Mathematics - 2014-08-19 (page 1 of 4)

Ted Shifrin

00:01

Yes, you're almost half my age ...

Max

hello

can someone quickly help me out - i forgot what it is called when you have two integrals or sums where the bounds of the inner one depend on the value of the outer one i.e. integrate over x from 0 to 1 and y from 0 to x

ah, convolution is the word i was looking for :)

MrWho

01:24

@skullpatrol @DanielFischer : Is it bad to take Calc I and II + Linear algebra + physics in the freshman semester of physics?

Daniel Fischer

I don't know. Can you even take Calc I and Calc II in parallel?

MrWho

@DanielFischer I can, I think

@DanielFischer I know the bone structure of calc I and II

I'm just no skillful in linear algebra and multi variable calculus.

@DanielFischer Does it harm?

Daniel Fischer

I mean, "are they offered in the same semester?" I'd have thought they were offered in alternating semesters.

skullpatrol

I would not recommend it.

MrWho

@skullpatrol @DanielFischer They're offered in different semester, since I was late, most of the classes are closed, right now, I'm thinking of rescheduling the whole program.

I have to register right now !

I do really need your advices.

skullpatrol

01:33

Remember math builds on itself.

Daniel Fischer

I can't advise on that @MrWho. Only generally, don't bite off more than you can chew, but enough that you have something to chew on.

MrWho

@DanielFischer I know what you're saying,tell me your opinion about this : Calc I + Linear Algebra + Fundamentals of Chemistry + Lab + Social and behavioral sciences?

Daniel Fischer

Sorry, no idea.

MrWho

@DanielFischer The question is, does linear algebra rely on calc I and II?

Do I have to know the whole calc to take linear algebra in Uni?

Daniel Fischer

@MrWho Linear algebra doesn't need Calc or anything. You need linear algebra for almost everything, however, so it's a good idea to learn that early.

MrWho

01:40

@DanielFischer So if I put linear algebra in First semester it's good?

Daniel Fischer

And good night, everybody, I'm off to bed.

@MrWho Yes, that's fine.

MrWho

@DanielFischer Oh thanks, bye :)

Mike Miller

bonjourno

Mike Miller

02:07

goodbyeo

900 sit-ups a day

03:51

I wonder if this is the record for length of suspension on SE. Anyone seen longer?

Mike Miller

04:06

@900sit-upsaday I've seen five-year ones, but not 10

Pedro Tamaroff

04:37

@900sit-upsaday WAT.

That's amazing.

The Substitute

04:49

Off topic: When defining the rationals by the cartesian product of the integers and the natural numbers modded out by ~ where $(a,b) ~ (c,d)$ if $ad=bc,$ how does one show transitivity without using division?

If $(a,b)~(c,d)~(e,f)$, then $ad=bc$ and $cf=ed$. I'd like to say $(a,b)~(e,f)$ since $e/f = c/d = a/b$, however, I don't feel like I should allow to divide since that would be using the fact that we already have rationals (while I'm in the process of defining the rationals).

AndrewG

if $(a,b)$ ~ $(c,d)$ and $(c,d)$ ~ $(e,f)$ then $ad = bc$ and $cf = de$, so $daf = adf = bcf = bde = dbe$ (I think?) implies $af = be$

Jasper Loy

05:07

@MrWho It would be good to take linear algebra before multivariable calculus.

The Substitute

@AndrewG, yes, that's it

AndrewG

you may need to mention that there exists a g such that $(d,1) = (1,g)$ for that last implication

but that sort of is "using division"

Martin Sleziak

05:27

It's not using division. It is using cancellation law. (Which is valid in any integral domain.)

The Substitute

@MartinSleziak yes. thanks

Alec Teal

06:04

Morning

Jasper Loy

07:45

@DanielFischer I just found out that integrals of Banach-valued functions are called Bochner integrals, and that there are manifolds more general than Banach manifolds called Frechet manifolds.

Balarka Sen

08:49

@Alizter Ah, you told me, right. I forgot.

Nick

09:01

I have just begun to integrate!

It feels like a new phase in my life.

Studentmath

@Ted! @Balarka!

I am looking for a proof of Chernoff-type bounds on lower and upper tail of bionmial distributions, specifically the one around the expectation. Anyone know where I can find one?

Gah, guess I will have to prove it myself

Rajesh D

09:20

Some illustrations added : mathoverflow.net/q/165038/14414

Jasper Loy

@Nick Do you mean antidifferentiate?

Balarka Sen

@Nick integrate what?

Nick

@JasperLoy: Yes :D

Balarka Sen

hello @Studentmath

hello @nick

Studentmath

How's it going @Balarka?

Nick

09:23

@BalarkaSen: Simple baby stuff that's irrelevant to you.

Balarka Sen

@Studentmath not bad. how 'bout you?

Studentmath

Stuck trying to find some proof for what I am reading in a paper, but otherwise fine

Maybe I will ask for reference on the main site

Nick

@BalarkaSen: For example, this

Balarka Sen

@Nick you're doing good. keep going.

Nick

:D Yay

Btw, what is $\int{uv\cdot dx} = uv\cdot dx + \int{(\frac{du}{dx} \cdot \int{v\cdot dx})}\cdot dx$ called?

Balarka Sen

09:28

@nick when i first learned how to antidifferentiate, i always used to amuse myself with $\int 1/\log(x) dx$

@Nick uv dx doesn't make sense.

Nick

@BalarkaSen: Does no one call it integration anymore?

@BalarkaSen: u and v are functions of x. Now, it makes sense?

Balarka Sen

@Nick call what?

Nick

@BalarkaSen: Antidifferentiation.. sigh

Balarka Sen

@Nick no, it still doesn't. $uv \cdot dx$ is an infinitesimal. how can i make sense of that without the int symbol?

4 mins ago, by Nick

Btw, what is $\int{uv\cdot dx} = uv\cdot dx + \int{(\frac{du}{dx} \cdot \int{v\cdot dx})}\cdot dx$ called?

Nick

Whoops

$$\int{uv\cdot dx} = u\int{v}\cdot dx - \int{(\frac{du}{dx} \cdot \int{v\cdot dx})}\cdot dx$$

Balarka Sen

09:33

@Nick we call it integration when the limits are given.

Nick

Oh

Balarka Sen

@Nick Err... the product rule?

$$\int u dv = uv - \int v du$$

Nick

Oh

Balarka Sen

it is the product rule

just differentiate both sides, see what happens.

Nick

That's an easier way to remember it!

Hahaa

Balarka Sen

09:36

there is nothing to remember when it comes to math

it follows logically

Jasper Loy

@BalarkaSen 2 times 2 is 4 is memory.

Balarka Sen

that's an axiom.

Nick

I get it: $uv = \int udv + \int vdu$

Balarka Sen

uh-huh.

Nick

It's natural

I should go apologize to Newton and Leibnitz now.

Balarka Sen

09:39

Nick

@BalarkaSen: Could you lend me your copy of Spivak?

Balarka Sen

@Nick ever heard of blah?

look it up there.

Nick

Blah

Blah, Blah Blah or Blah Blah Blah may refer to: == Music == Blah Blah Blah (Iggy Pop album), 1986 Blah Blah Blah (Blahzay Blahzay album), 1996 Blah Blah (album), a 2006 EP and song by Lady Sovereign Blah...Blah...Blah...Love Songs for the New Millennium, a 2004 album by Scum of the Earth === Songs === "Blah Blah Blah" (Gershwin song), 1931 "Blah Blah Blah" by Nicola Paone, 1959 "Blah Blah Blah" (Iggy Pop song), 1986 "Blah Blah Blah" Longpigs B-side 1996 "Blah Blah Blah" by Heinz Erhardt "Blah Blah Blah" (Kesha song), 2010 == Other media == Bla Bla, a 2011 National Film Board of Canada...

Jasper Loy

@Nick Try en.bookfi.org.

Balarka Sen

right.

Jasper Loy

09:43

No need to be so secretive.

Nick

Wait, should I be searching for Spivak or Blah?

Balarka Sen

@JasperLoy i don't want to take the responsibility for linking to an unofficial site, sorry.

Nick

@BalarkaSen: Sorry, Blah's not an author of any known book.

Balarka Sen

search for Spivak

Chris's sis

Last night I did a bunch of amazing discoveries...

Jasper Loy

09:46

The best calculus book is actually Lang's A first course in calculus and his Calculus of several variables.

Balarka Sen

I liked Piskunov however.

Nick

@JasperLoy: Jaspy, I'm trying single variable. Gotta take baby steps here.

Jasper Loy

@Nick I am single and available.

2

Chris's sis

@BalarkaSen Did you know that the series here math.stackexchange.com/questions/882621/… can be computed without pen and paper? (this is the art of solving problems)

Balarka Sen

@Chris'ssis nope.

Nick

09:49

@JasperLoy: Jokes aside, how are you?

Jasper Loy

@Nick Same, still trying to get better.

Balarka Sen

@Chris'ssis that's nice.

Chris's sis

@BalarkaSen Yeah, I worked a lot on it. I'm going to publish it in some article. I need some articles before publishing my book.

Balarka Sen

go ahead.

Jasper Loy

@Chris'ssis You can publish the book as 100 articles, lol.

Chris's sis

09:51

@JasperLoy :-))))))

Nick

@JasperLoy: That's a great idea!

I got to make lunch, any mathematical ideas?

Balarka Sen

@MikeMiller

I think I am unsure of why 1 --> Aut_H(G) --> Aut_N(G) --> Aut_N(H) is not exact at the right.

@Nick what ideas?

Nick

@BalarkaSen: for Lunch. PS: Spivaks a lot of fun!

Balarka Sen

mathematical ideas for lunch?

like deciding the probability of picking up a piece of tomato from your plate of noodles while eating randomly?

Nick

... No, like what I should make. Noodles sounds good.

Balarka Sen

10:00

or the standard distribution of butter in your sandwich?

Nick

Sandwich is nice too.

...

Balarka Sen

great. have fun with those.

Nick

Wait, how the heck did you know that I only had Maggi and bread in the kitchen?

That was scary spot on.

Balarka Sen

science of deduction, i mean.

Nick

... Ofcourse Dr.Holmes

Balarka Sen

10:02

=P

and AFAIK, I doubt Holmes had a doctorate.

Nick

I must have been thinking of someone else.

Balarka Sen

Of course. You were thinking of Dr. Watson.

i have to go and decide what to do -- do some math or read Sherlock.

Nick

@BalarkaSen: Both will give you the same amount of serotonin buzz.

Balarka Sen

wat

Nick

Also, I don't think Dr. Wilson is what came to mind when I said Dr.Holmes

Balarka Sen

10:10

Wilson?

ok, i gotta run.

Nick

Yes, Wilson

@BalarkaSen: Bye :D

rehband

12:06

@Chris'ssis Chris, how did you become so good at solving integrals & sums?

Chris's sis

@rehband I don't know how good I'm, but as it also happened in other areas, I always managed to get a high peak when I loved the things I did. Well, it was a time when I learned alone and had to answer all my questions alone. Then, I read some books, papers, I visited sites, and the most important thing I began to create my own questions, I was challenging myself.

@rehband I hope to be one day like Ramanujan or beyond. I worked a lot and I'll continue to work a lot, I'm a hard worker.

Nick

@Chris'ssis: And ofcourse you'll get to that level beyond doubt.

robjohn

@rehband: just try to learn something every day.

rehband

@Chris'ssis Awesome, me too :D Long way to go for me haha. I shall continue doing exercises from that book now

@robjohn Will do

Nick

Could anyone please tell me if my answer is right?

Chris's sis

12:17

@rehband Well, I give you a point that is helpful. Try to solve each question there in more ways (where you can). Doing like that, you'll become pretty good after a while.

rehband

@Chris'ssis Ok, will do. I still need to at least look at hints for most of them.

Chris's sis

@robjohn Yesterday I created & computed a mind-blowing series ...

robjohn

@Chris'ssis which one?

Chris's sis

@robjohn $$\sum_{n=1}^{\infty}\frac{ 1}{n^2} \left(1+\frac{1}{ 2}+ \cdots +\frac{1}{ n} \right) \left( \zeta(2)- \sum_{k=1}^{n} \frac{1}{k^2}\right)$$

robjohn

I will take a look at it...

Chris's sis

12:33

@rehband Do you see $2.58.$ in that book? It's an open problem. I recommmend you the version when $n=3$. It's simply fantastic. The version in 3 variables I met it independently in my research, but glad I also saw it there.

rehband

@Chris'ssis Wow, looks crazy :O

Chris's sis

@rehband It has a very nice closed form.

rehband

@Chris'ssis I wouldn't even know where to begin calculating it

Chris's sis

@rehband Yeah, but it's crazy awesome too. :-)

rehband

@Chris'ssis For sure

skullpatrol

12:36

►

Chris's sis

@rehband During the time I gave it some mathematicians, no one did it so far. Maybe some didn't do it because it simply looked too ugly to them. I was impressed by its beauty from the beginning.

rehband

@Chris'ssis Haha :D

Chris's sis

@rehband I worked for some days (2, 3?) on it.

rehband

@Chris'ssis What did you find?

Chris's sis

@rehband Here

3

rehband

12:39

@Chris'ssis Wow, it looks like magic, I applaud you

Balarka Sen

Have you thought of a corresponding $[0,1]^n$ version @Chris'ssis?

Jasper Loy

@Chris'ssis You are a genius.

Balarka Sen

Let's all star it.

Chris's sis

@rehband yeah, it's about magic there ... :-)

@BalarkaSen Sure, you can find such a version in Ovidiu Furdui's book.

@JasperLoy A genius that fails many job interviews ... :-)

Jasper Loy

@Chris'ssis The interviewers are not fit to judge you.

Balarka Sen

12:42

I was under the impression that they were not fit to judge anyone.

Nick

@BalarkaSen: What do you usually mean by $\zeta (x)$

Balarka Sen

@Nick $$\sum_{n=1}^\infty \frac1{n^x}$$ mostly

Chris's sis

@JasperLoy At the last interview I felt like the most stupid person in my country. They seemed like some gods that knew everything.

rehband

@Chris'ssis What jobs are you applying for?

Balarka Sen

@Nick If you are talking about $\Re[x] > 1$

Nick

12:43

@BalarkaSen: Now, what is $\Re[x]$?

Balarka Sen

Real part of a complex number

blue

do we know the rank of the additive subgroup of $\Bbb Z[\zeta]$ generated by the primitive roots of unity? since the sum of primitive roots is an integer, it can't be freely generated by them.

Nick

Oh

Balarka Sen

@blue!

Chris's sis

@rehband FMEA coordinator (en.wikipedia.or/wiki/Failure_mode_and_effects_analysis) It's similar to the mathematical analysis, but where you analyze processes, not functions. It's a very hard job.

blue

12:44

ah drats I have to go on laptop to pin the star thing

Balarka Sen

responsibilities.

Nick

@BalarkaSen: And if it's not?

Balarka Sen

@Nick then things get a wee bit complicated.

Nick

... I'll take your word for it.

rehband

@Chris'ssis Ok, nice

Nick

12:46

@BalarkaSen ..and $\{x\} = x - \text{floor}(x) $?

Balarka Sen

what about it

Chris's sis

@rehband So, when you are ready, try to find a solution to that integral. You'll be impressed by its beauty. The way to go (at least my way) is absolutely fascinating.

Nick

@Balarka: What is $\int{\{x\}}\cdot dx$ ?

rehband

@Chris'ssis I'll work frantically, but it's gonna take a while regardless :) Can't wait though

Balarka Sen

@Nick I am not the integral guy here. But it should be relatively easy. Start by integrating $\lfloor x \rfloor$

Nick

12:47

.... How do we do that?

Balarka Sen

Well, I'd see it's behavior on piecewise intervals to begin with.

Nick

Its not continuous... I think we need limits

Balarka Sen

maybe, maybe not. i don't usually think about integrals much, ask @Chris'ssis

Nick

@Chris'ssis: Doth this silly mortal be wrong in asking thy lordship a silly query?

rehband

@Nick Haha

robjohn

12:53

@Chris'ssis I have reduced it to $$\sum_{j,k,n=1}^\infty\frac1{kn(k+n)(j+n)^2}$$ I will work on it again in a bit...

Nick

@Chris'ssis: $$\int{\lfloor x \rfloor}\cdot dx\space =\space ?$$

@BalarkaSen: I just looked into differentiating ${\lfloor x \rfloor}$ as well.

Balarka Sen

Differentiating that is pretty straightforward.

Daniel Fischer

Chat guidelines | $\LaTeX$ in chat

@robjohn Pin ^^ ?

Nick

Balarka Sen

13 mins ago, by blue

ah drats I have to go on laptop to pin the star thing

Nick

12:58

@BalarkaSen: Yeah, nice series, ugly graph

Jasper Loy

@DanielFischer @blue can pin too but he needs to do it as @anon, lol.

Daniel Fischer

@JasperLoy Didn't see blue was here.

Nick

@blue: You're @anon !??

Balarka Sen

Grr @Jasper, you leaked the facts.

Daniel Fischer

@Nick No, they only share a body.

Balarka Sen

12:59

Ah, here is he.

anon

grumbles

Transcript for

$Mathematics$ Mathematics