I’m currently pursuing a B.S. in Mathematics with a minor in Statistics at San Diego State University. After I graduate, I plan on pursuing a Master’s, and eventually a Ph.D. at a high ranked graduate school for Mathematics (EPFL, ETH Zurich, Cambridge, etc.). Assuming I get a very desirable GPA, extensive research experience, and academic awards/achievements/honors, how good will my chances actually be once the admissions factor in the school I went to for my undergrad? (I’m not exactly sure how San Diego State University stacks up internationally, but I wouldn’t say it’s a low-tier school)
I think SDSU might be around 500-600 internationally and around 130 in the United States.
Depends on what you want to do with your PhD. The only reason to do a PhD at a top University is to increase your chances of an academic position, For most other jobs, a solid department will be enough.
I looked at the CVs of a few grad students at some top universities, and yes, your SDSU undergrad could hurt you. However, doing a Master’s at a better university, like a state flagship, would allow you to gain admission to a top university in math for your PhD. On the other hand, if you have good GPA, great GRE, awards, publish something, and have a faculty member at one of these universities who wants you to work with them, that would work too. In any case, you really need to contact faculty at these universities and ask them. It never hurts to reach out to a faculty member and talk to them.
Subject - gifted students wash up in all kinds of places, for all kinds of reasons. There is no inherent reason why you can’t get to any grad school from SDSU, but making it happen will take work- and genuine ability.
First, in case this isn’t already familiar to you, a word about the grad school structures in the US and Europe:
=> In the US math PhDs typically start straight after undergrad, with the masters being incorporated. They are typically fully funded. Many universities do not offer a terminal Masters in Math. Note that the Math GRE is critical in the US, but not used in most other places.
=> In Europe, it is more common to do a masters (which you pay for) and then a PhD (which is typically stipended, but not necessarily fully funded- depends on the country & the institution).
In general, for any PhD program, your actual research experience will matter a lot. Although it matters in both places, when applying for PhDs in Europe there is more emphasis on how your research interests align with that of specific researchers. Are you spending your summers doing full-on research (REU or similar)? Whatever research work you do - and where you do it- will make a difference, and is the best way to offset a less-known/ranked program. Among other things, it’s a great way to get the additonal LoRs you need. I know a current math PhD student (in a top US program) who came from a middling undergrad university, but who spent summers doing research work for the NSA.
Cambridge does a nice ‘reality check’ for seeing how prepared you are for their Masters program (called Part III, because it builds on their undergrad parts I & II).
http://www.maths.cam.ac.uk/postgrad/part-iii/prospective/preparation/resources
Note that your home state has 2 of the top places in the world to do a math PhD (UCLA & UCB), well ahead of either of the Swiss schools (of course, if you are Swiss that is a different thing!).
@Twoin18 can speak to the intensity of maths at Cambridge- my guess is it would either be a dream come true for you or a nightmare!
The undergrad course is intense, and Part 3 is even more competitive because your result in that determines whether you get PhD funding. In my time at least there were 5 pure and 5 applied funded places per year for U.K. students and almost invariably the top pure math students were ranked above the applied math students.
But after that a PhD is pretty quick (3 years) compared to the US and often quite self-directed (not necessarily at all collaborative). The intensity depends on how much pressure you want to put on yourself, but I found it to be far more relaxed than the undergrad course. Of course that depends how much inspiration you can come up with, a friend (who is now a math professor at Oxford) said all you needed was 2 hours of inspiration in 3 years.
One thing to look at/target is the Churchill scholarship (https://www.churchillscholarship.org) if your university is a partner institution, as some of those scholars use the money to do Part 3 (since it’s just for one year). It also gives an idea of the standard of attendee. But note that the University of Utah has won one of these scholarships in four of the last five years (usually for math) so it’s not just about elite US colleges.
Funding for a PhD can be hard to come by for foreign students, typically you need a competitive external scholarship like a Gates. But if you were truly at the top of the heap in Part 3, then your department (or more likely college) might find a way to keep you.
I think math is one of those field where your undergrad school does matter a little bit more, but you can certainly get into a top-ranked math PhD program from SDSU.
Here is a quote from the PhD admissions FAQ at a program consistently rated #1 in the world in it’s field (not math, but related) with an acceptance rate of around 3%:
“Coming from a lesser-known school is not much of a handicap, if other parts of the application are strong.”
I know of many Aztecs who have gone on to stellar PhD programs in that particular program. Are you currently working with professors in the department? Have you been selected to be on one of their research teams? They are a very approachable and supportive group, and are doing some amazing research.
If you aren’t already involved, joining or going to a few of the SIAM events might prove beneficial.
[Decided to delete my response regarding the “mediocre school” comment. 
]
I suspect “many” is a slight exaggeration, unless one is talking about a very broad stretch of time. Only 5 SDSU graduates have gone on to earn a PhD in math or statistics over the last 5 years, an average of 1 per year. UCSD and UCLA have produced 37 and 43 in that same time frame, respectively.
I agree with juillet – math is one of those fields that seems a bit snooty about where students did their undergraduate studies. My SO recently finished a PhD in pure math in a top 10 math department, and I don’t think I met a single student in his department who hadn’t gone a top university or one of a handful of LACs (namely Reed and Harvey Mudd) for undergrad. Coming from somewhere else may not disqualify you in admissions, but you do face more of an uphill battle.
Please refer to my wording. I made a mistake with a preposition. I should have used “from” instead of “in.” SDSU’s BS for math is in applied math. Many of their applied math grads and those with masters in applied math have gone onto PhD programs. The nature of applied math means that often their research will lead them to PhD programs that aren’t necessarily in math, but in some STEM programs in which math can be applied - physics, engineering, etc. depending upon the area of their research focus.
Are the numbers similar to UCLA? Of course not. Maybe someday. But for a Cal State school that has definitely grown in rigor over the past 20 years, the baby steps have turned into great strides in many areas for the university.
“math is one of those fields that seems a bit snooty about where students did their undergraduate studies”
I’m not convinced that it’s snootiness, more that extremely talented math students are usually precocious and stand out even in elementary school, and are more readily identified by testing and math competitions and then accelerated and tracked towards top schools. In contrast, someone with talent in say chemistry or literature wouldn’t necessarily be identified so early and very likely wouldn’t be accelerated in the same way from middle school onwards.
Of course there will also be some mathematicians who will end up at their state flagship, which might not be perceived as so elite, depending on their location. And undoubtedly some talented mathematicians (especially those who are on the spectrum and don’t have ECs and leadership in high school) might find they don’t get into a top school that’s using holistic admissions.
(to continue from @Twoin18…)
or come from homeschooled families / non-college oriented families / families from which the range of 3rd level options is narrow / etc. I know current math PhD students from all of those backgrounds, some of whom had no thought of being mathematicians before college.
I think @Fish125 makes a seriously relevant point: exactly what field you decide to go into will affect which PhD you decide to go for (both university and subject).
Further, what is a ‘high-ranked’ university is *not[/] a uniform thing at the PhD level. One of my collegekids didn’t apply to a couple of the ‘Ivy League’ colleges for PhD, because they are simply not as strong in her field as other universities. A CCer whose daughter did undergrad at Cambridge is now doing her PhD at the University of Bristol (? might be Manchester/not remembering), because the top researcher in the world in her area of interest is there, and she was thrilled to get the spot.
As you learn more about what end of maths you find interesting (esp by doing research internships) and start looking into PhD programs you will start building a better sense of what programs are interesting to you, which is the key. The best advice for choosing a place to do a PhD is to start by finding an area within your subject that is so interesting to you that you are genuinely interested in spending 3-6 years marinating in that subject.