Mathematics - 2012-07-16 (page 2 of 4)

@JonasTeuwen He's called Einsiedler. He looks a bit like a general or soldier. Quite scary, I thought. Now I read an old exam protocol and the notes said "The atmosphere was very tense."

Jonas Teuwen

@MattN Aha, I know Einsiedler.

Matt N.

9:08 AM

Then I thought: "I am a dead person."

Jonas Teuwen

@MattN So you are just scared...

Matt N.

@JonasTeuwen What?? How come that?

Jonas Teuwen

@MattN Hmm, yeah, I can imagine that he can make it tense, but he still is reasonable.

Matt N.

He will execute me.

Jonas Teuwen

@MattN Nah.

@MattN He will not.

Matt N.

9:09 AM

@JonasTeuwen No, you don't understand: I have to do it.

Jonas Teuwen

@MattN If you really don't know the stuff, go there and tell him that you want to cancel and try again next possible period.

@MattN Oh, why?

You cannot take it another time?

Matt N.

@JonasTeuwen Cancelled it too many times. I have run out of time.

Jonas Teuwen

@MattN Run out of time in what way?

What usually happens in these cases is that the "bad" things that can happen are surely exaggerated.

Matt N.

@JonasTeuwen There is a time limit in which you can collect n credit points for this BSc's. But I can only take so much stress per term. So I didn't collect that many points. So it's this term or never.

Jonas Teuwen

@MattN Then you should talk to some university official, the student dean or whatever it is called there.

Matt N.

9:11 AM

@JonasTeuwen So how come you know him?

Jonas Teuwen

I am pretty sure they have exceptions.

Matt N.

I'm honestly scared to death.

Jonas Teuwen

@MattN I studied stuff he did, studied other material.

Yes, I understand, but I don't see a good reason why.

Matt N.

@JonasTeuwen So you know his stuff but you have never met him in person.

Jonas Teuwen

@MattN I would not worry too much about the collection of points now, nothing to do about it.

@MattN I have met him!

Have to remind myself where...

Matt N.

9:12 AM

@JonasTeuwen I don't. I only worry about the exam.

Jonas Teuwen

@MattN Priority 1) Exam. I would just go.

Martin Sleziak

Your exam is today @MattN?

Jonas Teuwen

@MattN He will not execute you, just make it a bit hard on you perhaps, but you can be honest in the fact that you do not understand it well enough yet.

I mean, if you try some bluff... that will make it tense.

Martin Sleziak

functional analysis?

Matt N.

@MartinSleziak No, on the 20th of August.

@MartinSleziak Yes.

Jonas Teuwen

9:14 AM

@MattN What... the 20th?

Martin Sleziak

Don't you think t.b. would be disappointed if you did not go?

Jonas Teuwen

@MattN What are you worrying about, you have plenty of time! If you have trouble with it just ask us!

Perhaps, tb might be so sweet to help you a bit too, but I don't know. Can always ask?

Martin Sleziak

BTW you have plenty of famous people teaching you there - Halbeinsen, Einsiedler.

Matt N.

@JonasTeuwen Wow. I think this is actually great advice. I think I will tell him exactly that: I'm not very good at this, I studied a lot and I want to pass. So I hope you will pass me.

Jonas Teuwen

@MattN No, skip the last sentence.

Matt N.

9:15 AM

@MartinSleziak Halbeisen is very nice.

Jonas Teuwen

@MattN The point is... if you just start saying stuff that are basically nonsense because you don't know it well... 8-).

Then stuff can get quite tense.

@MattN In any case, priority 1) Calm down.

20th of August should be fine, I have seen his course notes.

Matt N.

@MartinSleziak I have actually thought of that. And the answer is: probably yes, so I have to go. But it only makes it worse: he will be disappointed if I suck. Regardless of the grade: he's spent all this time on me and I still don't get it because I'm slow :,(

Jonas Teuwen

Just looks a bit like a phone book, but for the rest it is not so hard.

@MattN Nah, you are thinking for him.

He spends many time on other people as well, so that would not be of any negative impact on his "disappointedness".

Martin Sleziak

Anyway, I think you still have time to learn quite a lot.

Jonas Teuwen

You have time to learn it 10 times.

Matt N.

9:17 AM

@JonasTeuwen He's been helping me already, like every day. Not just mathematically, but talking to him cheers me up and makes the whole thing much more bearable and less depressing.

Jonas Teuwen

@MattN That's what friends are for uh...?

Matt N.

But I have to study commutative algebra for the exam on the 9th of August!!

Jonas Teuwen

That is a BSc course?

Matt N.

Yes.

Jonas Teuwen

When is the resit for commutative algebra?

Ah! Kickass. I wish I studied there.

Matt N.

9:18 AM

@JonasTeuwen Ok.

Jonas Teuwen

@MattN Did you already speak to the student counselor?

Matt N.

@JonasTeuwen There are no resits.

@JonasTeuwen No.

Jonas Teuwen

@MattN Maybe you should do that.

They helped me with similar problems (very similar).

Matt N.

They won't help me understand faster and better.

Jonas Teuwen

And I'm pretty sure the Swiss ones are also good enough.

@MattN Yes, but they can help you with the practical nonsense which is poisoning your mind.

Matt N.

9:19 AM

I want to understand this lecture. Before the exam. And in general.

Jonas Teuwen

Which makes you think it has to work and it has to be faster.

Matt N.

Well.

I think you and Martin have already helped me just now : )

Do you count as counselors?

Jonas Teuwen

@MattN Good, but anyway speak to the student counselor if you "ran out" of possible resits.

@MattN Sure.

@MattN They might tell you about possibilities to get extensions and what not. Very useful, also they might tell you that faster, faster, faaaaster is bullshit.

Additionally, you are paying for them already, so use the service 8-).

Matt N.

: D

Jonas Teuwen

I took like 8 resits for an exam.

Matt N.

9:22 AM

@MartinSleziak I will do of course.

@JonasTeuwen At my uni you can resit each exam at most once. After that it counts as failed.

Jonas Teuwen

Well, I didn't show up 6 times, then the student counselor was like... well, this is not going to work this way!

Matt N.

No matter how much time in total you have left.

@JonasTeuwen : D lol?

Jonas Teuwen

Yes, but the counselors can probably override it.

Like: "Im Krank Im Kopf, Bro...".

Matt N.

Hm. Actually maybe you are right. I should find out where this counselor is.

@JonasTeuwen Wouldn't I have to have a proper doctor for that? I think the counselor at uni is just a psychologist who you can talk to.

Though maybe that's wrong.

Oh dear. Today is probably a bad day because I woke up early again and I'm very tired.

Jonas Teuwen

@MattN Yes, maybe, but... doctor? Bit overkill initially. The counselor is more for practical things like extensions and so on and they might send you to the school psychologist. That one can see if you are indeed very Krank or not.

Matt N.

9:25 AM

Thanks @JonasTeuwen and @MartinSleziak. I feel much less stressed now.

Jonas Teuwen

Counselors see mostly overstressed students anway.

So, they are quite used to handling those people.

Matt N.

But I think they will see that I'm quite normal : /

Jonas Teuwen

@MattN Excellent. Now have a walk.

Matt N.

: D

Jonas Teuwen

@MattN Well, maybe you are...? Just very stressed up about basically... not much.

But that also warrants help.

Matt N.

9:26 AM

@JonasTeuwen I think you are right.

It's nothing.

I just have to ignore that there is an exam.

Just study and then go there and do it.

Tell Einsiedler that I want to pass.

Jonas Teuwen

Hmm, yes and talk to the counselor about the practicalities and advice. They have many students with such problems, although it probably doesn't like like that for you. Because they, well, hide it. Like you probably.

Matt N.

@JonasTeuwen These are the notes.

I missed that deleted comment.

Jonas Teuwen

@MattN I know them :-).

Matt N.

Ah : D

I think I won't.

Jonas Teuwen

@MattN Actually, those notes contain not so much material if you understand the idea behind it. I would try to go for that first and then the technicalities.

Matt N.

9:32 AM

@JonasTeuwen No. The reason why I'm so bad at maths is because I'm so insecure. And I'm insecure because I suck at doing sums and basics and technical details.

I need to work on that.

Anyway.

Jonas Teuwen

@MattN Yea, good observation I think.

But understanding what is going on is really the most important part.

Don't fear the syntax.

You are probably way better at it already when you stop caring if you do it wrong or right. Happened with me.

Matt N.

You need to do it right during the exam.

Jonas Teuwen

Can make mistakes. Just not retarded ones.

Matt N.

Yeah, exactly.

But retarded ones are my specialty.

Anyway. I'm going to stay logged on here (for now) but going back to studying the notes.

Jonas Teuwen

@MattN Or have a walk.

Matt N.

9:34 AM

See you later! And thank you!

Jonas Teuwen

See you!

Henning Makholm

10:46 AM

@PeterTamaroff You missed me by a few minutes, I think.

user19161

11:06 AM

@old What a lovely new avatar you have!

Old John

@JasperLoy Hi. I changed it last night when we discussing whether it was a good idea to use a real photo as an avatar.

I thought it suited my advanced years :)

user19161

@OldJohn Hmm. Use whatever you like, not what others like.

Old John

@JasperLoy I quite like this one for now - I was getting bored seeing my own photo

user19161

@OldJohn Yeah I like it too. You look like God now.

Old John

@JasperLoy Hmm - not quite the image I was trying to project :(

user19161

11:12 AM

@MattN Hey though you don't like to talk to me, I just want to wish you good luck! May you overcome whatever problems you have!

J. M.

@Old John, nice caricature.

:D

Old John

@JM Thanks :)

Bit worried that it makes people think of god - might have to change it

Rajesh D

Hello

user19161

@OldJohn I got that idea only because someone mentioned it I think.

user19161

@RajeshD How do you find Kuhnel so far? Good right?

Rajesh D

11:25 AM

@OldJohn : IMHO I don't think it makes think of god. It makes me think of an old eskimo

@JasperLoy I have not started it yet Jasper, just had some other work, hope I'd start soon.

Old John

@RajeshD That is OK - I don't mind that image

Rajesh D

@HenningMakholm and @OldJohn look the same a bit.

Old John

@RajeshD Nah - he looks much younger

Rajesh D

agree

NickHaliday got a funny gravatar. I guess its Shaitan or something. I am not sure what it is?

J. M.

@RajeshD Looks like Bat-somebody...

Rajesh D

11:32 AM

yes

Jonas Teuwen

Hmm... second pass grading 8-(.

Rajesh D

@JonasTeuwen people fail?

Jonas Teuwen

Fail more people in the second pass.

Rajesh D

I don't know what second pass means?

Jonas Teuwen

First person grades, then a second one the same stuff.

Rajesh D

11:34 AM

Oh too much of a scrutiny

Ilya

@Jonas: hey!

how are you?

@Rajesh hulo

Jonas Teuwen

@Ilya Hi :-).

I'm okay, you?

Ilya

fine

how is grading?

Jonas Teuwen

@Ilya Sucks.

Ilya

:l(

(the sad Pinocchio smiley)

Jonas Teuwen

11:41 AM

@Ilya 8-).

Rajesh D

@JonasTeuwen How are you doing?

@Ilya Hi

Ilya

@Jonas: if I'm working with contraction semigroups, Hille-Yousida gives necessary and sufficient conditions that a linear operator (A,D(A)) generates a contraction strongly continuous semigroup, or not necessarily strongly continuous?

Rajesh D

@JonasTeuwen How are you doing?

Jonas Teuwen

@Ilya It is a $C_0$ generating theorem :-).

@RajeshD Okay as I said to Ilya. You?

Rajesh D

fine

Ilya

11:44 AM

@JonasTeuwen cool, so if I satisfy conditions, then I get continuity for granted?

Jonas Teuwen

@Ilya Yes!

@Ilya Did you see the book?

Ilya

I only have to be able to verify conditions now, hack

Rajesh D

Oh No, I wanted to ping @Ilya but it got to @Jonas by mistake...anyway same to Ilya

Jonas Teuwen

@Ilya You also have Lumer-Phillips.

Ilya

which is for Hilbert space?

not my case, unfortunately - I don't have cool basis measure

Jonas Teuwen

11:46 AM

@Ilya Hmm,... I thought not? Just Banach.

Ilya

ok

I'll take a look

and I'll need to talk to you, perhaps

that's why I wondered when are you free

Jonas Teuwen

@Ilya Yes, tomorrow and the rest of the week!

@Ilya It is raining... gently.

Looks like a bloody mousson.

Ilya

@JonasTeuwen not that red :)

Rajesh D

12:05 PM

@Ilya @Jonas : suppose there is a periodic function which is smooth but with one problem, it is not defined at one point (in the main period and hence in every period). Can we still talk about its Fourier series, and other transforms, etc.,?

out for a jog

Ilya

so in which way is it smooth then?

robjohn

Good day all!

@Ilya if you stroke from the front to the back :-)

2

Ilya

animal-surface-function?

that is just more a vector field, I guess

with a singularity

:)

robjohn

@Ilya fuzzy-logic-function :-)

but I was thinking animal function

Jonas Teuwen

@Ilya Mm... One point? Same Fourier series, right bro?

Ilya

12:21 PM

I didn't work them since my BSc, but one is also interested in uniform convergence, no?

@JonasTeuwen and also, same with what?

Jonas Teuwen

12:33 PM

@Ilya Uh, integrals :-). It is an integral transform, it cares very little about bad points.

BenjaLim

1:02 PM

yo yo yo yo yo yo

user19161

Yo!

user19161

@robjohn Can't you also do it from the back to the front?

robjohn

1:29 PM

@JasperLoy yeah, but it's not as smooth that way :-)

Former_Math_Addict

@robjohn You can stroke it to the east and stoke it to the west...

Frank Science

Hello, everybody.

user19161

1:50 PM

@Former_Math_Addict Congrats for finishing rehab!

Frank Science

@JasperLoy Which dictionary software are you using?

user19161

@FrankScience Software? I don't install any. I either check paper dictionaries or search online.

Frank Science

@JasperLoy Oops. I intend to try dictating VOA special English.

user19161

@FrankScience What is VOA?

Frank Science

@JasperLoy Voice Of usA.

Jeff

2:01 PM

Hi folks. A web site says the Predicate logic symbolization of "If any belugas live in North America, then Shamu is a beluga" is $(\exists x)(Bx & Nx) > Bs$. Shouldn't the 'exists' really be a 'for all'?

anon

\&

well, it says if there is a beluga living in NA, then Shamu is a beluga. (unfortunately "belugas" plural can mean "either singular or plural" when taken casually.) that's existential.

Henning Makholm

@Jeff It it was a $\forall$, it would mean that "if everything in the world is a North American beluga ..."

Matt N.

If I have $\| x + y \| = \|x - y\|$, can I conclude that $x=y=0$?

anon

no. just means x,y are orthogonal.

square both sides and use polarization

Jeff

@HenningMakholm ok. i see now. ty.

@anon ty

Henning Makholm

2:09 PM

@MattN x can be arbitrary if only y=0. Or vice versa.

Jeff

(what a great chat room!) :D

Matt N.

@HenningMakholm Now that you mention it it's quite clear. Thanks.

Polarization gives me $\|x+y\|^2 + \|x - y\|^2 = 2 \|x\|^2 + 2 \|y\|^2$

anon

I meant subtract, not add them.

Matt N.

What I posted is what is called the polarisation identity. Is using that not what you meant?

anon

I meant this

Matt N.

2:14 PM

Yes. I am trying to show that if I have a vector space satisfying the polarisation identity then this^ defines an inner product. So I'm trying to show that if $(x,y) = 0$ then $x=y=0$.

Since it's zero I have $\|x+y\| = \|x-y\|$. Now I want to conclude that $x = y = 0$.

Jonas Teuwen

$y = x$?.

anon

$(x,y)=0\implies x=y=0$ is not a property of inner products is it?

Matt N.

Ah crap, I need $(x,x) = 0$.

anon

$(x,x)=0\implies x=0$ is

Matt N.

Doh. x_x

Thank you.

Henning Makholm

2:16 PM

@MattN Sorry then. I assumed by default that your x and y were reals :-)

Matt N.

@HenningMakholm : )

unNaturhal

2:27 PM

Hi guys!

Any interesting function to study? (real-valued of real variables)

J. M.

@unNaturhal sine, cosine, exponential...

unNaturhal

@JM It's the same. But I prefer if in any case you put Absolute values :)

J. M.

Well, you were asking for interesting...

user19161

@unNaturhal But on a more serious note, have you studied the trigonometric and exponential functions in detail? They are really important.

unNaturhal

@JasperLoy In detail? What do you mean?..

user19161

2:33 PM

@unNaturhal For example, do you know how they are defined in various ways analytically, from which the definition of $\pi$ follows?

Gigili

@JM Everyone's opinion is bound to be subjective.

Hullo.

user19161

@Gigili Indeed, everyone's opinion is bounded in the space of opinions.

CLarue

Is there a way to get the Tex on the chat to format?

unNaturhal

@JasperLoy Mmmmh.. I know the various sets of definition of the various function (sin, cos, tan, cotan, arctan, arcsin, arccos), how their chart is (indicatively).. there is something else that I have to know?

user19161

@CLarue Yes, use math.ucla.edu/~robjohn/math/mathjax.html

CLarue

2:38 PM

Excellent, thanks

user19161

@unNaturhal Ah I see you know not what I am referring to. I was talking about how they are defined rigorously in analysis. You studied analysis right?

unNaturhal

@JasperLoy Yes, right

user19161

Sometimes the simple things you studied in high school takes hundreds of pages to formalize.

unNaturhal

(I'm studing right now for the exam xD)

user19161

@unNaturhal OK good luck!

user19161

2:41 PM

@unNaturhal You may find such a treatment in any good analysis text, for example Rudin's chapter on Special Functions.

unNaturhal

@JasperLoy Yeah, but I studied it again at the college (but there wasn't hounders of pages... just 10.. 20)

@JasperLoy Ehm.. I just wanted an exercise, a function to study, 'cuz I finish all exercises on my notes..

user19161

@unNaturhal OK, then you should go have a beer now!

unNaturhal

@JasperLoy Ahahahahah

user19161

@unNaturhal There is no point doing routine exercises over and over again. It's a waste of time.

user19161

In fact the more routine exercises one does after obtaining some proficiency, the more stupid one becomes.

unNaturhal

2:47 PM

@JasperLoy It isn't comfortable...

@JasperLoy o.o

user19161

@unNaturhal Therefore I used the adjective "routine" and the noun "proficiency" without which the statement is false.

CLarue

Completely contrived: Let $f(x)$ be the number of consecutive increasing digits after the decimal point in the decimal expansion of x, unless it's 10, in which case $f(x)=0. Let

oops

one moment

Let $g(x)=\sum_{n=0}^\infty f(x-n)10^n

$

anon

you can edit your own comments withing a time interval

CLarue

and delete, good to know

J. M.

@Gigili True.

user19161

2:52 PM

@anon I wonder why they can't make the time unlimited...

robjohn

3:22 PM

@JasperLoy transcripts and histories and ...

Gigili

@robjohn And whatnot. Hello!

robjohn

@Gigili how was your weekend?

Gigili

@robjohn Quite boring, yours?

robjohn

@Gigili quite nice. We saw a murder mystery/dinner on Saturday night.

It was quite entertaining.

Gigili

A murder mystery? Sounds exciting.

robjohn

3:28 PM

Too much of the mystery was contained in a postcard that had been written tersely and was read quickly. I guess you have to make it so that not everyone gets it, but that seems like cheating a bit.

user19161

@robjohn Well, all movies cheat you of your time!

robjohn

@JasperLoy Only if you didn't like the movie, I would say.

user19161

@Gigili It's about me killing you with one bullet as you instructed that day.

Gigili

@JasperLoy On the condition that you weren't killed with one bullet beforehand.

robjohn

Jul 9 at 13:29, by Gigili

@JasperLoy Kill me with one bullet.

user19161

3:43 PM

@robjohn I just noticed you are up so early today.

robjohn

@JasperLoy early? I've been up for at least 3 and a half hours.

@JasperLoy what time is it there?

user19161

@robjohn 11.46 pm. I don't sleep normal hours though.

user19161

@robjohn I took your time to be LA time.

Gigili

Hi @Ilya?

Ilya

hi @Gigili

robjohn

3:49 PM

@JasperLoy It is and it is 8:48 AM here.

Gigili

@robjohn Wow, you get up at 0500 AM?

That's really something.

@Ilya hawaryoo?

Ilya

@Gigili fine, what about you?

Gigili

I'm OK, thanks.

Matt N.

4:07 PM

@robjohn Do you happen to know about Fourier series?

Hm, seems to be away. Then I'll badger Jonas when he's around.

unNaturhal

4:19 PM

Excuse me

When a function is odd

I can study it for $(0; +\infty)$? Just like as it was even?

robjohn

@MattN. what's up?

Matt N.

@robjohn Hey! I've been thinking about Fourier series. They are the representation of a function $G \to \mathbb C$ in terms of its characters, right?

And in functional analysis we usually take $G=S^1$, right?

robjohn

@unNaturhal I'm not sure what you mean exactly, but since $f(-x)=-f(x)$, if you know the values of $f$ on $[0,\infty)$ then you know the velues of $f$ on $(-\infty,0]$

unNaturhal

@robjohn It's exactly what I want to know :) Thanks! :D

robjohn

@MattN. Fourier Series deal with periodic functions, essentially on $[0,1\pi]$ or some compact interval.

Matt N.

4:25 PM

@robjohn Well we get $G = [0,1]/\sim = S^1 = \mathbb R/ \mathbb Z$...

robjohn

@MattN. Ah, yes, I was misreading your initial commnet

Matt N.

Then we can scale that to whatever we like.

Or shift it by the period.

@robjohn I've been thinking for which functions we should be able to compute Fourier series.

And I thought that say, $f_n$ is periodic on $[-n,n]$ so that we can compute its Fourier series.

robjohn

@MattN. by which functions, are you asking which domain, or simply given a compact domain, which functions on that domatin?

Matt N.

Then by letting $n$ tend to $\infty$ we can also compute Fourier series of non-periodic functions.

anon

...

Matt N.

4:29 PM

@robjohn Given a compact topological group $G$, which functions $G \to \mathbb C$ have a Fourier series.

Hm. I'm not too sure actually.

@anon "..." = "your question is so dumb that it has left me speechless"?

I understand Fourier series on finite abelian groups. Now I'm trying to generalise.

anon

I'm not sure if $n\to\infty$ works out generally. At any rate, is the Fourier series is a special case of representing a function via inverse Fourier transform with the Haar integral?

Matt N.

I don't know what the Haar measure is. But the way I learned it a Fourier series is writing the function as a linear combination of the characters of its domain.

anon

that is true, but you're looking for a more general way to frame the idea

Matt N.

More general in what way?

anon

"linear combination" needs to be generalized to Haar integral, I believe. Consider $G=\Bbb R$ with uncountable dual group $\cong \Bbb R$. The inverse Fourier transform needs to be an integral (coefficients of the linear combination are in fact inverse Fourier transforms of the original function).

Mark Dominus

4:41 PM

@anon: use of $\vee$ for logical or predates $\wedge$ for logical and by quite some time. $\vee$ is an abbreviation for Latin "vel". Until mid-20th century logical and was symbolized by "&", concatenation, or dot. Apologies if you already knew all this.

anon

I didn't. But mid-20th century was like three of my lifetimes ago!

Matt N.

@anon Right. I didn't realise the dual of $\mathbb R$ was isomorphic to $\mathbb R$. In fact, even now that you tell me it still seems inconceivable. The dual of $R/Z$ is isomorphic to $Z$. And as a set, $R/Z$ is the same as $(0,1)$ which is (as a set) isomorphic to $R$.

Mark Dominus

"The symbol ∧ for logical conjunction "and" was first used in 1930 by Arend Heyting." jeff560.tripod.com/set.html

But $\vee$ goes back to 1902 in the work of Russell.

anon

Well, sets are rather barren.. The dual group requires group homomorphisms to be continuous, which is key. We can think of $S^1$ as being a piece of $\Bbb R$ chopped out with boundary conditions forcing the dual group to discretize. (Speaking informally.)

Matt N.

Yes ok, but it's not obvious to me how the identification of zero and one forces the characters to become discrete.

anon

4:46 PM

What's really cool is the dual of $\Bbb Q$ is the adeles $\Bbb A_{\Bbb Q}/\Bbb Q$.

Zhen Lin

Hmmm... this rings a bell...

anon

@MattN. the elements of the dual of $\Bbb R$ are just complex exponentials. If you force $e^{i\theta 0}=e^{i\theta 1}$ this makes the available $\theta$ values turn from a continuum into a discrete thing.

Zhen Lin

@MattN. You asked this question before, in a way.

Matt N.

@ZhenLin Yes in a way.

Transcript for

$Mathematics$ Mathematics