(These days if I ask a question at school my instructor is of the opinion that delivering the answer is the best course of action, as opposed to gentle nudges in the right direction)
In a side note, we had some friends over the other day, they saw my maths books out on the coffe table and we had a conversation about nevber having used algebra since school
and while I have done plenty of algebra since school, it's been aeons since I have actually had to apply any of my calculus :(
Yeah, pre pandemic, I thought, hey how hard can learning stats proper be, I dug up an MIT OCW for stats, looked at the first few problesm and realised I was way outta my depth
lol, like I see the issue with getting your homework answers spoon fed to you
that prevents you doing the work and develoiong the understandings, but if you arent beeing spoon fed, and talking around a problem, that winds up being the sort of behaviour you want students to engage in, right?
i would defer to people with more experience in professoring. i had some unfortunate experiences, it was always a race to the answer. my colleagues told me that it used to be different. but it wasn't different for me
many of my students were uninterested in anything other than the numerical answer to the question.
not all. i am still in correspondence with some of them.
one of them babysat my daughter about a year and a half ago. our parents had known each other prior to the whole academia thing. we knew each other without knowing it.
I mean, there is a larger issue around the problem of education system being largly a certification excercise and seen by the majority of students to be a means of improving their job prospects, hence understanding being less important than passing exams
but that is a BIG issue, that really is a doozy to try and resolve
i think you have adequately identified the problem. and also why many feel left out of this system (= people who do not have four-year degrees, including several members of my family who do not have time for other debates).
it is a divisive issue.
my mother did not go to college. she has more sense than a lot of people. but in the US at least going to college involves a significant investment of money. if this money is not available, people become upset. they rightfully recognize that they are being shut out of something.
i have no answers.
her sisters went to college. she was very conscious of the fact that the money was there for her sisters but not for herself. i really don't understand why education is expensive. the providers of education are not overpaid.
there's all of this infrastructure on top of university instruction. it seems to become more and more expensive, without limit.
Yeah, but now we are straying a little too far from the scope I had intended (though into a larger and really interesting issue). I was more thinking about how my uni experience might have panned out if I had of been an avid user of this site. On the one hand I probably would have improved my grades, handing in fewer assignments with silly errors.
education isn't unrealisticly priced globally though
i am generally in favor of students using all resources. i copied a lot from textbooks. but i understood what i was turning in. that's the hard part to test.
my wife is an academic and sometimes in the position of encouraging people to go to graduate school, when it is a near certainty that they will not financially benefit. she is conflicted about this role. i suggested that she abandon it.
And at least in Germany ( the one other example I know about because my partner finds the Australian system so backwards) university is more or less free (there are trivial admin costs)
Yeah, I had a friend who used to work in uni admin, who was in the position of councelling students not to abandon their PhD's despite any evidence it was in the students interest not to
she is now being shunted out of the workplace due to childcare protections that we would love to have in the united states. i want the option. i don't want women to be shunted out of the workplace. it's goofy.
maybe that is too strong a phrase. i have first-hand experienced the incentive to not work after having a child. germany has quite a bit of systems in place to compensate people, give them child care, etc. on the surface it is a positive thing. underneath the surface, maybe it's a tool for pushing women out of the workplace. i don't pretend to know.
i was very annoyed with my wife when she did not get a job at a swedish university where she had studied as an undergrad. "everything could have been fine!" i said to her.
I live in Australia, never saw snow until I was 19. Man did I act like a small child that day (incidently in a country where snow was pretty normal, I musta looked like such a tourist in hindsight)
Snow angels are so much more fun than sand angels (which no one does for pretty good reason)
i also went down a hill on a piece of cardboard. my hosts had to explain to the local children that i had never seen snow before (which is why i was pelting them with snowballs). and that i didn't speak swedish. they pitied me.
So I think I did make another mistake on my integral, but I think I have to leave it for today. For the integral of the $y^2$ term, I followed the advice to to integration by parts, setting $dV = y^2$ and $u = e^{y^2}$ which leaves me with a more complicated integral to solve $\int y^3 2e^{y^2}dy$
(I left out all the constants in that expression because I am lazy)
will have to pick this up tomorrow thanks for the mental image / chat @leslietownes
when my wife and i were in edinburgh we did a lot of eating from this restaurant downstairs from our hotel room. it was indian in name only. everything came in about an inch of oil. it was the true scottish experience.
i have no idea what boundaries people are patrolling. i will offer unsolicited advice on your tex. unsolicited is the key. don't ask me for anything, i only chime in when i'm not wanted.
I reallyreally should just stick to pen and paper and stop f$cking about with tex. @robjohn I've just been working through excercises in my calc book and I get it now. I was wondering how you determined to use $u=\frac{y} {-2\lambda}$ but now I realise you just went backwards. Rather than decide what substitution to make, you differentiate the exponential term, see what is left over and then collect the remaining terms into the $u$ function!
That feeling of realising you understand something that you know you didn't five minutes ago is great
If I have a continuous function $f$ over an interval $(0,T)$ and I consider any partition $P_h$ of $[0,T]$ where each interval $[t_i,t_{i+1}]$ is length $h$ is it true that $\lim_{h\to 0}\sup_{P_h} \sup_{s\in [t_{i},t_{i+1}]} | f(s)-f(t_{i}) | =0 $ ?
seems like this should definitely be true but im having trouble with details
I don't know what "any partition where each interval is length $h$" is supposed to mean. there is at most one such partition. In any case, this follows from uniform continuity.
@jay You need uniform continuity in as much as $\lim_{h\to 0}\sup_{P_h} \sup_{s\in [t_{i},t_{i+1}]} | f(s)-f(t_{i}) | =0$ is essentially a restatement of uniform continuity. So, yes.
because it always takes that one value and not the other
this feels like you're asking something akin to "why is the sky blue and not green". there's an answer for why it's blue, but there's no good reason for why it is not green other than it being blue and blue not being green.
@SrijanM.T Indeed, $1+\tan^2(x)=\sec^2(x)$ is an identity, and so is $\sec^2(x)-\tan^2(x)=1$. Why should $\tan^2(x)-\sec^2(x)=1$ be an identity? It's always false.
I want to check if my proof is valid.
$\text{exp}(\frac{x}{x^2+y^2})$ is bounded on $\sqrt{x^2+y^2}\geq\epsilon>0$ where $x,y\in\Bbb R$ and $x>0$.
Proof. Since $\frac{1}{x^2+y^2}\leq\frac{1}{\epsilon^2}$, for each $x\in\Bbb R$, $\text{exp}(\frac{x}{x^2+y^2})\leq\text{exp}(\frac{x}{\epsilon^2})$...
I want to check if my proof is valid.
$\text{exp}(\frac{x}{x^2+y^2})$ is bounded on $\sqrt{x^2+y^2}\geq\epsilon>0$ where $x,y\in\Bbb R$ and $x>0$.
Proof. Since $\frac{1}{x^2+y^2}\leq\frac{1}{\epsilon^2}$, for each $x\in\Bbb R$, $\text{exp}(\frac{x}{x^2+y^2})\leq\text{exp}(\frac{x}{\epsilon^2})$...
![i.imgur.com/1fRSZWd.png]](https://i.imgur.com/1fRSZWd.png]){kind=link}
![i.imgur.com/Og8rJ6k.png]](https://i.imgur.com/Og8rJ6k.png]){kind=link}