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Advice on preparation for math before the start of biostat phd?

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Hi everyone,

I am planning to start my biostat phd at one of the top 5 biostat programs this fall (let's say it's either UNC or Michigan). It is qutie exciting, but one of the concern I have is the intensity of theoretical coursework. I got an A for real analysis as an undergraduate but it was a while back, and it did take me some time and effort to get that A. I wouldn't say that I can remember more than half of what I learned, and that's indeed a bit concerning. Before the start of the program this fall, I am hoping to start early from now and through the summer to get familiar with some of the course content that will be covered during the first two years of the phd degree. I was wondering if anyone wouldn't mind pointing me to some textbooks or sources that I can look into? Should I also go over some texts in real analysis? Thanks in advance for anyone who offers suggestions.

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I'm doing the same for Statistics PhD programs. I can't recommend MIT open courseware enough for reviewing Real Analysis/learning more advanced probability theory. They have exercises, book chapters, and problem solutions. They even post exams with solutions so you can test yourself. It's really helpful with harder books like Rudin because they provide lecture notes where Rudin is lacking and points you to doable problems instead of the crazy impossible stuff. I'd also recommend reading/working through some more rigorous applied math books. Examples are like Linear Algebra by Friedberg, Insel, Spence and Applied Analysis by Hunter.

Edited by trynagetby
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The first-year courses at these programs shouldn't be too theoretical.  The really theoretical stuff will be more in the second year.

For calculus, I'd make sure to know how to do basic integrals and differentiation, such as with exponential and log functions, basic multivariable stuff, and integration by parts.

For linear algebra, the basics will be fine -- personally I'd watch the 3Blue1Brown videos because they're awesome.

For probability, Harvard's Statistics 110 course is great, freely available online, and only slightly less advanced than a Casella-Berger class in my opinion.

For analysis, you probably won't need much in the first year - basic notions of convergence and uniform convergence, how to do epsilon-delta proofs.  An easier analysis book like Abbot would be fine.

I'm not sure if those programs use R or SAS, but learning the basics of programming if you don't know them will also save you lots of time.

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  • 3 weeks later...

On a somewhat unrelated note, spend some time learning R, Python, SAS, Julia or whatever the dominant language is in your department (probably R) - it will make life a lot easier. If you're burned out from studying theory, mess around with programming. Watch vids, do tutorials, make your own package from scratch.

My first semester applied class assignments took probably 2x as long because I had to learn new concepts and also had to mess around with implementing it in R. Our undergrad only used SAS so it was a rough few months transitioning to R. I really regret not spending a few weeks over the summer to get a head start when I had a ton of free time.

Edited by statsguy
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4 hours ago, csheehan10 said:

@statsguy lol what sadist made you use SAS for all of undergrad, that's just cruel.

This was circa 2006, at a "teaching" undergraduate school where 2 (maybe 3) of the professors were from NC SAState. Times have since changed, fortunately.

Edit: adding that when I was a PhD student, I took a Biostat elective that used SAS (although the instructor allowed R). And this was a very-high ranked Biostat department around 2011 ish? It's not totally unreasonable, as SAS is still widely-used in industry even to this day, which is where a good chunk of Biostat PhDs end up going. And at least at the time, SAS did some things better (e.g. anything involving mixed models) than the two major R options at the time (lme4, nlme).

Pretty sure it took me nearly a full day just to acquire and install SAS. 

Edited by statsguy
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Michigan's department doesn't have as much theoretical training, so I think it's less of a concern.

UNC offers a "math boot camp" for incoming 2nd year students that reviews linear algebra and analysis. If you've seen some stuff before, I think it's more than sufficient. IMO, the most important topics in real analysis for biostats are (in [approximately] increasing order of importance):

  1. Limits (epsilon-delta proofs, finding limit, showing limit exists)
  2. Sequences (boundedness, convergence, uniform convergence, Bolzano-Weierstrass, Cauchy sequences)
  3. Infinite series (showing a series converges / is finite, Cauchy criterion, absolute convergence)
  4. Continuity
  5. Integration (Riemann, Darboux, Riemann-Stieltjes)


In general, real analysis is really about putting bounds on stuff. So if you can do that, you're in pretty good shape.

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