5 ms·

If we take this to the extreme, should they have to study real analysis so they understand where calculus comes from as well, or would you prefer we start at se

If we take this to the extreme, should they have to study real analysis so they understand where calculus comes from as well, or would you prefer we start at set theory? Maybe we should delve into philosophy to understand the basis of mathematics so we can truly understand our statistics. The point is that you have to pick a cut-off somewhere as your foundation to build upon. I doubt much understanding of calculus is required for the vast majority of statistical inference, but I'm certainly no expert.

elashri 4y ago
You don't need to understand where is calculus come from to tqke real analysis. Hell most academics who use calculus everyday did not study real analysis and they are fine. This extreme angle is not relevant. The difference is that you can't fot example understand physics without calculus but you can understand and study calculus without real analysis.
- Tainnor 4y ago
  > Hell most academics who use calculus everyday did not study real analysis and they are fine. That's an American perspective, I believe. In many European countries, many STEM students routinely learn real analysis. In fact, the term "calculus" doesn't even exist in e.g. German, it's all called "Analysis". Sure, a course tailored for physicists, chemists or computer scientists may (or may not, depending on the institutions) have a different focus, may emphasise proofs less etc., but the underlying concepts (what are the real numbers, completeness) are generally taught.
  - imtringued 4y ago
    I'my always confused by Americans and their calculus because I really don't understand the essence of what difference there is between real analysis and calculus. The internet answer of "calculus is real analysis for engineers" doesn't help because you can have real analysis tailored for computer scientists and it is still real analysis.
    - Tainnor 4y ago
      As far as I understand, calculus = analysis without proofs - or at least without rigorous proofs. You might do some hand-waving and elementary transformations, but you're probably not gonna invoke the Least Upper Bound axiom of the real numbers.
- spookie 4y ago
  I've a bachelor's in CS, and I've learned real analysis. As someone pointed out, maybe being in an European university led to it. And it's probably, the most useful course I've taken. If you're going to perform a bunch of floating point ops, I hope you've taken real analysis. They're enough of a Russian roulette to begin with, let's make sure you aren't making my day worse hunting down for some weird ass rounding error.
  - zozbot234 4y ago
    If you're going to perform a bunch of floating point ops and are not using interval arithmetic to precisely bound the result (and perhaps constructive real arithmetic, if you want guarantees of tight-enough bounds), you'll need a numerical analysis class as well. Real analysis will teach you about the theory of how real numbers are defined, but computation and the need for approximate results throughout bring challenges of their own.
    - spookie 4y ago
      Very much true. Have taken it as well. My train of thought was more along continuity and such, since I'm mostly working on CG right now. But I guess Numerical Analysis has even greater value in the context I provided above.
    - flopriore 4y ago
      Definitely yes, actually I'm studying computer engineering in Italy (still bachelor degree) and it's mandatory to have the exams of Mathematical Analysis I and II and also the exam of Numerical Analysis, where they teach you floating point numbers, Lagrange interpolation, Gauss method, non-linear equations and quadrature formulas.

elashri 4y ago

You don't need to understand where is calculus come from to tqke real analysis. Hell most academics who use calculus everyday did not study real analysis and they are fine. This extreme angle is not relevant. The difference is that you can't fot example understand physics without calculus but you can understand and study calculus without real analysis.

Tainnor 4y ago
> Hell most academics who use calculus everyday did not study real analysis and they are fine. That's an American perspective, I believe. In many European countries, many STEM students routinely learn real analysis. In fact, the term "calculus" doesn't even exist in e.g. German, it's all called "Analysis". Sure, a course tailored for physicists, chemists or computer scientists may (or may not, depending on the institutions) have a different focus, may emphasise proofs less etc., but the underlying concepts (what are the real numbers, completeness) are generally taught.
- imtringued 4y ago
  I'my always confused by Americans and their calculus because I really don't understand the essence of what difference there is between real analysis and calculus. The internet answer of "calculus is real analysis for engineers" doesn't help because you can have real analysis tailored for computer scientists and it is still real analysis.
  - Tainnor 4y ago
    As far as I understand, calculus = analysis without proofs - or at least without rigorous proofs. You might do some hand-waving and elementary transformations, but you're probably not gonna invoke the Least Upper Bound axiom of the real numbers.
spookie 4y ago
I've a bachelor's in CS, and I've learned real analysis. As someone pointed out, maybe being in an European university led to it. And it's probably, the most useful course I've taken. If you're going to perform a bunch of floating point ops, I hope you've taken real analysis. They're enough of a Russian roulette to begin with, let's make sure you aren't making my day worse hunting down for some weird ass rounding error.
- zozbot234 4y ago
  If you're going to perform a bunch of floating point ops and are not using interval arithmetic to precisely bound the result (and perhaps constructive real arithmetic, if you want guarantees of tight-enough bounds), you'll need a numerical analysis class as well. Real analysis will teach you about the theory of how real numbers are defined, but computation and the need for approximate results throughout bring challenges of their own.
  - spookie 4y ago
    Very much true. Have taken it as well. My train of thought was more along continuity and such, since I'm mostly working on CG right now. But I guess Numerical Analysis has even greater value in the context I provided above.
  - flopriore 4y ago
    Definitely yes, actually I'm studying computer engineering in Italy (still bachelor degree) and it's mandatory to have the exams of Mathematical Analysis I and II and also the exam of Numerical Analysis, where they teach you floating point numbers, Lagrange interpolation, Gauss method, non-linear equations and quadrature formulas.