of acceptance date): Colorado State (30), Baylor (66), University of Missouri (Mizzou, 37), Ohio State (24), and South Carolina (51) rejected: Illinois (UIUC, 22), Texas A&M (13) I also applied and got waitlisted at Rice (29), and I withdrew my application after I decided to accept an offer elsewhere.

I'd add more in the Pitt/Virginia Tech through Baylor range (US news 35ish-60's). Some of those are still not safeties despite their ranking (e.g., NYU), but I think you'd get into a good amount of schools in that range. My profile was quite similar to yours, and I got accepted to all of the ranked 30+ that I applied to.

I don't know anything about applied math PhD programs, so I'll just speak to statistics PhD programs. I think it would be helpful for you to read through some of the applicant profiles over the last few years. If you can take all the classes you mentioned and get good grades in them, you'd be competitive for pretty much any stats PhD program. Honestly, your current math background would already make you competitive at mid-tier stats PhD programs. You only really need a couple more advanced math classes (e.g., real analysis) and strong letters of recommendation to be competitive at higher ranked programs. The only math class I had that you don't have right now is a semester of undergrad real analysis, and I got accepted to a couple top 30 programs.

I think you'll get into many top 10 stats PhD programs and probably any biostats PhD program. I seriously wouldn't be worried about getting in to a good program if I were you. Since you'll probably get in pretty much anywhere, try to focus more on program fit. Location, potential advisors, research areas, funding, curriculum, etc. are all important. Not all statistics PhD programs will be extremely theoretical, although most will require a similar degree of theoretical core coursework. If you like bio applications, a biostats program may be a good place for you, but many stats programs have heavy research in bio applications as well. Just depends on the program.

I would pick the undergrad thesis advisor and probably the lecturer you've had multiple courses with, assuming you have a good relationship with them. Very few undergrads have done any meaningful statistical research, so I don't think an admissions committee would expect that of you. Your undergrad advisor will be able to attest to your general research ability and potential though, which is definitely important. It also sounds like you have a good relationship with them and have done some good work, so it's a no-brainer to me to pick your thesis advisor. Between the lecturers, it probably doesn't matter much which one you pick as long as you've developed a relationship with them and they can attest to your good work and ability in the classroom.

Looks like you have great grades, test scores, and depth of mathematical coursework along with some research experience with solid LoR's. I think you would be competitive pretty much everywhere for PhD programs, just depends on what you want (location/research area/etc.). Any ideas what kind of research you want to do, or do you have any geographical preferences?

If you're at strong university known for grade deflation, I wouldn't be too concerned about the B's. A C in Real Analysis I might raise some eyebrows though, but I could be wrong. What are these "more difficult" classes you mentioned? I hope ranking isn't your #1 factor when choosing which program to attend. Keep in mind you'll be in that department working with those people for 4-5+ years, so you need to make sure you also weigh other factors that affect your day-to-day life and happiness. On another note, I can't even fathom paying 50k/year for an undergraduate degree. There are a lot of solid programs outside of the top 5 though, so you definitely shouldn't feel bad if you end up finding a lower ranked program that is a much better fit in other aspects (people, research areas, location, funding, etc.) It sounds like you're doing a lot this summer and in the fall that will greatly strengthen your application. In addition to those things, I would really focus on building solid relationships with your professors. Go to office hours, show genuine interest in their research, ask good questions. I didn't decide that I wanted to do a PhD until around the same time as you (around spring of my junior year), and I think one of the things that really strengthened my application even though I didn't have a super deep math background or any publications was that I had great relationships with some professors who wrote me very solid letters of recommendation. If you want more specific feedback about which programs may fit your profile, I suggest posting some more details (like specific courses and grades, relevant previous research or other experience, research and location preferences, etc.)

I think you'd be competitive at any of those schools since you have solid grades and a good depth of math coursework from a good school. Usually you need 3 LOR's, and I think having at least one from a professor who can attest to your research potential would be wise.

One big reason I chose the program that I am currently attending is because the majority of PhD grads from my department go into industry and have great placements. My goal has pretty much been industry from the beginning, and the same is true for probably about half of my cohort. Biostatistics PhD programs tend to be more applied than Statistics programs, so as long as you have the basics (like calc 1-3, linear algebra, real analysis), you shouldn't worry too much about taking a lot of additional advanced math classes just to have them on your transcript. A lot of this is program dependent though, so just make sure you understand the level of mathematical rigor at each program you're looking at applying to by reading through the list of required courses. Keep in mind though that having a deeper math background can go a long way in putting yourself ahead of other applicants.

I don't know about NC State's program, but many Stats PhD programs allow you to leave with a Master's if you choose not to continue after two years or so. If you're open to the idea of a PhD but aren't 100% sure, I think going to a PhD program that offers this option would be the way to go. That way, if you decide after a couple years that you really like research and want to continue your PhD route, you can just continue what you're doing. If you decide to leave with a Master's, you could do that too. This would also allow you to be guaranteed full tuition + stipend instead of having to pay tens of thousands of $$$ for a Master's. Obviously, I wouldn't suggest that anyone should go into a PhD program solely with the idea of leaving with a Master's. However, if you think that a PhD might be for you, there's nothing wrong with trying it out and seeing how you like it.

I got a new 2021 Macbook Pro (14" model, M1 Pro CPU) last month to replace my old Windows laptop. Since the Apple silicon chips have been out for a little over a year now, it looks like a fair amount of compatibility issues with various software have been resolved at this point. However, I have seen some issues pop up here and there so far that require a little bit of a workaround (for example, TensorFlow is not currently supported on M1 macs, but it looks like Apple has their own solution to this). As time goes by, I think any lingering problems should be resolved fairly quickly since all of the new Macs are being built with Apple's CPUs. I really like my new computer and don't regret my choice at all. If you like MacOS and the cost isn't too much of an issue, I would say go for it. Tidyverse and other common R packages have worked just fine for me.

For everyone who has received all (or most of) their admissions decisions already, feel free to add your profile to the 2021 Applicant Profiles and Admission Results page! I'm sure future applicants would appreciate it.