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I would add statistics to this list. Science and pretty much all the numbers quoted out there are based on statistics.

jacobolus 11y ago
It’s impossible to reasonably understand statistics without studying calculus. Everyone I’ve talked to who took a statistics course without first studying calculus had an overly formulaic, theoretically wishy-washy, and often wrong understanding of the meaning of basic statistical distributions and techniques.
- grayclhn 11y ago
  Um... I feel like there is likely to be a lot of selection bias in your experience. Now, I would notice that, having taken calculus before statistics myself, but...
- thaumasiotes 11y ago
  The introductory economics courses at my school didn't require calculus. This would have been less annoying if every single topic hadn't been explicitly introduced as finding the slope of, or area under, particular curves.
  - TeMPOraL 11y ago
    Those who don't learn calculus have to reinvent it, poorly. C.f. so-called "AUC" [0], which is apparently an important metric in medicine. [0] - https://en.wikipedia.org/wiki/Area_under_the_curve_%28pharmacokinetics%29 https://en.wikipedia.org/wiki/Area_under_the_curve_%28pharma...
    - stdbrouw 11y ago
      What exactly bugs you about AUC? What about ROC curves?
- stdbrouw 11y ago
  Not necessary at all. You can teach most of the interesting parts of statistics with just the binomial distribution and numerical techniques like bootstrapping. Nothing about that is wishy-washy, it's just a modified curriculum that sidesteps some interesting things that require calculus but in return allows you to focus on some other really interesting things that don't require it. There is, for example, nothing rigorous about being able to prove and use the Central Limit Theorem – the whole point of the thing is that it's an approximation and not always a very good one at that. And this is the origin of many statistical techniques and tests: computational shortcuts. The fact that these shortcuts require a good understanding of math doesn't suddenly make them any more central to a conceptual understanding of statistics than they are. Two good examples of good stats intros that are light on the math: Allen Downey's Think Stats http://greenteapress.com/thinkstats2/ http://greenteapress.com/thinkstats2/ or the more traditional/frequentist http://onlinestatbook.com/ http://onlinestatbook.com/.

It’s impossible to reasonably understand statistics without studying calculus. Everyone I’ve talked to who took a statistics course without first studying calculus had an overly formulaic, theoretically wishy-washy, and often wrong understanding of the meaning of basic statistical distributions and techniques.

grayclhn 11y ago
Um... I feel like there is likely to be a lot of selection bias in your experience. Now, I would notice that, having taken calculus before statistics myself, but...
thaumasiotes 11y ago
The introductory economics courses at my school didn't require calculus. This would have been less annoying if every single topic hadn't been explicitly introduced as finding the slope of, or area under, particular curves.
- TeMPOraL 11y ago
  Those who don't learn calculus have to reinvent it, poorly. C.f. so-called "AUC" [0], which is apparently an important metric in medicine. [0] - https://en.wikipedia.org/wiki/Area_under_the_curve_%28pharmacokinetics%29 https://en.wikipedia.org/wiki/Area_under_the_curve_%28pharma...
  - stdbrouw 11y ago
    What exactly bugs you about AUC? What about ROC curves?
stdbrouw 11y ago
Not necessary at all. You can teach most of the interesting parts of statistics with just the binomial distribution and numerical techniques like bootstrapping. Nothing about that is wishy-washy, it's just a modified curriculum that sidesteps some interesting things that require calculus but in return allows you to focus on some other really interesting things that don't require it. There is, for example, nothing rigorous about being able to prove and use the Central Limit Theorem – the whole point of the thing is that it's an approximation and not always a very good one at that. And this is the origin of many statistical techniques and tests: computational shortcuts. The fact that these shortcuts require a good understanding of math doesn't suddenly make them any more central to a conceptual understanding of statistics than they are. Two good examples of good stats intros that are light on the math: Allen Downey's Think Stats http://greenteapress.com/thinkstats2/ http://greenteapress.com/thinkstats2/ or the more traditional/frequentist http://onlinestatbook.com/ http://onlinestatbook.com/.