Mathematics - 2012-06-26 (page 1 of 5)

Jordan

12:00 AM

I really need to learn to focus, I wasted all day today not studying

user19161

@Jordan And what did you do?

Jordan

Procrastinate

anon

I get a feeling that somewhere in the world, black hats have gotten together and created a search engine specifically for sites with robots.txt

shadow google

user19161

Who knows how to make gmail not record "most contacted"?

user19161

I can set it to add contacts myself but that is another story.

user19161

12:03 AM

Oh, for once I appeared in the "frequently in room" list here!

user19161

@Jordan Less procrastination, more discipline then.

anon

"frequently in room" list?

user19161

@anon Click on "info" near top right.

Jordan

I am a little surprised I am not on there

That is a competitive list

user19161

@Jordan It changes according to an unknown algorithm.

Peter Tamaroff

12:12 AM

@JasperLoy Yeah I know that.

anon

Is there a limit to how many times a comment may be edited? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Peter Tamaroff

@anon Not times, but time. There is a finite amount of time.

anon

apparently that's the case

Mark Dominus

I thought it was 5min

Peter Tamaroff

@anon BTW, I was telling rob I got Modern Algebra by MacLane and Birkhoff

Seems to be an awesome text, I got it for 15 bucks more or les, hardcover.

anon

12:20 AM

@PeterTamaroff I was reading that in Reno. I loathe some of the notation used.

Peter Tamaroff

@anon It has Group Theory, Class Algebra, Transfinite Arithmetic, Rings and Ideals, Galois Theory and other simpler stuff.

@anon Hahaha well, it is an old text.

@anon What is Reno?

anon

Nevada

like, $f^*$ and $f_*$ for images and preimages.

Peter Tamaroff

@anon Well, it is a cool notation IMO.

Succint.

user19161

@anon 2 min.

anon

impossible for me to remember which is which :P

user19161

12:24 AM

@Weiler That pair wrote two books: Algebra and A Survey of Modern algebra.

user19161

@weiler I see you have gone incognito.

user19161

Algebra has more advanced topics than the other book, but both start from scratch.

Mark Dominus

meta.stackoverflow.com/a/33939 says that comments can be edited for 5 minutes.

Weiler

@JasperLoy I have the latter.

@JasperLoy I'll go back, I guess.

user19161

@MarkDominus Oh, sorry if I was wrong then. Anyway these things change all the time.

user19161

12:27 AM

@Weiler I have the former.

Weiler

Am I sounding harsh here?

@JasperLoy So you know quite a good deal of algebra right?

Mark Dominus

@JasperLoy Quite so. You might be correct that it is now 2m.

user19161

@MarkDominus It's interesting how you suddenly appeared in chat on a number of occasions after I commented on something.

Weiler

(If you studied from it)

anon

I'm not sure about biology being the best subject for it. And there is a spectrum, so some of the "higher-functioning" autistics can indeed explain themselves to some extent. (See "Born on a Blue Day" for instance.)

user19161

12:28 AM

@Weiler Well, I forgot everything. But I'll start reading up again if I were to apply to grad school.

user19161

@anon Yes, there is the autism spectrum. Then there is Asperger's too.

Mark Dominus

@JasperLoy Strange that I have not noticed you before.

user19161

@MarkDominus Well, maybe it was someone else, and maybe I had another username!

Jordan

I need to get a B on this test to have a chance in the class I think

user19161

@Weiler You will be comforted then to know that it does have some things the other one does not contain that are important as well.

Weiler

12:30 AM

@anon Well, that'd mean the autism has been "cured" in some degree.

@JasperLoy It's cool it has Group Theory, Class Algebra, Transfinite Arithmetic, Rings and Ideals, Galois Theory.

Mark Dominus

I have just edited a three minute-old comment.

user19161

So I was looking at some meta posts on whether we should give hints or complete solutions. I guess both are allowed and have pros and cons.

user19161

So I guess I'll just go by my gut feeling when answering questions as to how complete the answer should be.

Mark Dominus

I edited a 4m old comment, but after 5m the "edit" option vanished.

user19161

@MarkDominus OK, so I think it is 5 min right now.

user19161

12:34 AM

Haha, you actually bothered to find out.

anon

Well, I can prime factorize 81^100 in less than 2.5 minutes.

Mark Dominus

You had the same username in 2010.

user19161

@MarkDominus Are you talking to me?

Mark Dominus

Yes.

user19161

@anon So can I.

user19161

12:36 AM

@MarkDominus Yeah but I was also Will Hunting and Clark Kent at some other points in time.

user19161

Not to be confused with the Clark who asked about tensor products that Ben mentioned.

user19161

@weiler Now I must mentally make the map weiler=peter.

Weiler

@JasperLoy lol. I'll ask amod to change it back.

@anon I have a problem here.

user19161

@Weiler Hey, if you keep asking them to change they will be pissed!

user19161

Your changes might crash the whole network!

Weiler

12:39 AM

@JasperLoy I didn't ask yet. @Eugene didn't tell me who to contact.

user19161

@Weiler An exception to the 30 day rule seems to be if you create a new account. Then you can change it there and copy to all the rest.

Weiler

►

über trippiness

user19161

@mark Are you a potato?

Mark Dominus

Not to the best of my knowledge.

In fact, I am a parsnip.

user19161

Ah, well I only know about potatoes.

Mark Dominus

12:43 AM

I only know about blue squares.

user19161

@MarkDominus Haha, you remembered that I was a blue square?

user19161

Maybe I shall use that again.

Jordan

oh lawd

this same question came up like 4 times in the review problems for my test and I am pretty sure something like it but more difficult will be on the test

user19161

@Jordan What's up?

Jordan

$\int_0^5 2 \pi (3t^2) \cdot \sqrt{36t^2 + 36t^4} dt$

Weiler

12:46 AM

@Jordan start by taking $36t^2$ out

Jordan

I made that into $36t^2(1+t^2)$

Weiler

@Jordan Where's the $\sqrt{}$?

Jordan

but from here I am a little confused on how to proceed, I know I can make that into sinh

still there

Weiler

Yeah, that's true.

Why don't you try to find a primitive of the integrand and then use Barrow's Rule?

(so that the limits of integration don't get too messy)

Jordan

I don't know barrows rule

Weiler

12:52 AM

@Jordan Could you do it?

@Jordan It is $\int_a^b f(t) dt = F(b)-F(a)$, sure you do.

Jordan

oh I thought that was named something else

anon

just call it the fundamental theorem

Weiler

@anon FTC II

Jordan

Stewart probably names it Stewarts rule in his book

Weiler

It is actually a corollary to the FTC

@anon Hehe, look at this vector space:

anon

12:54 AM

they're both corollary to each other, so their order of presentation is actually arbitrary

Weiler

@anon True.

Jordan

I will just have to take this class over in a year probably

Weiler

$V= \Bbb R_{>0}$ , $K=\Bbb Q$ and $\oplus : a\oplus b = a \cdot b$ and $\otimes: m/n \otimes a = a^{m/n}$

Jordan

everything with college seems purposely drawn out to keep you there as long as possible to get as much money as possible from you

Weiler

@Jordan Haven't you watched American Pie: The wedding?

Jordan

12:56 AM

nope

Weiler

YOU DON'T SCORE UNTIL YOU SCORE.

Jordan

why does this same thing come up so many times

I skipped that problem and went back and it came up again

$\int_0^1 \sqrt{36t^2 + 36t^4} dt$

Weiler

@Jordan $$\int\limits_0^1 {\sqrt {36{t^2} + 36{t^4}} } dt = 3\int\limits_0^1 {2t\sqrt {1 + {t^2}} } dt\mathop = \limits^{{t^2} = u} 3\int\limits_0^1 {\sqrt {1 + u} } du$$

Jordan

oh

anon

Helpful spacing commands: \, \; ~ \quad \qquad \hskip 1in (set $1$ however desired, even in decimals)

11\,1\;1~1\quad1\qquad1\hskip{0.5in}1 $$11\,1\;1~1\quad1\qquad1\hskip{0.5in}1$$

Weiler

1:04 AM

@anon Thanks for the brotip.

Bill Dubuque

@robjohn You missed a prime opportunity to fire your Bezout canons!

Weiler

@BillDubuque It is interesting how all your questions are linked to each other.

Bill Dubuque

@Weiler Mathematics is linked in many beautiful ways. Unlike linear-limited books, we have the capability here to make these links explicit.

Jordan

Oh no, I forgot to memorize eulers formula

Weiler

@BillDubuque Indeed. BTW, I'm Peter Tamaroff, I just changed my username. Do you know if any of you can change it back?

@Jordan $e^{i \varphi}=\cos \varphi + i\sin \varphi$?

Jordan

1:10 AM

eulers method

Andrew Salmon

@Weiler why did you change it?

Weiler

@AndrewSalmon I googled my username and Google spat out all the chat logs and stuff, which I found uncool. But I can deal with that.

@BillDubuque Is your avatar Klein's j-invariant in the complex plane? (Not that I know what that is, just found the Wikipedia page on $j$-invariants)

Bill Dubuque

@Weiler Yes, that's my gravatar

Weiler

@BillDubuque That is really high arithmetic right?

(Pardon the inevitable pun)

anon

modular forms

Bill Dubuque

1:14 AM

@Weiler yes, especially after a little moonshine!

Weiler

@BillDubuque Hahhah lol.

Jordan

memorizing eulers method seems like wasted effort at this point

Weiler

@Jordan It is very useful!

Jordan

I just need to get an A on this test

Weiler

@Jordan Then keep the rythm! =)

Jordan

1:16 AM

I will probably fail the test

failing this class really sets me back far, i don't know when I can take it again and I will have to before I can transfer

Means I can't transfer for another year or two

Bill Dubuque

@Weiler What do you want your Display Name to be?

Jordan

And then when I do apply for transfer it is for the next year, and I will be done with all the classes at this school so I will be wasting my time

9 years for a 4 year degree, no big deal

Weiler

@BillDubuque Peter Tamaroff

Bill Dubuque

@Weiler Ok, done.

Weiler

@BillDubuque Thanks.

@BillDubuque What is your opinion on Modern Algebra by MacLane and Birkhoff?

Jordan

1:23 AM

I can't believe how little studying I did in 4 days

I went over like 12 problems

Mark Dominus

I never heard the name "Barrow's rule" either.

Bill Dubuque

@Weiler I've only ever browsed it, so I really can't say. But given the distinguished authors, it is surely worth a look.

Mark Dominus

Wikipedia also has no entry for "Barrow's rule". Is it named for Isaac Barrow?

Weiler

@MarkDominus Yes.

Mark Dominus

That makes sense

Peter Tamaroff

1:27 AM

@MarkDominus It is mentioned in the FTC page of Wikipedia

Mark Dominus

Thanks.

Jordan

I cant get any of these answers

I am so screwed

Peter Tamaroff

@BillDubuque Bill, I have a conundrum going on.

Jordan

I have $x^2lnx - \frac{x^2}{2} = y^2 + \frac{2}{3} \cdot (3+y^2)^{\frac{3}{2}}$

for y(1)=1

anon

Hmm, saying a group is a direct product of subgroups is different from saying it is isomorphic to a direct product of subgroups.

Peter Tamaroff

1:31 AM

Say $v$ is a vector in $V$ and $k$ are scalars, such that $V$ is $K$-vector space.

In the property that $(a\cdot b)\cdot v=a \cdot (b \cdot v)$ shouldn't one more clearly write:

anon

two different binary operations?

Peter Tamaroff

$(a\cdot b)\otimes v=a \otimes (b \otimes v)$ where $ \otimes$ is the action from $K\times V$ to $V$ and $\cdot$ is the binary operation of $K$?

anon

I would not use otimes, because then it's confusable with the tensor product.

Also, it's called "abuse of notation."

Peter Tamaroff

@anon Well, whatever, make it a $\star$,

@anon Yeah I know, but it makes things confusing, like proving the vector space I mention above is one

Also

, for $(a+b)\cdot v= a\cdot v + b \cdot v$ one should write $(a+b)\otimes v= (a\otimes v) \oplus (b \otimes v)$

where $\oplus$ is vector addition (properly defined whatever the vector space is)

anon

If one is first introducing the notion of a vector space, using two different symbols for the scalar-vector versus scalar-scalar is a good idea.

@PeterTamaroff now you risk confusing with an element of the direct sum of vector spaces!

Peter Tamaroff

1:37 AM

@anon Hahhaha but that is just for now!

I'm not dealing with direct sums now.

Jordan

I dont get this

anon

However, if we simply write \cdot for everything, the correct symbols can be recovered unambiguously, so there's no inherent issue with using \cdot for both after this is clear.

Jordan

I need to make $ \int y dy = \int x dx$ equal to y(0) = -3

that seems impossible, the books answer seems like they just made it up

Rajesh D

Why no up/down votes for this?

Peter Tamaroff

@RajeshD TL;DR all over you, dude.

anon

1:39 AM

@RajeshD What the monkeys is the point of indexing things? The equalities apply to each triple a,b,c separately!

Argh.

Rajesh D

?? I did'nt get what is TL and DR?

Jordan

team liquid and diminishing returns

Peter Tamaroff

@RajeshD Too long, didn't read.

Rajesh D

team liquid?

ok

Jordan

teamliquid.net

Rajesh D

1:41 AM

@anon, yes the question isn't related to sequences actually

Jordan

jesus

no matter how many times I do this stupid u sbustituion problem I cant ge tit

I have never felt this bad before a test

this is going to set my life back like two years

user19161

@PeterTamaroff It's great, but in my opinion the other one is better!

Peter Tamaroff

@Jordan Which one?

Jordan

0

Q: Solve $y' = x + y$

I am suppose to use the substitution of $u = x + y$ $y' = x + y$ $u(x) = x + y(x)$ I actually forget the trick to this and it doesn't really make much sense to me. I know that I need to get everything in a variable with x I think but I am not sure how to manipulate the problem according to mat...

user19161

@Jordan Stop whining.

Peter Tamaroff

1:44 AM

@JasperLoy Hhaha well, I'm not aiming for really high algebra, and I have amazing luck I even got this one.

Rajesh D

@anon : But I don't understand how it managed to get 9 upvotes?

user19161

@PeterTamaroff Neither is too advanced. Both are suitable for undergrads.

Jordan

I think I will get to take a year break from math

Peter Tamaroff

If $u=x+y$ then $u'=1+y'$ then $y'=u'-1$

Then you get $u'-1=u$

user19161

@raj I see your new photo!

Rajesh D

1:46 AM

thanks

Peter Tamaroff

@JasperLoy Cool.

anon

@RajeshD Me either. I'm reading your answer, and it seems it can be substantially simplified. At any rate, I think there's an error, as you confuse HM with its reciprocal in the equation after "it can be seen that."

user19161

If you want really advanced general algebra, look for the three volumes by Paul Cohn.

anon

In particular, it should be AM / (GM^3 / HM)

Rajesh D

i'll see

Jordan

1:47 AM

this problem doesn't make any sense to me, I just can't do it on my own. I read through the solution and tryi t myself and I can't do it

user19161

@Jordan Don't you have tutors and lecturers there to help you?

Jordan

they are horrible

user19161

Aren't they better than asking people here?

Jordan

If you get lucky and one is a native english speaker then it can be okay, but they are always booked

no

user19161

It's hard to discuss math in a chat room.

Jordan

1:48 AM

I am better at math than most of them

I have to wait for them to go through the problem, I always finish the problem first

user19161

@Jordan Most of who?

Jordan

the tutors

user19161

Er, I doubt it.

anon

lol, that's a bad sign

Peter Tamaroff

@JasperLoy Yeah, same here.

Rajesh D

1:49 AM

@anon : Argh, I don't know how to forgive myself for doing this type of crap!

user19161

@jordan You saying you are better than your tutors, I think that's a joke.

Jordan

there is one tutor who is a native english speaker but he is a huge asshole about it, he laughs at people who are bad at math and thinks the classes are too easy

Peter Tamaroff

@Jordan Then why are you struggling?

Jordan

because I am bad at math

anon

@Jordan Reminds me of 13-year-old version of me.

Peter Tamaroff

1:50 AM

@Jordan That's a bad person, not a bad tutor, technically.

Mark Dominus

It is possible to be both.

Jordan

Someone really needs to jump that guy, so he can learn some respect

Peter Tamaroff

@anon Shame on you!

user19161

@Jordan Considering how you keep saying people here are talking down to you when they are not, I don't think he really laughs at you.

Peter Tamaroff

Arturo did it again

user19161

1:51 AM

@Jordan Maybe you need to learn that yourself.

anon

He should write a textbook some weekend.

user19161

@jordan Do you know how many people you have insulted here? Yet you say people lack respect. I am finding it quite amusing.

Peter Tamaroff

@anon Hahah, I proposed @Bill wrote one some day! I'd mindlessly but it!

Mark Dominus

Arturo is really amazing.

Jordan

Well when people say things are easy it isn't directly talking down to me but it is hard to interpret it otherwise

How do I insult people here?

user19161

1:52 AM

@Jordan Go figure out. You are not an idiot.

anon

popcorn

user19161

I have met too many people in this world who hurt others but keep saying others hurt them. I am very sick and tired of all these people.

Jordan

I still can not understand math.stackexchange.com/questions/159713/solve-y-x-y

Rajesh D

@anon : how to scratch out, latex code?

Jordan

I think I should just skip it, it is kind of in depth and a one-off problem

Peter Tamaroff

1:54 AM

@anon Silly. Nachos and cheese.

Jordan

I have an hour left to study tonight befoer the test tomorrow

user19161

@jordan My honest opinion of things is that you really should not be doing math, but you are free to choose your own path in life.

anon

@RajeshD don't bother scratching it out, that's only something you do if lots of people were exposed to a wrong version of some math and a big fuss was made. in your case, your answer has next to zero attention given to it, so you should just edit it out.

user19161

For example, I can't ride a bicycle, even though I have tried many times.

Jordan

There isn't anything else to do if I avoid math

Rajesh D

1:56 AM

ok

fine

anon

In fact scratching out latex without reason will just make it longer and even less likely to attract attention.

Peter Tamaroff

@JasperLoy Interesting. Get a gyroscope, dude.