wine in coffee cups

I can comment a bit on UW's program. It's new as a formal master's program and the first group of seven students is just finishing this spring, so not a lot of outcomes to report on yet. Two of the students are moving on to statistics PhD programs (one staying at UW, other going to Yale). The remaining are job hunting, to my knowledge, mostly looking at data analyst positions, I think at least two have accepted job offers already in the Northwest. The current first year master's cohort is larger, 18 students, not sure what their goals are generally. Most are from China, though there are a few US citizens. Next year, even bigger I would guess? RA funding is unlikely to happen for master's students, as the overall TA/RA situation is already tight for the PhD students and they get priority. I think some are master's students are graders for undergrad classes, don't know of any first years who TA or RA, one of the second year students TA'd. So in terms of funding to offset the cost of the program, in practice this is pretty limited so far.
 
The coursework is theoretical and shares a lot of the requirements with the statistics and biostatistics PhDs. If you are thinking at all about going on to a PhD, it's definitely good preparation, the coursework is undeniably rigorous. The first year theory sequence and the second year methods sequence involve a lot of homework and are particularly time consuming. For the most part, the offerings are traditional statistics classes, which are interesting and challenging but not direct professional training. For machine learning offerings specifically, see here (note the theoretical emphasis). There are some electives that could be useful to someone interested in a data science career who wanted to get a portfolio started, such as the popular new "machine learning for big data" class which demands a lot of programming and a substantial final project. The required first year linear regression class and elective nonparametric regression class also usually have final projects and a poster/presentation, again, perhaps nice for portfolio building and interview fodder. I haven't heard too much about the required master's capstone class, but I think it involved some sitting in on consulting sessions and seemed more practical than most of the other coursework, may be somewhat useful for learning how to bridge the divide between real problem posed by a non-statistician and a solution grounded in statistical theory.
 
The department forwards on job postings it receives to students, seems like a few per week, emphasis on local employers but some things from all around the country, but doesn't maintain any kind of job database or resume service. You can go through general UW career advising of course, job fairs and whatnot. Not sure how that compares to whatever UCLA does for its students. The university has an overall very strong reputation in statistics and computer science, though, and I don't think it would be hard to get employers to take your training seriously coming out of UW. Unfortunately can't tell you if this is worth the premium over a shorter cheaper program at UCLA.

I wouldn't wear a pit-stained baggy math t-shirt and white athletic socks, but I definitely wouldn't wear a tie. Button down shirt or nice sweater and non-denim pants for men, somewhere around business casual.
 
IIRC last year they said they would admit about half of the people they interviewed between flyouts and Skype calls to internationals. So I'd say you have a good chance, of course, but far from a sure thing.
 
Last year they had candidates meet just about every professor in the department in 30 minute meetings, typically the whole group meeting with one or two faculty at a time in their offices. The profs do most of the talking and describe the program, their research, life in the Research Triangle, etc., but you will have a lot of time for questions so make a nice long list. You'll also spend some time socializing with current students and will most likely go to dinner with some of them. They're great, pick their brains as much as you can.
 
You're not getting interviewed in a traditional sense, but you will definitely get asked by the director and probably quite a few of the faculty about potential topics/areas you are interested in, why you want a PhD, that sort of thing. (Not that you still don't get asked about these things on other visits even after getting in! It was very similar to the accepted student days I went to elsewhere but for the fact that I wasn't sure if I was admitted yet.) I had the impression they were screening for personality fit within the department and some degree of maturity/seriousness in purpose, so be yourself but be your best self.
 
Good luck, it's more fun than you think!

cyberwulf, I'm not sure I would hold up a perfect GPA as the standard for a stats applicant to be considered uber-competitive and in the peer group with aridneptune, but let's say something like >3.9 within math (with lots of courses), and not much lower overall from the kinds of schools you've heard of. Without weird weightings, that essentially means over 3/4 of math grades are A's and the remainder are A-'s, which sounds like a reasonable peer group to me. Given that, I'm quibbling with your quibble (instead of working on my research ) and think you're underestimating how many stats applicants are out there with comparable profiles.
 
I had a job some years back analyzing data for a consortium of 30-odd highly ranked private colleges, more or less the same ones that are vastly overrepresented among baccalaureate institutions in PhD programs. One of the fun facts I learned was that at pretty much all of these schools, math majors disproportionately had very high GPAs. My undergrad is a typical example: over one-third of math majors in my year graduated in the top 5% of students (>3.9 overall). Nearly all the rest were still in the top 25% of students (>3.7 overall, almost certainly higher in major). When I used to do resume review and interviewing in my old job, too, we looked for econ or math majors with high grades in statistics/econometrics classes mostly from fancy schmancy schools like Dartmouth and Wesleyan. There, too, I encountered a surprising number of students with very strong math backgrounds and grades. 3.9s in math, apparently not rare at all and not limited to those with math or econ PhD aspirations! Not certain why, but my observation is that a lot of students won't touch non-required math unless they've already gotten a lot of A's in the lower level courses. By this selection mechanism, then students who continue taking mostly math (and related classes in CS, econ, physics, or logic) will continue to get mostly A's and A-'s, especially since upper-level classes rarely curve.
  So sure, the best math majors mostly go to pure math PhDs, I wouldn't dispute that. But because of the high concentration of near-perfect grades among math majors, at most good schools there will still be at least one math-ish major (current or someone who graduated in the past few years) who meets the high grade standards in my first paragraph and is applying to statistics or biostatistics programs. In the aggregated stats applicant pool, count on at minimum a dozen strong applicants from LACs like Pomona, Swarthmore, Amherst, Carleton, Williams, a bunch more -- even little ol' St. Olaf is a powerhouse. I think I'm underestimating the LAC contingent actually. Then count on a couple dozen more applicants from the mega name-brand research universities (Stanford's programs alone must send out a half dozen people at a time and I think Chicago too). Throw in another couple dozen apps from other respected schools like UNC. Basically, name all the good private and public schools you can, and imagine that there's on average one current senior or recent grad with strong credentials applying to stats departments (because, again, high grades are not at all unusual for math majors). And surely most of the recommendations for this crowd are quite good, especially for the substantial portion of these applicants coming from small schools who get detailed personalized recs or those with access to bigger names?   Anyway, a couple dozen here and there ballparks to something like 60 applicants in the pool who are going to be at the top of the piles everywhere they apply, so I think a fair number more than what you have in mind. It would be a big pain, but you could look up profiles of first-year grad students at the top 15 or so statistics departments, and I bet you would find enough students who majored in something math-ish graduating with high honors (proxy for high GPA) at a well-reputed undergrad to substantiate my claim. In my cohort alone there are at least 6 of us who would meet that description, have to imagine the scene is similar elsewhere.

Since this thread has been revived, may as well follow up for future statistics PhD applicants who wondering what to do about the subject test. (n=1, though, people, n=1.) I had a 58%ile subject score. I submitted it to Chicago and got in. I did not submit it to Berkeley, Columbia, Duke, IA State, Michigan, Northwestern, or Washington but still got in. I did not submit it to CMU or Harvard and did not get in. I'm guessing that the presence/absence of that subject test score had little bearing on any of these results.

There is a current 3rd year biostat PhD student who was admitted off the master's pathway at the end of her first year. I'm pretty sure there is another who was also admitted to the PhD off the MS and would be a third year, but she took a job in Seattle a few months ago and I think is returning at a later point.
 
One thing you have to do to get accepted off the pathway is pass the master's exam at a designated PhD level. I don't know about the most recent exam, but in 2012 and 2013 only about 60% of statistics and biostatistics graduate students taking the exam passed at the PhD level.

Looks to me like you need like two more years of undergrad courses (a year of algebra, a year of analysis, topology, other topics like complex analysis or PDEs or differential geometry). You've only got the first half of an undergrad pure math major completed and don't meet the prerequisites for most graduate level math courses at these schools.

I was an applicant for several quantitative PhD programs (biostatistics, statistics, economics, and operations research) during the 2015 admissions cycle, and I figured that some of my experiences can help assuage the anxiety many of you are feeling. (For my background, you can check out my results here, under the same username "Transformiao": http://www.mathematicsgre.com/viewtopic.php?f=1&t=3297)
 
For biostatistics applicants: I was very successful in my applications for biostatistics PhD programs. The other people I've met during the visiting days / interviews came from various backgrounds, including mathematics, statistics, psychology, finance, economics, operations research, and two-way combinations of the aforementioned. Clearly, the major is just a name; as long as you have shown coursework in some hardcore math or stats courses, and some research projects clearly utilizing important statistical methods, I would say you're good. For me personally, I demonstrated my mathematical aptitude by taking the Math GRE subject test, did pretty well, and submitted my scores to all biostatistics PhD programs. If you do decide to take my route, I would say anything over the 60th percentile is strong and should be submitted. Of course, no worries if you can't take it - University of Washington clearly stated they do not recommend to take the Math GRE subject test (http://www.biostat.washington.edu/pro/faq), and when I attended a Harvard information session regarding the issue, a representative of the department said fewer than 10% of their applicants actually submit.
 
I'm ballparking it, but I would say for those who have taken only multivariable calculus (calculus III), linear algebra I (linear algebra with matrices), and non-calculus statistics courses, it would be very hard to get into the top 5 programs. If you are aiming for a top 5 PhD program with only the aforementioned, I would recommend a master's program as a stepping stone or some serious public health / biostatistics work in industry. 
 
As the pinned post "Before you start agonizing over your personal/research statement for stat or biostat, read this" has stated, biostatistics PhD programs are clearly a numbers game. While I worked hard on my SOP (even typing in LaTeX in hopes the admissions committee will subtly notice my academic suave), I don't believe it had much on my application. The time would be better spent on some last-semester coursework or GRE studying. In speaking of last-semester coursework, the timing of the admissions cycle might make things a bit awkward for some of the final hardcore, relevant classes to show up for the admission committee. I graduated from undergraduate studies in three years, and I personally believe taking a year to work in industry has helped make sure my final year's worth of classes, many of which were graduate level, were seen by the admissions committee. 
 
For statistics applicants: Many of my previous words for biostatistics apply for this, but it does strike me curious that my success rate for statistics PhD programs was not as good (I was only accepted to University of Chicago's master's program). I surmise here that the competition for statistics PhD programs far outstrips the competition for biostatistics programs. Here, I suggest people to perhaps take several more mathematics and computer sciences courses to achieve the top programs. 
 
For economics applicants: I can only speak for those who seek to specialize in econometrics. Even then, I would probably say my economics coursework is by far the weakest for this type of application. I only applied for two programs, and was rejected from both. Then again, the rejection letter I received from Yale indicated that I was one of nearly 10,000 applicants for less than 20 positions! So here, really, I would say you need to take many, many classes in economics and mathematics and perhaps even publish a paper. While I'm not quite as qualified to for economics, I have a close friend from college who has taken many of the statistics / mathematics coursework as I did, plus several graduate economics courses in undergraduate, plus a master's in economics at a reputable university, and yet still got into a rank 15 - 20 university in the end. Economics is very hard to get into for the top programs, and it seems to me that one should have an adviser in mind when writing the statement of purpose. 
 
For operations research applicants: My success rate for OR is second, after biostatistics. The admitted applicants I've met came mostly from an OR background, although I've met a few others with majors such as statistics, chemical engineering, and computer science. As for the math subject GRE, no OR department really talks much about it, and the one I found with Cornell, states it would be recommended (https://www.orie.cornell.edu/academics/doctor/apply.cfm). If you come from a slightly out-of-phase major or career with OR, I would say from personal experience that it would be fine as long as you have demonstrated strong mathematical abilities or related work in optimization / statistics / financial engineering. For example, I haven't formally taken an optimization class in my undergraduate studies, albeit I've taken far more statistics and probability coursework than the average OR undergraduate major and many other related quantitative courses that use optimization techniques. While this is still a numbers game, I do feel that more people I've met have worked in industry (or even the military) than I would say for biostatistics applicants. And even then, the people that worked in industry used techniques directly related to OR, as opposed to biostatistics applicants who used statistical techniques not necessarily with a biostatistics flavor.
 
I hope this helps many people!

I think your background sets you up very well to get into one of those graduate programs.  Even though you didn't major in math or statistics, you still got an excellent grade in Real Analysis, which is the class that admissions committees look for when they are trying to determine whether your math background is suitable for a PhD program.  IMO, a second semester of real analysis would be the most helpful for your application if you were going to take another math course.
 
In my opinion, unless you got a very good score on the GRE math subject test (75-80%+), don't bother submitting your score to schools that merely recommend it.  I think most schools realize that a multiple choice test on subjects ranging from number theory to topology is not the most predictive when it comes to statistics PhD outcomes.  However, it can serve as a proxy for general mathematical knowledge, which is why some schools like to have it.
 
Many of the schools that you listed are relatively small programs, which makes them harder to get into and narrows the range of research topics available in the department.  May I ask why you chose those specific programs?

I wouldn't even mention the withdrawal from analysis; it's a W, not an F, so there's no need to explain it.  If you do well in analysis this semester and ace the math section of the GRE, your profile is great and I think you'll be very competitive for any biostat program in the country.  I don't think you need to apply to nearly that many programs.

The catch is that your recommenders say will matter 10x more, doesn't matter how much you downplay your previous program. Those letters are the most important part of your application! Members of the admissions committee will be extra keen to hear what the faculty at your current program think about how you stack up relative to other students and whether you are a good candidate for a PhD. You have little control over whether and how your letter writers frame your leaving their program beyond whatever reasons you share with them. It will not look good if what they write is in any way at odds with what you write.
 
There is some relevant discussion in an old thread about transfers  a couple of biostatistics faculty who post, and a little more about recommendation letters from the perspectives of those same faculty starting  think to succeed in your plan, you need a firm handle on exactly why you are leaving and why you will be happier in a different stats PhD program. Then whatever those reasons are, you need to figure out how to make them sensible and palatable to the faculty in your program who will write your letters so that they can support your move. This means handling your withdrawal this semester and managing those relationships very, very carefully. You just aren't going to have great recommendations if they don't think you left for a good reason or know what you want.

Also, what are you doing in the year in between leaving and enrolling somewhere else? Is it going to be that much better for you than completing your second year in your current program?

Here's my contrarian vote for the advanced linear algebra course, assuming that's the theoretical and proof-based version of the more mechanical lower-level course. Special matrix decompositions (SVD, QR), eigenvalues and eigenvectors, orthogonality, changing bases, projections, block matrix properties, etc. are sooooo important and useful in statistics. I did well in the lower-level linear algebra class but didn't feel like I really understood a lot of this until I took the proof-based upper-level version.

I'm coming from a different field, but I think you should also be prepared for the possibilities that you will get nothing waived. I came to a US Planetary Science PhD program with a Masters in Astronomy from Canada and my current program does not waive any requirements if you have a Masters from anywhere. If your classes from your Masters overlapped with the required classes in your PhD, you will get to waive those requirements, however you will have to replace them with higher level elective courses.
 
Policies vary a lot from school to school though. Another school said they would waive the "minor" requirement for people with Masters, which is the equivalent of reducing your courseload by 80% of one semester. Another school said they evaluate this on a case-by-case basis. So it might be true that Biostats has uniform policies across all programs, but it's more likely that you will see varying policies at different schools. So, you should be prepared for the possibility of not having anything from your Masters (except for what you gained in experience) count towards a PhD.

This part is really important. You can leave your current department for whatever reason you like, but then you're going to have to make the case in applying to other programs why it'll be different there. I think it's a big problem if you can't articulate why some other institution is the place for you while your current one isn't, both from an admissions perspective and from a, like, just being satisfied with your life choices perspective. If the problem is that a PhD in general isn't right for you and not specifically that the department isn't right for you, then you're still going to be unhappy elsewhere. I have a few friends who left their original programs and went to different PhDs, but all involved a change in research focus that made their previous program not suitable.
 
And no, I don't think hiding that you were a PhD student in that previous program is prudent, or even necessarily doable. It's likely that at least one of your recommendation letters will say "I had m.cyrax in my X course while he was still a PhD student here in the Y Department of Statistics". Frankly, a letter that didn't mention this fundamental fact would have to lack context in other ways so as to be not a very good letter, I think. There's also probably going to be a Google breadcrumb trail indicating you were a PhD student there, and if you're a serious candidate for admissions somewhere, there's a decent chance you will get Googled.

If your goal is to prepare for PhD applications, in a choice between thesis vs. non-thesis programs, I personally would choose the thesis option. I assume your thesis is supervised by faculty in the Chicago statistics department. If so, that means you'll have at least one person who knows your research interests and capabilities pretty well who could write a specific and strong letter of recommendation (assuming you actually are good). Doing well in your coursework is going to be more or less expected, so I think good performance in a research-oriented theoretical statistics program will be more informative about your potential for PhD work than good performance in a coursework-only more applied biostatistics master's.
 
Also, cost of living in Chicago is much less than in Cambridge/Boston, which is something to consider since that will add to the cost of your degree. There are few cities in the country that match Boston in terms of hellishness and stress in finding (even barely affordable) housing in commuting distance of HSPH.

I am not knowledgable about these specific departments, but I'd like to say things about some issues you raised.

Funding: sounds like the differences in funding packages are not a concern here. If you have a livable stipend and the work it requires is not unduly burdensome according to current students, consider that good enough.

Professors who have no students: ask current students what the deal is. If it's just the case that what they work on happens not to mesh with the interests of current students, fine. But every department has its a-holes, and it's good to find out who they are before you decide. If this person is an intolerable a-hole, you should look for other options.

Professors with many students: talk to several of their current students and ask how independent the students' working styles are, how often they have one-on-one meetings, email responsiveness, group meetings and how useful those are, can they get attention when they face roadblocks or deadlines, how progress is monitored, if postdocs or advanced students of the same advisor competently guide newer students, etc. A huge number of advisees might not be a problem if the professor has stellar supervisory and organizational skills. I would worry if advisees suggest they often feel out to sea, abused and overworked, pressured into specific research directions they aren't interested in, or if favorites are treated well while everyone else is neglected.

Paraphrasing advice a friend (surely lurking, hi!) shared with prospectives recently: at some point academic differences between programs are too minor to matter in the grand scheme of things. You are considering departments that have similar reputations, adequate funding, (hopefully) multiple viable potential advisors, diverse research areas when you change your mind, and outcomes you are content with. I think quality-of-life considerations are the deciding factor. Anywhere you go, you will face research setbacks, career anxiety, existential crises, deadline pileups, advisor disagreements, and personal problems at inconvenient times. When those things inevitably happen, you want to have a supportive community of students to commiserate with. (Could happen in a tight-knit program, or could happen in a big program with enough like-minded people.) You should feel able to get mentoring from faculty besides your advisor and not be in a fractious political environment preventing this. You need a place where you can have some degree of work-life balance to preserve your physical and mental health.

Good luck with your eventual choice!

I am not knowledgable about these specific departments, but I'd like to say things about some issues you raised.

Funding: sounds like the differences in funding packages are not a concern here. If you have a livable stipend and the work it requires is not unduly burdensome according to current students, consider that good enough.

Professors who have no students: ask current students what the deal is. If it's just the case that what they work on happens not to mesh with the interests of current students, fine. But every department has its a-holes, and it's good to find out who they are before you decide. If this person is an intolerable a-hole, you should look for other options.

Professors with many students: talk to several of their current students and ask how independent the students' working styles are, how often they have one-on-one meetings, email responsiveness, group meetings and how useful those are, can they get attention when they face roadblocks or deadlines, how progress is monitored, if postdocs or advanced students of the same advisor competently guide newer students, etc. A huge number of advisees might not be a problem if the professor has stellar supervisory and organizational skills. I would worry if advisees suggest they often feel out to sea, abused and overworked, pressured into specific research directions they aren't interested in, or if favorites are treated well while everyone else is neglected.

Paraphrasing advice a friend (surely lurking, hi!) shared with prospectives recently: at some point academic differences between programs are too minor to matter in the grand scheme of things. You are considering departments that have similar reputations, adequate funding, (hopefully) multiple viable potential advisors, diverse research areas when you change your mind, and outcomes you are content with. I think quality-of-life considerations are the deciding factor. Anywhere you go, you will face research setbacks, career anxiety, existential crises, deadline pileups, advisor disagreements, and personal problems at inconvenient times. When those things inevitably happen, you want to have a supportive community of students to commiserate with. (Could happen in a tight-knit program, or could happen in a big program with enough like-minded people.) You should feel able to get mentoring from faculty besides your advisor and not be in a fractious political environment preventing this. You need a place where you can have some degree of work-life balance to preserve your physical and mental health.

Good luck with your eventual choice!

Yes, very similar email to the one you got. I contacted them about it mid-last week.
 
I also have the say, I think the tone of the original post is a little off-putting. You've gotten into a set of schools that most people would kill to have even a shot at, yet you're expressing frustration about getting waitlisted at a school that you admittedly wouldn't even consider. It's good advice for others to check their applications at CMU if they had the same issue, but some of the other stuff seems a little insensitive.

Just go up to the professors and say, "Since we're all going to die, it's obvious that when and how don't matter.” 

Crime isn't necessarily the main reason to avoid the U District (although the frequent UW alert emails about muggings are not comforting). The U District kind of sucks because not only do you pay a premium for proximity to the UW for units that are often not kept in great condition, but there isn't actually that much to do. If living near fun things matters to you, I would advise against the U District.
 
The Ave on a Friday or Saturday night is surprisingly pretty dead. A couple of places have good beer and decent food (Shultzy's, Big Time), but most of the bars on the Ave are just college bros drinking cheap pitchers of Bud Light, not even divey in a good way. You have to get outside of the U District to Wallingford or Roosevelt to find bars that have more of a neighborhood feel. Very limited places offering outdoor seating for the 5 months out of the year when we have nice weather. No good for cocktails or wine. Certainly a lot of cheap eats, but you get sick of the basic Thai, Vietnamese, teriyaki, or gyros offerings, especially when you have these for both lunch and dinner because you're a busy grad student and that's all that is convenient for you to pick up. For other kinds of food, brunch on the weekends, or really anything even the tiniest bit more upscale, you need to leave the U District. Far too many frozen yogurt and boba places. The concert venues are almost all in Capitol Hill or Ballard, you won't see much live music in the U District and will have to bus/bike. The nearest parks are still outside the U District proper (Cowen/Ravenna to the north, Green Lake to the north west). The main "fun" advantages the U District has over some other places to live are coffeeshops (still not amazing compared with Capitol Hill/Ballard/Fremont, but Trabant and Cafe Allegro are good to work in, Herkimer if you go to the far north end) and the movie theaters (Sundance, Grand Illusion, Varsity, a couple others whose names I don't remember).

If you are offered funding, take it. That either means they think you are one of the strongest incoming students, or it's a small program and you're going to have the opportunity to work closely with faculty (e.g. as a research assistant or on a master's thesis). In either case you are being set up to get good advising and have nice references for employment or for a PhD down the road.
 
Remember that rankings of departments are based on their faculty and PhD programs, which won't necessarily mean you get a good master's experience. As a rule of thumb, the larger the program, the more you're competing with other students for attention. Being one of the top students in your classes is the main way you distinguish yourself in a non-thesis MS program, and that's easier said than done in a big program with many other smart and hard-working people. For PhD applications, it matters that you get faculty enthusiastically on your side. To do that, I would guess that you're better off being one of the top couple of students in a smaller less-known master's program than being outside of the top few students in a large master's program that just happens to be linked to a highly ranked PhD. (The exception would be if that program happens to recruit a lot of its PhD students out of its master's cohorts.)
 
For jobs, this doesn't really matter, because employers mostly care about whether you have the experience they are looking for and come off as quick-learning and competent. I'd pick the program primarily based on the geographic area you want to be in and what kinds of jobs its graduates get, maybe with debt as a tie-breaker. A fancy name will open more doors nationally, but a regional job search is logistically much easier. For local job hunting, the added value of the fancy name is smaller since there is more of an awareness of the non-fancy programs nearby.

Hi All, 
 
I've seen some really nice scripts that scrape the Grad Cafe, but none had all the features I wanted. 
 
I wrote some of my own functions and put them into an R package called brewdata. If you're also interested in using R to parse Results Search data, then you can find brewdata on CRAN ( http://cran.r-project.org/web/packages/brewdata/). 
 
Please email or PM me with any suggestions or bugs you find. I'd welcome the chance to work with anyone interested in making their own improvements.
 
Thanks!
NW

It's not as if the only piece of information admissions committees will have available to them is a list of your publications. You can (and probably should) talk specifically about your research experiences in your statement of purpose. I would also hope that any letter writers with whom you've worked would convey details about your contributions to their projects. People making decisions don't need to infer the extent of your involvement solely based on authorship order.

You apparently go to UMN. UMN's biostat PhD program is one of the better ones, so let's take a look at exactly which math courses their program requires its students to take since they know the material and level of rigor. Their curriculum page says that incoming students without a master's degree in statistics or biostatistics need to take Math 5615H or Math 4603 their first semester.
Math 5615H: Honors: Introduction to Analysis I 4.0 cr; Prereq-[[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574; fall, every year. Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. Math 4603: Advanced Calculus I 4.0 cr; Prereq-[2243 or 2373], [2263 or 2374] or 2574 or # ; fall, spring, summer every year. Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions From this it is clear that the math UMN biostat needs its students to acquire during the PhD program is advanced calculus, not real analysis. In terms of applying, coming in with advanced calculus already completed ought to be good enough.

You don't need 40 hours per week (perhaps not even 40 hours total) and you don't need to spend any money thanks to all the internet resources out there. I had not taken calculus in about 10 years when I started my program and did not review anything before starting, which made for a rough adjustment back to school. Here's a pretty exhaustive list of the high school/early college math I used in master's-level theory and methods coursework:
Common differentiation rules (power, product, quotient, chain) Partial derivatives Univariate integration techniques: primarily integration by parts, u-substitution (I don't think I've ever needed trig substitution, actually just stay away from trig functions altogether). 90% of the integrals you evaluate will look like the definite integrals on my fave wikipedia page, if you can figure out how to do some of these then you're probably set. Infinite series representations, Taylor approximations L'Hopital's rule, general comfort evaluating limits, understanding of continuity and piecewise-defined functions From multivariate calculus: Jacobians and change of variables, inverse function theorem, iterated integrals and multiple integrals. You do not need to review line integrals, Green's theorem, all that physics-y vector field stuff. Linear algebra: vectors and matrices in general, multiplication, lengths/norms of vectors, orthonormal bases and rotations, matrix representation of linear transformations, projections, geometric interpretations of determinants, what positive definiteness is and how to test for it, eigenvalues and eigenvectors, inverting 2x2 matrices by hand, general awareness of special matrix decompositions (Cholesky, spectral, singular value) Logarithm and exponentiation properties in general, representation of exp(x) as lim n-> infty (1+x/n)^n Software: Mathematica is useful for checking your work, or just get good at using Wolfram Alpha if your school won't have a Mathematica student license. Knowing enough R to do simple simulations to check answers non-analytically is good too (e.g. how to generate a bunch of realizations from an exponential distribution and transform them, plot them against whatever distribution you're claiming they have)

You don't need 40 hours per week (perhaps not even 40 hours total) and you don't need to spend any money thanks to all the internet resources out there. I had not taken calculus in about 10 years when I started my program and did not review anything before starting, which made for a rough adjustment back to school. Here's a pretty exhaustive list of the high school/early college math I used in master's-level theory and methods coursework:
Common differentiation rules (power, product, quotient, chain) Partial derivatives Univariate integration techniques: primarily integration by parts, u-substitution (I don't think I've ever needed trig substitution, actually just stay away from trig functions altogether). 90% of the integrals you evaluate will look like the definite integrals on my fave wikipedia page, if you can figure out how to do some of these then you're probably set. Infinite series representations, Taylor approximations L'Hopital's rule, general comfort evaluating limits, understanding of continuity and piecewise-defined functions From multivariate calculus: Jacobians and change of variables, inverse function theorem, iterated integrals and multiple integrals. You do not need to review line integrals, Green's theorem, all that physics-y vector field stuff. Linear algebra: vectors and matrices in general, multiplication, lengths/norms of vectors, orthonormal bases and rotations, matrix representation of linear transformations, projections, geometric interpretations of determinants, what positive definiteness is and how to test for it, eigenvalues and eigenvectors, inverting 2x2 matrices by hand, general awareness of special matrix decompositions (Cholesky, spectral, singular value) Logarithm and exponentiation properties in general, representation of exp(x) as lim n-> infty (1+x/n)^n Software: Mathematica is useful for checking your work, or just get good at using Wolfram Alpha if your school won't have a Mathematica student license. Knowing enough R to do simple simulations to check answers non-analytically is good too (e.g. how to generate a bunch of realizations from an exponential distribution and transform them, plot them against whatever distribution you're claiming they have)