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Jun
22
comment How to study math to really understand it and have a healthy lifestyle with free time?
Here I mean casually that nobody "is close to" the boundary. If you're good enough at math such that accomplishing very difficult career mathematics doesn't significantly prevent you from having a good work/life balance, then your math skill is much, much higher than even an average math Ph.D. graduate from top universities. On the other hand, if you don't have math prowess that extreme, but you still doggedly work as hard as necessary to do advanced math for a career, then you almost surely do not have good work/life balance. Of course there can be exceptions; I claim they are highly rare.
Jun
3
comment How to study math to really understand it and have a healthy lifestyle with free time?
When you combine this with articles like The Economist's "The Disposable Academic" and you look at statistics about the rate of growth of adjunct staff who are expected to take over the bulk of teaching duties, while being paid far less, given less comprehensive benefits packages, and almost zero opportunity for career advancement, I do indeed think it's very unwise to pursue academia for the sake of getting into university-level teaching. It's almost like a lottery. Maybe 1/1000 of the top PhD grads goes on to have a fulfilling teaching career. The rest publish or perish & go to industry.
Jun
3
comment How to study math to really understand it and have a healthy lifestyle with free time?
@JesseMadnick When I was a grad student, I was actively discouraged from teaching. When I spent extra time preparing recitation notes and interactive examples for a probability course for which I was service as teaching assistant, my advisor actually took me aside and admonished me for not spending more time on research. It was the same story I heard from my peers, and from my many contacts and friends in academia at other universities and in many different disciplines (not just math or science).
May
14
awarded  Nice Answer
Apr
8
revised Expected Value of Flips Until HT Consecutively
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Apr
8
revised Expected Value of Flips Until HT Consecutively
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Mar
18
comment How to study math to really understand it and have a healthy lifestyle with free time?
@user21820 But if that's the standard we want to use, then the same is true for mathematics or statistics as well. Most of that work takes place in companies, defense labs, and R&D consulting firms who are notorious for only going after low-risk demo-ware. As a machine learning professional, I've seen this both with software and with formal math time and again, especially in mathematical finance. Why try fancier learning algorithms if simple OLS will get something (crappy) out the door right now? So if that is the criticism, then it applies just as well to math too.
Mar
14
awarded  Yearling
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
@JohnDonn Yeah, that's too bad. Once you do have enough points you should click on my user name to see other questions that I have answered and down vote those too, much as you seem to have followed me from the question about whether software abstraction is "mathematical" to this. If you follow me and downvote more, I may have to report it to a moderator. On this question though, I welcome a downvote. After reading your comment, which is correct, I still don't believe it applies at all to my answer or the original question. When you can, you should signal your disagreement with a down vote.
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
Well then it depends on what you mean. If you mean that because Brownian motion is continuous w.p. 1, and can derive a technical definition of the random-variable-valued "thing" that "is equal" to its "integral" ... then sure, that pedantic definition satisfies. That's clearly a very different thing than what the question is asking about, which is for examples where an attempt to do a naive Riemann integration leads to an unusual outcome that doesn't have the same properties of a conventional integral. Brownian motion certainly counts for that: what's the derivative of the integral of B_t?
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
Which type of integrability are you talking about? Riemann? Lebesgue? Lebesgue-Stieltjes? Ito? Stratanovich? Henstock-Kurzweil? ... be specific.
Feb
21
comment How to study math to really understand it and have a healthy lifestyle with free time?
@JohnDonn You've clearly never done software engineering. One of the core concepts in all of software engineering is to create abstractions that explicitly prevent manual implementation. Even apart from that, you've got things like functional programming with e.g. Haskell, which is essentially a manifestation of category theory and how to solve practical problems with it.
Dec
24
comment Easy example why complex numbers are cool
What definition of "cool" are we using here?
Dec
19
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Dec
19
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Oct
23
awarded  Quorum
Sep
26
answered Expected Value of Flips Until HT Consecutively
Sep
24
awarded  Autobiographer
Mar
14
awarded  Yearling
Jan
27
revised Examples of non-Riemann integrable functions that appear “in nature”?
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