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I expected to see something about probability and statistics but they're hidden with dozens of other topics in the electives > Any and every topic imaginable. A

by Zababa 4y ago

I expected to see something about probability and statistics but they're hidden with dozens of other topics in the electives > Any and every topic imaginable. Are probability and statistics not part of a regular mathematics curriculum?

anonymoushn 4y ago
I ended up with a math degree without taking any of these classes.
hither_shores 4y ago
No, they're fairly niche topics as far as the rest of mathematics is concerned. You'll see much more emphasis on them, and especially on statistics, in an applied math curriculum.
latency-guy 4y ago
In this matter, my opinion of statistics is that it does not really teach 'math', it teaches how to use 'math' to derive information. Pretty much applied math. I see this question as 'Why does math students not take Thermal Mechanics' or 'Why does math students not take Nuclear Methods'. The answer is just that, they do not teach math, they teach an application of math. Your math knowledge has not really grown.
- Tainnor 4y ago
  That's quite close to saying that applied maths is not maths, which many people would disagree with. If you have definitions, theorems, proofs, I'd say that's maths, and you definitely have that in a sufficiently rigorous statistics course. Of course, then there's the fact that statistics builds upon probability theory, and probability theory is, in a sense, a subfield of measure theory which in turn is about as mathematical as it gets (in the discrete setting, it also includes a fair amount of combinatorics).
- mindcrime 4y ago
  Pretty much applied math. Well... yeah. I mean, I might be wrong, but my default assumption is that when people on HN ask about learning math, unless they explicitly say otherwise, they are mainly interested in maths from an applied viewpoint. That is to say, I think most such inquiries are rooted in a basis of "I want to learn the math require to DO 'x'" where x might be "machine learning" or "circuit analysis" or whatever, as opposed to "I want to become a mathematician and advance the overall state of mathematics as a field." I say that at least in part because of an assumption that people who want to become mathematicians per-se are probably asking their questions on Mathoverflow or whatever, and not HN. EDIT: to be fair the specific sub-thread we're in here does contain this, which I guess justifies taking a "pure mathematics" position in this part of the overall discussion. Are probability and statistics not part of a regular mathematics curriculum? Still though, this seems to be a general issue with any maths related discussion on HN. It seems like a lot of people are commenting from a position of assuming that the initial question was based on an interest in pure / theoretical maths and the "I want to become a mathematician" idea. And I am somewhat skeptical that that is normally what's intended by the person asking the initial question.
Tainnor 4y ago
It will depend on the university. Where I studied, an introductory class to probability and statistics was mandatory, as was measure theory where probability theory was at least hinted at. Other universities may have even stronger probability theory requirements, or none at all. But it's certainly not an uncommon specialisation. Note that probability theory is not necessarily the same thing as statistics. While the latter builds upon the former, statistics is more about "given the data, what's the most likely distribution ", as opposed to "given the distribution, what's the data gonna look like" (probability theory). For mathematicians, the latter seems to be more relevant, as it's a more deductive form of reasoning.

by Zababa 4y ago

anonymoushn 4y ago

I ended up with a math degree without taking any of these classes.

hither_shores 4y ago

No, they're fairly niche topics as far as the rest of mathematics is concerned. You'll see much more emphasis on them, and especially on statistics, in an applied math curriculum.

latency-guy 4y ago

In this matter, my opinion of statistics is that it does not really teach 'math', it teaches how to use 'math' to derive information. Pretty much applied math. I see this question as 'Why does math students not take Thermal Mechanics' or 'Why does math students not take Nuclear Methods'. The answer is just that, they do not teach math, they teach an application of math. Your math knowledge has not really grown.

Tainnor 4y ago
That's quite close to saying that applied maths is not maths, which many people would disagree with. If you have definitions, theorems, proofs, I'd say that's maths, and you definitely have that in a sufficiently rigorous statistics course. Of course, then there's the fact that statistics builds upon probability theory, and probability theory is, in a sense, a subfield of measure theory which in turn is about as mathematical as it gets (in the discrete setting, it also includes a fair amount of combinatorics).
mindcrime 4y ago
Pretty much applied math. Well... yeah. I mean, I might be wrong, but my default assumption is that when people on HN ask about learning math, unless they explicitly say otherwise, they are mainly interested in maths from an applied viewpoint. That is to say, I think most such inquiries are rooted in a basis of "I want to learn the math require to DO 'x'" where x might be "machine learning" or "circuit analysis" or whatever, as opposed to "I want to become a mathematician and advance the overall state of mathematics as a field." I say that at least in part because of an assumption that people who want to become mathematicians per-se are probably asking their questions on Mathoverflow or whatever, and not HN. EDIT: to be fair the specific sub-thread we're in here does contain this, which I guess justifies taking a "pure mathematics" position in this part of the overall discussion. Are probability and statistics not part of a regular mathematics curriculum? Still though, this seems to be a general issue with any maths related discussion on HN. It seems like a lot of people are commenting from a position of assuming that the initial question was based on an interest in pure / theoretical maths and the "I want to become a mathematician" idea. And I am somewhat skeptical that that is normally what's intended by the person asking the initial question.

Tainnor 4y ago

It will depend on the university. Where I studied, an introductory class to probability and statistics was mandatory, as was measure theory where probability theory was at least hinted at. Other universities may have even stronger probability theory requirements, or none at all. But it's certainly not an uncommon specialisation. Note that probability theory is not necessarily the same thing as statistics. While the latter builds upon the former, statistics is more about "given the data, what's the most likely distribution ", as opposed to "given the distribution, what's the data gonna look like" (probability theory). For mathematicians, the latter seems to be more relevant, as it's a more deductive form of reasoning.