00:00 - 19:0019:00 - 00:00

12:00 AM
Nice, self-studying is the way to learn most math

Well I'm not proposing any changes to make se great again

hehe
hope so

just that people chill
if that can be an option
maybe make rep points exchangeable for weed

(a collegue of mine recently told me his brain has been eating itself since he got his job, I want to avoid that)

The greatest weed the shire has to offer!

12:01 AM
any mushrooms in the shire?

Oh we have those too and make tea with them
I dropped one joint twice and smoked three shrooms thrice.

@robjohn LOL

I can get to the mexican town where tourists get their shrooms in like 8 hours driving 20% over the speed limit

If I live to see the day that they're legal in my town or residence, I will switch from caffeine to seratonin tea while at home.

@AndrewMicallef Do NOT unfactor things that are beautifully factored. That is one of the most basic mistakes/sins that students make.

12:07 AM
I'm fine with just coffee

The problem is verrrrrry easy if you keep it factored and substitute in the integral (of course).

ahhh
what?
nvm (im actually doing that rn)

Factor out constants and you have $(x-b)^2$ to integrate. Do NOT expand it out. What should you substitute?

ohhh

u = x - b, du/dx = 1

12:08 AM
that was a lot of typsetting for nothing

Ssshhhh.

dammit
thanks Ted

Count on me to be a horrible person!

You should always use a table of integrals, and derive the easy ones first

now I can't unsee the image of Father Ted smacking a blackboard with a cigarrete hanging out and a bottle of whisky "Don't unfactor a fecking perfect factorisation

12:09 AM
Well, this Ted has never smoked anything and finds it repellent.

hah hah

Don't smoke :)

I'm only on your second lecture Ted, but I feel I learned something all the same, I am using a lot more english in my notes to my self

Oh, cool. :) Well, it does get quite hard later on, but as much as it helps you, I'm very pleased.

also I feel I missed an injoke somewhere, "and then I say to myself:" ausidence responds "self"

12:12 AM
That's one of my patented schticks ... but I had to encourage the class to do that at first. Then they did it without prompting.

This is where I was before Father Ted chimed in anyhow :
$$A^2 \left( \frac{b^2}{b^2 -2ab + a^2} -\frac{2bx}{b^2 -2ab + a^2} +\frac{x^2}{b^2 -2ab + a^2} \right)$$

I'm trying to teach people learning to ask themselves questions :)

ahh it is a good one

why did she leave

Always, always, always pull out constants from integrals and derivatives.

12:13 AM
I feel I will adopt it
do I need to pay royalties if I do?

I'll give you a discount 'cuz you're a newbie.

No use scihub

neat,
anyway, I really should get back to it, I've been on this book for nearly a month and am still on page 16
(mostly because I keep lurking here in my alotted study time)

@AndrewMicallef average if u ask me

I'm average in most respects (had an interview recently where that was my response to the question "what is your superpower?")
@TedShifrin gonna cite that message and go back a few steps.

12:18 AM
I interviewed for a facebook software dev position once

I've finally managed to drag myself to my computer after getting sick this morning (I made an egg white omlette and everything went south after I ate it)............I thought about the question from last night this morning before my calamitous meal. I got a solution and to me it feels like the right reasoning....@TedShifrin

and everyone that interviewed me had beginner english

True/ False: all interior points of $\bar{S}$ are points of $S$?

Claim: False.

Consider the set $[a,b]$. The closure of this set can be defined as $\overline{[a,b]} = (a,b) \cup \{a,b\}$ as in the frontier points are explicitly $a$ and $b$ individually. So if $x \in \overline{[a,b]}$ then it is in either $(a,b)$ or $\{a,b\}$. If $x \in (a,b)$ it is trivially an interior point. So now examining the case for the set of frontier points $\{a,b\}$, going back to the definition of an interior point of a set, it says that a point $x$ is an interior point if there exists an $\epsilon > 0$ such

and I messed up the parameters in a recursion
those two things were completely unrelated

12:23 AM
I don't know when things are beautifully factored
I feel like it's just practice
your brain rewires to know when a certain form is more useful
although I may be saying nonsense

I'm sure it comes with practice
I feel like that is a big part of it, you do this stuff enough and you just start to see when things are similar to an easier problem you have already solved in the past

yeah for sure

lol
what?

"Young man, in mathematics you don't understand things. You just get used to them.”
should I not use that word?

I just think Albert Camus, not John Von Neuman

12:29 AM
I read that guys famous book in high school
it's pretty dope
the foreigner or something

I'm sure there were uberchad mathemeticians, I just don't know of any

idk I read it in spanish
Well Von Neumann definitely classifies as one

I'm not sure if it counts, but the only badass mathamaticians story I can think of is that annectode of pythagoras telling the centurion to get out of his sun.
I need not to go down a rabbit hole of digging up badass von neuman moments ant solve some integrals

Von Neumann allegedly hosted a ton of parties in his house when he worked at the IAS
and he had high level clearence

IAS?

12:31 AM
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent postdoctoral research center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including Albert Einstein, J. Robert Oppenheimer, Hermann Weyl, John von Neumann, and Kurt Gödel, after they immigrated to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Although it is close to and collaborates with Princeton...

I get a department of the australian taxation office when i searched

that's probably cuz your a money launderer

allegedly

I promise your honor, the rolex is fake

Hey man, don't dis the imitations. Seriously brand naming is basically theft anyhow

12:34 AM
i bought a rolex
now my yatch goes faster

12:45 AM
@HereToRelax don’t

but wouldn't that require a breakthrough?
The last combinatorics question was almost a psq
but the dude added that he wanted a solution with probabilistic method and posted the official solution
It appears that was enough to save it from psq status
Also, no one added a probabilistic method solution

1:00 AM
so I have this:
$$\frac{ -A^2(a-b)^3}{3(b-a)^2}$$
can I do this?
$$\frac{ -A^2(a-b)^3}{3(b-a)^2} = \frac{ A^2(b-a)^3}{3(b-a)^2} = \frac{ A^2(b-a)}{3}$$

The first step is completely legit, and the second step is also completely legit (but if $(b-a)= 0$ then I'm not sure how legit it is).
Well I don't know if that helps
but it looks good to me
the expression on the right makes sense for more cases so I guess you may have to take that into account

oh, okay, $a$ and $b$ are both given as positive constants, but I take your point
that helped

you're a motor mechanic?

uh huh
filter spinner

Will I be able to put my car on neutral gear
when all cars are electric
I like when the engine is not connected to the wheels
it feels dope

1:07 AM
if it still has a mechanical transmission, sure

well yeah
but will that happen?

what a mechanical trans + electric motor?

well it doesn't have to be mechanical

yeah, all toyota hybrids do that

Oh that's dope
I like how the car feels when the motor isn't locked to the wheels

1:09 AM
(granted not full electric, but I can imagine they must have in Tesla,s given they have some models with a single motor)
that is a weird thing to enjoy
but good on ya :P

really?
I feel the car is super predictable
and it just goes with the flow
like it feels free

I dunno it is pretty predicable aother wise as well imho

Maybe if you're a genius

they aren't cosmic mysteries

well that's true
but I'm not experienced enough to now exactly how much the engine is going to slow the car when I downshift

1:11 AM
that is why you use your clutch
also that is a bad way of driving unless you are in a big rig
brakes are cheap to replace, engine components not so much
use your brakes not the engine to slow yourself
I used to drive like you do, then I became a mechanic :P

well my car is a 1998 civic
but I don't brake with the engine

it's not so much that it 'breaks' just that you apply unnecessry levels of force decreasing the lifespan and wearing down components that are timeconsuming and expensive to replace
Also, wasting fuel

what wastes fuel?

engine braking

I thought the fuel injector was mostly controled by the fuel pedal
gas pedal

1:14 AM
the engine speeds up when you engine brake
so more cycles
so more fuel

it doesn't speed up does it?

you are using the compression in the engine to slow yourself

it would be going faster if it wasnt locked to the wheels

it does if youu drop a gear to slow down
dont take my word for it, do the experiment
watch the tacho when you drop a gear

When you put the clutch in it revs freely doesnt it?
and then when it gets put into gear it slows down

1:16 AM
sure, over time

well I always double clutch like I should I don't like to granny shift

initially when you disengage the clutch if the transmission is going faster than the engine the tansmission drives the engine

oooh
that makes sense

that is what slows you down

ooh

1:18 AM
the engine trying to get back to the lower speed

I guess I'm dumb

np
I used to think like you do
Now I realise that automatics are actually a really great idea (no fun, but way better in every other regard)

but automatics feel so wrong
but I think that's because of the throttle curve of new cars
or something
my grandpa has an automatic car and the throttle is super unprecise

Really really off topic, but that stuff that ires rev heads is actually a fantastic idea from the engineering POV
basically the engine is full of components that wear out on a per cycle basis, so if you can keep revs low you maximise economy everwhere, but that hurts pple who like to hear the roar of the machine :P

So cars that feel terrible are actually really dope?

1:22 AM
uh huh

how tragic

I'm an old man, so that excites me more (the economics)

I don't like that the motors that use magnetic wierd fields need a computer
DC motors seem easier

uh, They all use computers
just in different ways

but some of the computers are dumb

1:24 AM
hahah

I prefer dumb computers

I like my computers dumb too
hidden states are a nightmare to diagnose
but economics is more powerfull than fun, and smart computers are generally more economical

I guess that makes sense but I don't like it

1 hour later…
2:40 AM
When you give instructions to your evil robot, don't forget to add, "but not me."

All my evil robots obey asimovs laws

dude what's this field called?
$\Bbb{F}_2:={0,1}$ it got addition operator which gives 0+0=0, 0+1=1, 1+0=0 but 1+1=0?
1=-1 ?
multiplication operator table is as follows: 0*0=0,0*1=0,1*0=0 and 1*1=1
is it okay to say 1=-1?
it's bit abstract and odd for me to digest

2:57 AM
yeah, 1=-1 in that field
-1 is just a thing that you can add to 1 and get zero.
if 1+z = 0 then you can call z by -1. even if z happens to also be 1.
sometimes in this context people use other integer notations in relation to fields. for example by "5" they mean not the integer 5, but whatever 1+1+1+1+1 happens to be in the field. which in your field is also 1.
there's a map from the integers into any field given by sending the integer n (when positive) to the n-fold addition of 1 with itself, and similarly with additive inverses. and sometimes people just write "n" in the field when they mean the image of the integer n under the map.
so you get equations like 1=-1 and 3=5=1 and stuff. it's not integer arithmetic, it's arithmetic in the context of that addition operator.

3:14 AM
I already know the ideal correspondence between $R$ and $R/I$ but why this implies there is an ideal correspondence between f(A) and ideal of $A$ which contains $ker(f)$? where $f:A\to B$ is a ring homomorphism

isomorphism theorem

Oh, right

3:28 AM
oops others are not element of the field sorry
it makes sense now

@dc3rd I hope you're feeling better. Food poisoning from an egg white omelet seems unlikely, but ... I don't know if other people commented, but for the example of $S=(a,b)$, the statement that an interior point of $\bar S$ is in $S$ is correct. I don't know why you keep trying to prove that it's wrong there. I told you that you needed to find more inventive examples.
Howdy, @Thor.
@Andrew Define "old man."

4:27 AM
@TedShifrin hmm, I'll pass. But in the context of that conversation, old enough to not get excited by loud revving cars

4:43 AM
0

I tried to understand this answer. As far as I understood, as $f(A)\subset B$ is an integral extension, $f(A)/(f(A)\cap I)\subset B/I$ is also integral extension. Then he use lying over theorem. In what way? What prime ideal in $f(A)/(f(A)\cap I)$ should I use?

think of how troubling it would be if the answer were no.

What do you mean

i'm joking (i don't know the answer) but the premise of the joke is, what if you somehow stumbled on a gap in all of mathematics and nobody could answer it.
that would be a real "uh oh" moment, i think.
you literally meant, can somebody present in the chat right now answer this, which for the moment, the answer appears to be no. that is less troubling than what i was contemplating.
somebody should hop on it. it seems like the kind of thing that a person somewhat more experienced than myself in algebra would be able to have insight into.
the lure of imaginary internet points will draw someone into posting an answer. that usually happens when i'm writing an answer to a linear algebra question.
maybe 1/4 of the time i think 'no, that's not too good of an answer, i'll still post mine.' 3/4 of the time i upvote and hit cancel or escape or whatever it is.

dude, what are you smoking?

currently i am under the influence of ginger turmeric tea.

4:57 AM
omg, 911 now

which isn't tea at all, but i can't bring myself to say 'tisane.' i didn't have that kind of upbringing.

new vocab word for me

if it says tea on the box it's tea, i don't care about biological definitions. it can legally be called tea.

went to an r&b session at the riggers loft in richmond this afternoon
went w some friends which was nice.
insane prices for tiny plates of over prepared snacks.

i have yet to go out with friends. many of my closest friends are high risk and we're not all vaccinated. i'm still leery of public places but probably that is just a psychological complex of mine.

5:01 AM
im in desperate need of social activity
we cycled back which was nice

that sounds like a nice day out. and a bit of uphill on the back end of that i imagine.

tiny bit. i went for a proper ride earlier this morning to get my jollies out
exercise is my drug
and at the moment that means cycling

i use herbal tea, and a tiny bit of birding. there's a duck pond near by, i take my daughter there, she bothers the geese while i just sit there. it's therapeutic.

that is nice. does she feed them bread thereby sentencing them to a lifetime of dependency?
so i used to get lectured

she does not. we sneer at the people who do.
there's a tree with a hollowed out hole in it and often there is an egyptian goose inside. it's usually the highlight of the trip.

5:04 AM
we would have been the subject of your derision...
very nice. the suez goose.

it's funny, wikipedia says they like to rest in hollows of trees. it's cool when the birds behave according to the manual.

i used to like to sketch them.
very therapeutic, plus you notice all sorts of detail that would pass by otherwise

very nice!

he's there every weekend.
most people don't know about him because he's somewhat high off the ground and just minding his own business. sometimes we tell people about him. if they don't seem like the type of degenerates who will attempt to feed him and create a lifetime of dependency.
i joke. i do not have strong feelings unless someone leaves a feeder out when there is a feeder-spread disease going around. an interest and appreciation of birds will do more good than harm, even if you toss them the odd bit of bread every now and again.
i sometimes, rarely, give our crows peanut butter.

5:18 AM
Yo @leslietownes I want to share more nightmare formatting with you

i will steel myself.

i used to feed robins & wrens growing up. sometimes the robins would land on my hand and eat.

its a pdf with no paginations
so one long scroll

i love watching robins fight in the early spring. there's nothing pleasant about it. things really kick off. from such innocuous looking birds.
andrew my initial thought on formatting is this looks great. i wonder about the use of color, if it's supposed to convey information or if it's just a sytlistic choice. some people are very deliberate users of color.

I'm just a sucker for colours I guess

5:22 AM
in the definition i think you mean A((b-x)/(b-a)). with parentheses around the inside bit so you get A(1) when x = a.

(I haven proofed below the part where I cheated to sketch the function also)

that's mostly clear from the computation but not clear in the initial definition. you have to scratch your head for a minute.

yeah I do mean that (or at least I use that definition to find A)

or at least i did.
maybe it's just i have a hair scratching disease.

I should revise that
I don't want to scratch my hairs out in the futuer
I think colouring stuff is fun, in this case I used it because I couldn't figure out how to get eqrefs working in jupyter, so I wanted it to be clear which part of the equation I was dealing with in each pass, without being able to cross reff the normal way.
also I cheated and used wolfram alpha for the algebra at the end, not sure how bad I should feel about that

5:26 AM
there are a few people who use it to indicate things that are changing, so you can see pieces of expressions being substituted into other expressions somewhat more clearly. i find it effective but i understand it, if i didn't understand it maybe it would be distracting.
i'd worry about teaching out of it and then having a student ask me if something should be red or blue.

yeah, that I think can be dangerous, I guess the trick is not to overdo it
I think sparing use of colour is the way to go

i did have a convention in one course where i'd write things that were useful slogans and thoughts to have but not the basis of formal reasoning or computation in light blue. sometimes you want to speak to students in a different register. it sort of worked.

what was the course? and why only sort of worked?

it was linear algebra. it only sort of worked because some people still took those remarks as some kind of coded messages about what the real stuff was supposed to be. i think they forgot about the color system.
in the end i don't think it helped the stronger students and it may have annoyed some of the weaker ones. i only did it once.

fair enough, I find semantic highlighting a nice touch, but I can see how it can be distracting / can be read too much into by someone who isn't fully following

5:31 AM
i think quite a lot of expository choices are made for the benefit of the top 20% of the class because the 80% may be unreachable under time constraints.
i'm pontificating again.
i'll take off my pope hat.

That is a shame for the bottom 80%, (I think I was in that cohort, though it didn't help that I took linear algebra in the same year as the first iphone came out, and sat with a group of people who wanted to show off all the cool stuff you could do on your phone...)

i was bottom 80% in my first linear algebra class. i was mostly tired. i had an unworkable living situation with people who were up all night.
i wouldn't have noticed colors on the board. i remember literally falling asleep in class, it was the only place i could get some quiet. i used the instructor as a form of white noise.
i sat in the back, the lecture hall was large enough that i expect he didn't notice.
if he did, i apologize. i was annoyed when students would do that when i taught. i'd just tell them to go home.
have a friend take notes, catch up on sleep, come back on wednesday.

did you know that the european 911 is 112?

yeah
066 in mexico

isn't it sometimes 999?

5:40 AM
in ireland 999 works too

i should work this out before i go to europe. seems like it is good to know.

in mexico none work
one time a dude pulled out a taser on me and I called them to tell them and they hung up on me

haha

It was pretty funny tbh

i never used it in ireland. the police were 30+mins away at night so we took care of stuff ourselves.

5:42 AM
we've had stuff like that. someone broke into our house while we were home, the cops couldn't be bothered. one time my wife was assaulted while walking our baby, again, nothing. but if some teen is looking in susipcious in an alleyway they show up.
in my hometown my dad's coworker had a police scanner on most of the time, you'd get the weirdest reports. people do bother the police about the strangest things.

For some reason I thought it was more of a third world problem

technically ireland is part of the 3rd world

it is highly variable in the USA. to the point that it might depend on the side of the street you live on.

@HereToRelax the use of the term has changed over the last 80 yrs

5:45 AM
yeah I guess it might depend

the first world referred to uk, usa, etc, the second world were the axis powers and the third world the non aligned nations

sometimes I feel like mexico isn't third world
but it's only for very short periods of time

i haven't consulted the more recent definitions. with rising stratification of wealth the concept seems fairly useless now.

very true

the convo was getting too mathematical, i had to lob a bomb in

5:47 AM
in los angeles you can go from some of the nicest housing and office buildings to an enormous tent city in about five minutes.
thanks for that.

where were we

Psi is real so is equal to its conjugate. also, it's sometimes in blue, For Some Reason.

coloUrs should be used sparingly
sortof watching galaxy quest right now
its brilliant

i remember liking it very much.

sad thing is my wife & i watched it years ago and i am enjoying it again as if i had never seen it :-)

6:03 AM
if you luck out eventually you get to the point where you get to meet new people every day.

the delights of aging...

Don't mind my clones.

1 hour later…
7:22 AM
If $R$ is a local ring then $R^\times \to (R/I)^\times$ induced by $R\to R/I$ is surjective?
I is an ideal of R

3 hours later…
10:12 AM
Is it true if you have a Dynkin system $D$, and a subset $A\subset D$ that is closed under finite intersections, then $\sigma(A)\subset D$? (here $\sigma(A)$ is the sigma-algebra of $A$)
This set $A$ has more properties, but I don't know if I need these

10:32 AM
Bit china coin

11:07 AM
0

I was actually reading some proof of Noether's normalization lemma but in the proof, it uses some basic property (at least the proof stated like that) of homogeneous polynomial. Suppose $k$ is an infinite field and $A$ be a finitely generated $k$-algebra. Let $x_1,...,x_n$ generate $A$ as a $k$-...

'the homogeneous part of highest degree' can have several terms right? like in $f(x,y) = x^3y^3+x+x^6$ then it would be $x^3y^3+x^6$
Let $f(x_1,...,x_n)=0$ where $f$ is a polynomial of $n$ variable over a field $k$. Let $F$ be the homogeneous part of highest degree in $f$. Then there exists $\lambda_1,...,\lambda_{n-1}\in k$ such that $F(\lambda_1,...,\lambda_{n-1},1) \neq 0$
The proof of this is
because if $\lambda_i$ does not exist, then we have $F(x_1,...,x_{n-1},x_n) = x_n^{\text{deg}\ F}F(x_1,...,x_{n-1},1) = 0$ by homogeneity.
I don't understand what is this. I mean how x_n^{\text{deg}\ F} can come out?

11:29 AM
when we talk about the graph of af(x+b/2a) = a(x+b/2a)^2(Dont need value of y axis right now so not written )
This is Q.E graph using completing the square method
So , first I draw graph of x^2
Then , af(x)
Then shift
If you notice , the value of turning point I,e -b/2a changes.
It is Sth else now.
How is that possible
Turning point changes to -b/2a^2

12:21 PM
(removed)

2 hours later…
2:04 PM
the answer wrote deg_nF there and I suspect the intended meaning of that is 'lowest power of x_n which divides all terms in the expression'

or in other words it's just factoring the largest power of x_n you possibly can

@loch But the resulting should be x_n^{deg F}F(x_1,..,x_{n-1},1) so every $x_n$ should come out

2 hours later…
4:23 PM
my daughter's singing about her imaginary friend again.
interesting mental math exercise in how this could be possible. many commenters are convinced that it isn't. twitter.com/TheoShantonas/status/1380536139954655237

1 hour later…
5:40 PM
very interesting...

what's interesting is how the worms managed to figure that out in the first place.

@AlexDoe I fell in love with you!

Who are you, excuse me?

XD

6:28 PM
This is a proof I saw before which I asked

6:43 PM
If n variable polynomial $f(x_1,...,x_n) =0$ then each homogeneous part is zero?

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