Mathematics - 2020-05-29 (page 2 of 2)

@TedShifrin yeah, but clicking on the image just brings that image up. The other link is there so that the higher resolution image does not take up so much screen real estate.

Ted Shifrin

Gotcha, @robjohn.

@Arnold: I don't know what your question is. You can do long division and get a quadratic plus a remainder term.

robjohn

on the main site, it can be set up so that clicking on the low res image brings up a high res image.

a perspicaciously curious mind

( (2.3)^3 + 4 ) / ( 2*(2.3) - 1 ) @ArnoldFernández

user462942

Hi @TedShifrin

Ted Shifrin

7:48 PM

@a, what does $x=[2;3>$ mean?

hi @Joanna

Arnold Fernández

See-> x=[2 ; 3>

Nota x=2.3

Ted Shifrin

We do not know what that means, @Arnold. You have to explain.

a perspicaciously curious mind

4.4908333... @ArnoldFernández

user462942

@TedShifrin Your Lie brackets answer was cool -- though difficult for me to understand. Once, I got a Lie brackets project in Applied Math, with applications to robotics. Something about computing all the different ways an object can move to in its configuration space, subject to constraints (parallel parking was the simplest example to learn of, I think). I kinda regret not taking that project.

Ted Shifrin

Yes, the Lie bracket application to parking cars is a classic and quite fun. I've included it in homework for graduate differential geometry several times.

user462942

7:54 PM

@TedShifrin I see -- interesting.

Arnold Fernández

What it's the solution for 3a^2+1/a if 3<a<19

Ted Shifrin

That question does not make sense to me, I'm sorry.

Do you mean what values do you get for that function on that interval?

Arnold Fernández

What's the interval for 3a^2+1/a if 3<a<19

Ted Shifrin

Do you know calculus?

Arnold Fernández

The idea is not to use advanced mathematics

a perspicaciously curious mind

7:58 PM

Then sub in the values.

Ted Shifrin

That only works if you know the function is increasing or decreasing.

It is, but how do we check without calculus?

I guess there is tedious algebra, which I am not going to even think about.

genescuba

Lets say I have two people whom I trust equally and one tells me that an event occurs with $a$ probability and the other tells me an event occurs with $b$ probability. I want two average these two probabilities together. I should be taking the harmonic mean of a and b right rather than doing (a+b) / 2

Arnold Fernández

It's a math problem for high school students

a perspicaciously curious mind

ask them to sub in 3, 4, 5, ... ,18, 19

and graph the solutions

Arnold Fernández

Mmm, whit graphs is easy

I know

The text is to find the most ingenious way.

Ted Shifrin

8:04 PM

Prove that the function is increasing on that interval.

user462942

8:18 PM

@TedShifrin do you think the research in the mathematics of data science is here to stay, or do you think it will fizzle out in a few years?

genescuba

Anybody have any idea? I think arithmetic mean may be ok here

Ted Shifrin

@Joanna I don't know enough to respond.

user462942

@TedShifrin ok, no worries

user462942

@TedShifrin How could I find a nice problem to work on, like an application of Lie brackets, that might result in a good paper? A mathematics professor at our dept. said to read papers and then find unfinished aspects of those papers, as a start. What do you think?

Ted Shifrin

Yes, reading papers is where you start. Lie bracket is just a tool, like a derivative.

user462942

8:35 PM

@TedShifrin I see; but how does one know that if they follow up on some unfinished aspect of a paper, that that project is worth the effort and valued by the community? It seems that one must run the problem by a more senior academic in order to know.

user462942

Sorry, annoying question.

Ted Shifrin

Yes, that's why advisers are important.

user462942

Yeah ...

user462942

Thanks @TedShifrin :)

Ted Shifrin

Sorry I don't have a magic wand for you.

user462942

8:38 PM

@TedShifrin I know :(

user462942

@TedShifrin Did you always have more ideas / problems to work on than time?

Ted Shifrin

Well, no, because I was more a teacher and book writer than researcher. But I did my share of the latter.

user462942

I see

user462942

@TedShifrin I met someone who went to UGA and they said the college town there is pretty unreal, with tons of parties. Do you participate in the lifestyle? I'll be at a school that's located in what's often considered the top college town in the U.S. I wonder what life will be like for me. I'm not an undergrad, so I wonder whether I would even participate in the social scene that I'll be surrounded by. I am guessing I wouldn't really have the time to do so.

Ted Shifrin

LOL, not in that lifestyle, I didn't. Other than Boston/Cambridge, I have no intelligent guess for the "top college town."

Balarka Sen

8:50 PM

There's sure as hell not going to be serious parties until a year or two anywhere in the world, much less in the US

Ted Shifrin

Yeah, I doubt there will be classes in buildings.

Just parties in Tromp hotels.

user462942

haha I see :)

Hi @Ted, by the way

Hi, a A Balarka.

Nice.

8:57 PM

I wouldn't even be surprised by Americans organizing big "end of the lockdown" parties

user462942

@AlessandroCodenotti Yeah ...

Leaky Nun

it isn't even halfway through 2020

Stan Shunpike

9:20 PM

@TedShifrin hey ted!

Ted Shifrin

Hi Stan.

user462942

@LeakyNun Yeah, seriously -- I work at a cafe to make ends meet. And, I've been staying at home (with pay) for almost 2.5 months, though it feels like forever now that I haven't worked.

a perspicaciously curious mind

that parenthetical remark is a huge plus

Stan Shunpike

@TedShifrin you were right about explaining the concept. We had a follow up problem and I didn't understand it as well as I would expect given the grade i got

so perhaps a lesson for the future is i should be able to clearly articulate why i got something right and, if i cant, more learning to do

Ted Shifrin

Fair enough.

user462942

9:32 PM

@aperspicaciouslycuriousmind Yeah ... I'm very grateful. Maybe you could even guess which cafe it is. It might be the only one that offers pay during a catastrophe. The work is grueling, but the benefits turned out to be top of the line, compared to the industry standards.

Balarka Sen

Here's a nice lemma which literature attributes to Borel (something more general is true, but let's leave it): Suppose $f_0, f_1, f_2, \cdots : \Bbb R \to \Bbb R$ are smooth functions. There is a smooth function $F : \Bbb R \times \Bbb R \to \Bbb R$, $(x, t)\mapsto F(x, t)$ such that $\partial^i F(x, 0)/\partial t^i = f_i(x)$ for $i = 0, 1, 2, \cdots$.

user462942

Pizza time, bye everyone :)

Balarka Sen

That is to say, it is possible to find a deformation of $f_0$ which follows $f_1$ upto order $1$, follows $f_2$ upto order $2$, ...

a perspicaciously curious mind

cya

Starbucks?

Balarka Sen

I misspoke; $F$ is only defined in a neighborhood of the origin in $\Bbb R \times \Bbb R$