EpiMath

Also from Stanford, from longer ago... The Fourier Transform and its Applications by Bracewell. McGraw-Hill. Extremely well written with great examples and some fascinating problems. I highly recommend it. Discrete transforms are a bit of an afterthought in a final chapter, but enough to dig in and see how the FFT works.

If you are responding to my comment, I agree with you. I like the R language very much and use it. I may not have said what I meant well enough. What I mean is that there is a tendency with R programmers and much more so with SAS or Stata not to think about the guts of the program and what is really happening. The data frame in R is a nice framework for thinking and programming, but it does not promote thinking about whether i/o is to disk or memory, or whether iterations or loops or recursion is efficient, or overall program efficiency, reuse etc. Programmers tend to rely on the underlying system to worry about memory allocation disk i/o etc. There are many problems where these details matter. So much time is spent on the statistical problem and what procedure or function to call, rather than the algorithm at a deeper level. These details can be handled, but are not so "front and center". Matlab and others similarly. I have seen enterprise-class servers brought to their knees by a poorly written R program... ( you can say lots of things about how that should not be possible, or how that can happen with other languages, and I'd agree, but I still think it is more likely in a context that does not encourage programmers to think "closer to the metal" about where data is and what is happening to it. )

I've seen some great R code too... so this is a complicated topic and has to do with who is writing the code as much as R itself.

I've spent my career thinking about these same issues. And certainly Fisher was, well, abrasive to put it mildly. I've read much of his early work and I think the intended context has mostly been lost. Many modern statisticians ( of the "frequentist" persuasion ) use a strange and awkward combination of fisherian and neyman-pearson. We talk about "p-values" but then interpret them as hypothesis tests with long-term error probabilities ( Fisher disavowed this interpretation of p-values, and insisted they did not have a long run probabilistic interpretation but were a measure only of evidence against the null in the particular experiment. ) I think Fisher gets a bad rap for a lot of later bastardization of his work. ( I'm sure it did not help that he was not a likable person, or his valid but misguided and testimony about tobacco. )

Still, I'm sympathetic to your position and can understand how you'd come to that way of thinking. I'm not convinced even a diehard Bayesian would completely disagree with Fisher's more restricted and stringent interpretation of p-values. Or at least they would see it as a big step up from the more common usage you are referencing.

Interesting, thanks. ( Like your username too, despite him being slightly denigrated in the linked article. ) I personally think that it is good to have a basic grounding in some kind of fundamental "real" programming language before you get into s-plus ( R ) or any other more domain-specific language. The main reason being that you will better understand the compromises, limitations and shortcomings. I like R but as a programmer I've seen some awful code written in it!

I've just spent the last hour or so at this site ( found via reddit/math ) and it is pretty amazing. Well worth a look! Also the link at the end to mathics was new to me and looks interesting.

Epidemiologist here. Many studies account for it and we are acutely aware of this problem and have some sophisticated methods for dealing with unmeasured propensities. And randomized trial are "epidemiologic" studies too. Not everything in epidemiology is observational. Simpson's paradox is taught in 1st year intro to epi courses. There is also a lesser known "reverse-simpson" which comes from overgeneralizing specific results.