Mathematics - 2015-04-09 (page 1 of 4)

Ixrec

00:02

@evinda If I'm understanding the question right, it seems like two nodes a and b will only maintain the same relative order under all topological sorts if the path(s) between them are one-way only, eg there is a path from a to b but not vice versa

so working that out algorithmically would probably mean running something like Djikstra's and checking what paths turn out not to exist

evinda

@Ixrec I want to find algorithmically the number of nodes, that are not connected to each other with any path, and have the same relative order.
Suppose for example that we have graph and the nodes are a,b,c,d,e.
b and c, b and d, c and d, a and c, and d are not connected to each other.

Ixrec

if they aren't connected by any path, how do they have any order at all?

evinda

I mean something like that @Ixrec

Ixrec

ah, ok

seems like after the first "fork" in the graph you can rearrange the remaining nodes however you want

evinda

We apply DFS and we compare the finishing time and create a list with the nodes in descendind order based on the finishing times @Ixrec

Ixrec

00:07

so traversing the graph until the first fork gets you the list of "stable" nodes, in this case just e

ah no we also have a < b no matter what

and we can do things like diamonds

hmm

derp

assuming you're only interested in DAGs

an arrow from a to b means that a and b always have the same relative order

and that property is transitive

so that's easy to calculate

evinda

@Ixrec I am only interested in DAGs... but calling the list that we can get from a topological sorting isn't unique so there isn't only one possible path

@Ixrec And it doesn't hold that two nodes always have the same relative order

Ixrec

if it's a DAG, there is by definition at most one path between any two nodes

just because one topological sort puts a in front of d doesn't mean there is a path from a to d (there isn't)

er, wait

correction: in a DAG, all paths between two nodes go in the same direction

so if there is at least one path from a to b, then a and b always have the same relative order

your statement implies that the result of a topological sort is a path through all the nodes; obviously that's not true for graphs like the one you drew above

evinda

@Ixrec Always doesn't the list that we get contain all the nodes?

Ixrec

it contains all the nodes, but it's not a path

evinda

I meant that the result will be a list @Ixrec

@Ixrec And since at some steps we will have different paths that we could follow, there could be several lists

Ixrec

00:21

I think I got that part when I saw your diagram

evinda

@Ixrec And I want to find from two different lists the number of nodes, that are not connected to each other, and have the same relative order.

Ixrec

wait, you want to work out if two nodes are connected or not based solely on topological sort output, without any further access to the graph?

I doubt that's possible

also, what do you mean by "not connected"? if you mean "there's no path from one to the other" then that's the same thing as having the same relative order

evinda

@Ixrec What do you mean with "without further access to the graph" ?

Ixrec

in which case if you had all the topological sorts you could do it; only some of them wouldn't work

@evinda "without any additional information about the graph"

evinda

@Ixrec I mean that "there's no path from one to the other"

Ixrec

00:27

ok, then I'm pretty sure this is only possible if you have all possible topological sorts; just two of them won't tell you very much

evinda

Suppose that we have all the topological sorts. How can we find the number of the nodes that have the same relative order and the number of nodes that don't have the same relative order? @Ixrec

Ixrec

in that case, you just look for pairs of nodes that always have the same relative order in those sorts

I don't think there's any way around brute-force checking every pair in (potentially) every sort

and g2g now

night

evinda

@Ixrec So do we have to look at each topological sort the number of pairs that have the same relative order and find the minimum?

Sayan Chattopadhyay

02:22

Hi@DiscipleofBarney

Disciple of Barney

Hello @SayanChattopadhyay

Sayan Chattopadhyay

How are your jokes going......@DiscipleofBarney

Disciple of Barney

Well

Sayan Chattopadhyay

@JC574 I got the value for epsilon yesterday and computed the proof
$\epsilon$=$min[\frac{\epsilon}{{1+c}^2},1]$

Is it right

Its(1+c)^2@JC574

Karim Mansour

02:51

4

Q: Complete example of haar measure on compact groups like $GL(n,R)$

I am currently reading the proof of existence of haar measure, but I learn better mostly by examples so I would like examples of explicit computation of haar measure mainly on any $Gl(n,R)$ or any lie groups and please also explain the details as I didn't take a course in harmonic analysis I want...

added bounty

Sayan Chattopadhyay

03:28

Hi @JC574

Sayan Chattopadhyay

04:53

youtube.com/watch?v=HtWvNvcTFys the best song i ever heard

The Dark Side

05:20

Dear mods, drawing your attention here

Downvotes on 5 different answers within a total of 3 minutes probably qualifies as serial downvoting, no?

The Dark Side

05:41

@robjohn (Pinging to draw attention, for the above.)

Sayan Chattopadhyay

Hi @Ramanewbie what are you working on?

Sayan Chattopadhyay

06:13

One has
x/1+x^2−c/1+c^2=(x−c)1−cx/(1+x^2)(1+c^2)
and therefore
∣∣∣x/1+x^2−c/1+c^2∣∣∣≤|x−c|(1+|c||x|)
When |x−c|≤2 then |x|≤|c|+2 and therefore
1+|c||x|≤(1+|c|)^2
independently of x.
Now let an ϵ>0 be given. I claim that
δ:=min{ϵ(1+|c|)^2, 2}
does the job.
Hence proved@Balarka

Balarka Sen

True, but would have preferred if you had done it yourself rather than getting the answer from here.

You have merely copied and pasted Christian Blatter's answer :P

Sayan Chattopadhyay

Oh i have just checked my answer from his by posting a question

Balarka Sen

hard to believe :P

ᴇʏᴇs

@Bal What can you believe

Balarka Sen

anyways, i stick to my opinion : you should revise the chapter on continuity, seeing that you're having trouble with the proofs. a bit carefully this time, and do all the exercises.

Sayan Chattopadhyay

06:18

i took |x-c|<1 and only change i made was |x-c| greater than or equal 2

Balarka Sen

hi @ᴇʏᴇs

Sayan Chattopadhyay

hi Mr eyeglasses

but @BalarkaSen i still didnt understand something about my definition of continuity why is it wrong

the limit one

Balarka Sen

your definition of continuity is correct, but it does nothing to help you prove that a function is continuous.

try reading the chapter carefully, you'll get the ideas.

@ᴇʏᴇs how are your studies with topology going?

ᴇʏᴇs

@Bal Okay I guess

Sayan Chattopadhyay

ok i will come back to you again

ᴇʏᴇs

06:24

@Bal I'm gonna try to get to the fundamental group section in Munkres by September

Balarka Sen

@SayanChattopadhyay then you also have to show regions of convexity/concavity and increase/decreases of $x/(1+x^2)$.

Sayan Chattopadhyay

ya i remember

Balarka Sen

@ᴇʏᴇs Definitely, it's cool stuff. But make sure you know Uryshon metrization theorem and Tietze extension theorem before it. They're the most nontrivial theorems in point-set topology.

ᴇʏᴇs

@Bal Okay

@Bal Actually my topology class might do those next semester

Balarka Sen

good, 'cause they are cool stuff.

uryshon's theorem actually tells you that most hausdorff spaces are metric spaces.

Disciple of Barney

06:31

@TheDarkSide You should wait a while before sending such info to mods

ᴇʏᴇs

@Bal next semester we cover metric spaces, topological spaces, continuity, Hausdorff condition, compactness, connectedness, product spaces, quotient spaces, basic category theory, basic homotopy theory, fundamental group, covering spaces, homology

Balarka Sen

sounds nice.

Huy

How you doing, @BalarkaSen?

Balarka Sen

so-so. what about you?

Huy

My back hurts. I think I slept in a bad posture. Apart from that pretty good. Haven't done any serious maths for a while though.

What are you studying these days?

Balarka Sen

06:42

Linear algebra, mostly. I have ignored fundamentals for too long.

Huy

Like what exactly?

I can't imagine you not knowing the important stuff about linear algebra.

Balarka Sen

I don't know about rank-nullity theorem, for example. :P. Barely know about inner products.

Huy

Wow, really? You never used linear algebra then, right? :D

I even taught my students rank-nullity theorem, without proof however.

Balarka Sen

Technically, never. I know, it's pretty sad to not study such basic stuff but doing algebraic topology.

Huy

I see. Good for you you're looking at it now.

I'm sure it will be useful in whatever field you'll decide to focus on in the future.

Balarka Sen

06:47

I will be studying forms in the far future, so I guess some knowledge in linear algebra will turn out to be helpful.

Huy

Differential forms? You'll be too ashamed to tell Ted though, I suppose?

Balarka Sen

I have told Ted :P

Huy

:D

Balarka Sen

I will be studying multivariable calculus.

Huy

I see. I should do that again too, at some point. I hardly remember anything about it.

Balarka Sen

06:52

@Huy You've ever done Artin's algebra?

Huy

@BalarkaSen: No, I did Bosch's algebra.

Our professor was German, so we used a German textbook.

Why?

Balarka Sen

Ah. Artin actually does loads of linear algebra alongside algebra, so I am studying it from there. It does linear algebra quickly but steadily with many nice exercises and has the added advantage of me getting to revise algebra.

Huy

I see. But you've done loads of algebra, right? :D

Balarka Sen

Yes, but a little revision doesn't hurt. Gone through a few exercises this week.

Sayan Chattopadhyay

@BalarkaSen the function will be concave up for all values of x>1 and concave down for all values x<1. Am i right?

Balarka Sen

07:01

@Huy Artin teaches algebra pretty unconventionally. I goes through basic linear algebra, talks about group theory and then says a lot of stuff about symmetry, finishing with billinear forms and linear groups in chapter 8. The later chapters goes through rings, fields, basic algebraic number theory and galois theory.

Sayan Chattopadhyay

@BalarkaSen?????

Balarka Sen

@SayanChattopadhyay sorry, was a bit busy with other things. no, what you say is not right.

Sayan Chattopadhyay

oh....

let me try again

Huy

I only know the "popular" approach, doing groups, rings, fields and Galois theory.

Balarka Sen

I have personally never studied all of Artin. Going to do it this time, I guess.

Incurrence

07:05

Nice picture @Disc

Balarka Sen

I liked his style in group theory because while Dummit-Foote rambles on and on about semidirect products, Artin says almost nothing about it but gives a short intro to Todd-Coxeter algorithm to make sure that the groups he gets by counting extensions are well-defined.

It's cute.

@Sayan How did you find $x > 1$ and $x < 1$? Maybe writing down your approach will help?

Sayan Chattopadhyay

@BalarkaSen will it be concave up for x>-1 and concave down for x<-1

Balarka Sen

no, that's false. How're you coming up with these numbers?

Do you know how to inspect convexity/concavity of a function?

Sayan Chattopadhyay

using inflection points and the second derivative

Balarka Sen

So what have you tried so far for x/(1+x^2)?

Sayan Chattopadhyay

07:15

Sorry but can you wait for a minute i am checking my computations

user143442

are centers limit cycles?

Sayan Chattopadhyay

I made a mistake in computation

Balarka Sen

OK? So what are the inflection points you get now?

Sayan Chattopadhyay

i just found the mistake

i have to solve it

is it $\frac{4plus or minus \sqrt{20}}{2}$

Balarka Sen

Hell, no.

Disciple of Barney

07:27

@Incurrence It sure is

Sayan Chattopadhyay

oh...

Balarka Sen

Please post your approach so that we can point out what you're doing wrong.

Sayan Chattopadhyay

@BalarkaSen the second derivative is this right $$-\dfrac{2x}{{\left({x}^{2}+1\right)}^{2}}-\dfrac{4x{\cdot}\left(1-{x}^{2}\righ‌t)}{{\left({x}^{2}+1\right)}^{3}}$$

Incurrence

@DiscipleofBarney You downvote a heap

Balarka Sen

i can't read that.

Sayan Chattopadhyay

07:33

i know thats why i am typing it again

Disciple of Barney

@Incurrence I do my share, I clean up. You clean up more than I do though

Sayan Chattopadhyay

$-\frac{2x}{x^2+1}^2-\frac{4x\cdot{1-x^2}}{x^2+1}^3$

Balarka Sen

blergh

Incurrence

I have no idea what you did with that latex lol

Sayan Chattopadhyay

why is this not coming

Incurrence

07:36

$$-\frac{2x}{(x^2+1)^2}-\frac{4x\cdot(1-x^2)}{(x^2+1)^3}$$

Something like that??

Sayan Chattopadhyay

yup

is this the second derivative

ok

Balarka Sen

@SayanChattopadhyay yes, that seems ok.

Disciple of Barney

Not sure how pizza has so many more votes than I do though @Incurrence

Sayan Chattopadhyay

ok now wait

Incurrence

@DiscipleofBarney He does more than 40 a day

Sayan Chattopadhyay

07:38

set this = 0

Disciple of Barney

I have 360 and pizza has 507. How does he do that

Incurrence

@DiscipleofBarney He only downvotes questions that are there on the day

and he votes to delete some of these

If he downvotes and then it is deleted

Sayan Chattopadhyay

@BalarkaSen you will get the points

Incurrence

It still counts as a downvote, but he gets the vote back

Sayan Chattopadhyay

inflection points right?

Incurrence

07:39

So he gets $2$ downvotes for the price of that $1$

Disciple of Barney

Ah yes, that has happend a few times, to me

Balarka Sen

yes, @Sayan.

Incurrence

If he downvotes 40 in a day, and 10 of these get deleted he can get 50 now(and then some of those 10 can get deleted. If I had deletion privileges :\

Balarka Sen

So how the hell did you find $\frac{4 \pm \sqrt{20}}{2}$?

Disciple of Barney

@Incurrence I am a little surprised, I only really started voting a lot in the past couple weeks and I am already a top voter of the past year.

math.stackexchange.com/users?tab=Voters&filter=year

Sayan Chattopadhyay

07:41

oh wait the inflection points are plus or minus root 3 right

Incurrence

@DiscipleofBarney Oh so am I xD

Disciple of Barney

Yup. Seems like people don't vote enough, no wonder there is so much crap (not even upvotes)

Balarka Sen

@SayanChattopadhyay yes. now determine the regions of convexity/concavity :P

Sayan Chattopadhyay

:p i feel so ashamed of myself

Incurrence

@DiscipleofBarney Yep, maybe +.1 rep for each vote :)[jokes, I don't know what incentive would be good]

Balarka Sen

07:44

@Sayan The rest you can do by yourself, no need to tell me about it. The regions of increase/decreases is really no big deal either, you just have to inspect the first derivative.

Just study continuity carefully once again.

Sayan Chattopadhyay

Fine...then can i start algebra pls....

Balarka Sen

No. You still haven't mastered calculus.

Sayan Chattopadhyay

Awww......

Balarka Sen

Struggling with a single problem for two days is a sign.

Sayan Chattopadhyay

Onlyy continuity took me that long thats it...

Balarka Sen

07:46

And continuity is the most basic calculus.

If you don't understand continuity, studying about topological quantum field theory is pointless :P

Sayan Chattopadhyay

THats why i am saying after doing continuity

i will do linear algebra:p

or multivariable

Balarka Sen

No, after doing continuity, you will revise calculus by doing exercises.

Not sure if you've studied the required set theory either.

Sayan Chattopadhyay

oh my god i have finished set theory atleast calulus also but.......

Balarka Sen

Doing linear algebra after studying set theory and calculus is a good idea perhaps but I can't really say anything about it because I am studying linear algebra right now :P

@SayanChattopadhyay Well, you weren't able to count dearrangements then.

Sayan Chattopadhyay

You are studying that now????
why you have done till homology that means you have finished everything behind it right

Oh that was a different case i was just going out of sorts on that one

Balarka Sen

07:51

Nope, I haven't. I never studied linear algebra in depth.

Sayan Chattopadhyay

But Linear algebra dosent apply calculus right?

Balarka Sen

@SayanChattopadhyay OK, then count the number of bijective functions from $\{1, 2, 3, ..., n\}$ to itself.

@SayanChattopadhyay Calculus is a requirement for studying linear algebra, if that's what you mean.

Incurrence

@BalarkaSen Why are you testing him on this?

Balarka Sen

@Incurrence Because he claims to have studied set theory. He should be able to count bijective functions if he knows basic combinatorics that is in Hammack's book.

Sayan Chattopadhyay

No. of injective functions are $n!$ right @BalarkaSen

Balarka Sen

07:57

Prove it.

Incurrence

Injective to a set of the same size

Balarka Sen

Plus, prove that all the injective functions from a finite set A to itself are bijections. You need a theorem in Hammack's book, so we'll see if you have studied it properly.

Incurrence

@BalarkaSen You can do this without any theorems

Sayan Chattopadhyay

so lets see f(1) can take n values,f(2) can take n-1 values ,f(3) can take n-2 values and so on so the total number functions will be:
n*n-1*n-2*n-3............*3*2*1 and that is n!

The other one lets see

Balarka Sen

Very good.

Now prove what I have said above.

Sayan Chattopadhyay

08:00

Thanks a lot

Disciple of Barney

(he said sarcastically)

Incurrence

What textbooks have you already finished @Sayan?

Sayan Chattopadhyay

i did Hammock at the verge of finishing apostol only calculus as balarka sen told me not to do linear algebra

now

Disciple of Barney

@SayanChattopadhyay Study whatever you want, learning mathematics is not some linear path where you got to finish calc first and then do something else.

Sayan Chattopadhyay

Its not that.......but i do require calc in higher mathematics a lot and i think you require it Topology which is what i want to do

Balarka Sen

08:09

huh, and where does taking nonlinear path leads me to? going back to linear (no pun intended) algebra after studying algebraic topology.

Disciple of Barney

as an aside I disagree, I think putting off linear algebra is silly, and its nice to know linear algebra for just about everything you would study, either directly or through analogy

Balarka Sen

@SayanChattopadhyay i never told you not to do linear algebra. i told you not to do abstract algebra.

:P

Sayan Chattopadhyay

That does include linear algebra :p

Balarka Sen

no, it doesn't

linear algebra is way fundamental

Disciple of Barney

Are you saying you didn't learn any linear algebra while trying to study algebraic topology (in which case I am guessing you didn't understand much or going to linear is a breeze)

I also disagree with not going to abstract algebra

Balarka Sen

08:11

@DiscipleofBarney Well, I was only familiar with the basics of linear algebra.

Sayan Chattopadhyay

oh wait why is the breeze flowing the other way ....do linear and abstract algebra first then calc.............................

Disciple of Barney

I am not saying that

Sayan Chattopadhyay

Then?

Balarka Sen

It didn't hamper my understanding of algebraic topology as far as I studied it though.

Disciple of Barney

Do what your interested in and what you got to learn to do what your interested in

Balarka Sen

08:12

I am satisfied with the amount of understanding I gathered while studying it.

But I don't believe it's possible to understand cohomology without knowing forms, which finally leads to knowing a load of multivariable calculus, to study which I need to know linear algebra.

Disciple of Barney

Having some background in analysis or calculus is nice for studying topology (you didn't mention what sort of topology) is nice for concrete motivation and examples

Balarka Sen

I disagree : no analysis whatsoever is required for topology. calculus is enough.

Incurrence

I'll be back later, going to go for a walk

Disciple of Barney

No calculus is needed either, its mostly just having some maturity and it is nice to have some examples to draw from

Balarka Sen

well, i don't believe you can understand continuity in the sense of maps between general topological spaces if you don't understand continuity for functions from $\Bbb R$ to itself (nudge : @sayan)

robjohn

08:20

@TheDarkSide This should be taken care of automatically.

308

Q: What is serial voting and how does it affect me?

I just noticed that I lost a bunch of points from my reputation score on Stack Overflow, and I used the "reputation" tab on my user profile page to try and track down the cause. During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question ti...

support faq reputation voting serial-voting

Disciple of Barney

Topological spaces are so absurdly general that its that continuous functions $\mathbb{R} \to \mathbb{R}$ are not that comparable to continuous functions in general topological spaces. Like I said its nice to have as examples, but I don't see why learning about continuous functions and then learning about specializations to metric spaces or just $\mathbb{R}$ would be more difficult than learning continuity in calculus, which tend to try to "hide" or obfuscate the topology.

(and every general topology book has those examples)

Balarka Sen

Wait a second. Rank-nullity theorem looks like a mere consequence of the splitting lemma. What the hell.

Disciple of Barney

Its not harmful to at least try if that is what your interested in, that is basically what I am saying

Balarka Sen

Blergh. It's just splitting lemma.

Disciple of Barney

Are you studying linear from a particular book? @BalarkaSen

Balarka Sen

08:29

@DiscipleofBarney I dunno, one might wonder what the point of a function that pulls back open sets to open sets really is.

@DiscipleofBarney Yes.

Disciple of Barney

Which one?

Balarka Sen

Hoffman-Kunze and alongside Artin. I prefer Artin over Hoffman, though.

Disciple of Barney

Is it Artins Algebra? or does he have a linear book too.

Balarka Sen

That is it. Artin talks about a lot of linear algebra alongside abstract algebra, though.

Indeed, half of his book is about linear algebra.

Disciple of Barney

You might like this book: arxiv.org/abs/math/0405323

Balarka Sen

08:34

wondering what could be the point of renaming a fundamental result in algebra by rank-nullity theorem

@DiscipleofBarney Thanks!

Disciple of Barney

It doesn't have exercises, so you might have to make your own or use relevant sections of hoffman and kunze, and doesn't do a ton with matrices. Also you may have to suplement some relevent sections that the book assumes you have some experience with, but I think it might be a better alternative for someone who has some mathematical background

iwriteonbananas

zup

Disciple of Barney

Because people normally study the concrete example of the splitting lemma first!

@BalarkaSen

Balarka Sen

Thanks, I am checking it out right now. As I said, I am familiar with basic linear algebra and have some experience with vector spaces as I have studied modules (sounds lame to study modules before vector spaces, right?), so I guess that's the book I want.

Disciple of Barney

(repeats whole conversation with you had with sayan to you)

Balarka Sen

08:40

@DiscipleofBarney Well, you can guess how much normal my study is.

But splitting lemma is really a general nonsense theorem, there's no apparent connection with rank-nullity theorem.

Chris's sis

Greetings

Balarka Sen

I've never seen rank-nullity given as an example either in Dummit-Foote, now that I think about it.

Disciple of Barney

Thats alright, as you might guess I don't think necessarily studying things in a strict order is good, most learning is done through necessity to do what your interested in or studying what you are interested in.

Balarka Sen

@DiscipleofBarney I have background in calculus and set theory, mind you. :P

iwriteonbananas

i thank jesus for the exercises in hatcher. praise the lord

Disciple of Barney

08:43

How much set theory do you know?

Balarka Sen

Familiar with naive set theory pretty well. Axiomatic set theory, only the basics.

Why, though?

@iwriteonbananas They're good, indeed.

Have you done 2.1.10?

Disciple of Barney

Just curious what you meant by set theory, plus I like set theory

Balarka Sen

@DiscipleofBarney ah. you're interested in axiomatic set theory + logic and those stuff, then?

Disciple of Barney

I like those things, also descriptive set theory and infinite combinatorics seem really interesting, although I don't know much

Balarka Sen

@iwriteonbananas Before doing 2.1.10, you might want to have a look at the paragraph on pg 108-109 where hatcher talks about geometric interpretation of cycles (bordism!)

you'll get a good motivation for doing that exercise then.

Jasper Loy

08:50

@Chris'ssis Hello. I feel better today.

Chris's sis

@JasperLoy Hi. That's great! Did you do anything special?

Balarka Sen

it took me a few days to digest what he said though, so dive in at your own risk. most students just skip his "rants".

@DiscipleofBarney cool.

dunno anything about that stuff.

Jasper Loy

@Chris'ssis I think I need to start all over in life, and change all my old habits and old ways of thinking that are destructive, like dwelling too much on the past. Someone said something very powerful to me yesterday which helped me.

Chris's sis

@JasperLoy Well, yeah, dwelling too much on the past is not a good idea. The present and the future matter only.

Balarka Sen

@DiscipleofBarney You're a grad student, I guess?

Disciple of Barney

08:54

@BalarkaSen No, not in school at the moment

Balarka Sen

ah, i see. self-studying right now, then?

Jasper Loy

@BalarkaSen He is a disciple of Barney.

iwriteonbananas

@BalarkaSen ok i wasnt gonna do 2.1.10 but i'll do it now

Disciple of Barney

Hello @JasperLoy

@BalarkaSen Yes

Jasper Loy

@DiscipleofBarney Hi, Barney is cute.

Balarka Sen

08:56

nice.

iwriteonbananas

btw. isnt $H_0$ the same thing as $\pi_0$?

just the set of path components

Balarka Sen

yes, that's true.

iwriteonbananas

kk just checkin

Disciple of Barney

@JasperLoy I will tell Barney that, I am sure he won't be creeped out at all... ;P

Balarka Sen

@iwriteonbananas If you haven't done it already, 2.1.22 is recommended after you do 2.1.10. It is essentially a baby-version of cellular homology.

After you've done 2.1.22, let me know and I will give you a problem.

Jasper Loy

09:00

@BalarkaSen Hatcher seems to have many many exercises.

Balarka Sen

Yes, it has a lot of exercises. That's why I like the book.

iwriteonbananas

ok 2.1.22 looks a bit nasty...

whatever, i'm dong 10 now

Jasper Loy

When I write my book, it will have no exercises.

Balarka Sen

@iwriteonbananas the keyword is the long exact sequence

ok, have fun with 2.1.10

iwriteonbananas

for ex. 10?

Balarka Sen

09:01

no, 22.

iwriteonbananas

ok

Jasper Loy

@Chris'ssis Will your book have exercises?

Chris's sis

@JasperLoy My book is going to be a collection of problems with integrals, series and limits major part of them coming from personal research.

Jasper Loy

@Chris'ssis My book will have no exercises, but it will be written in 30 years time.

Chris's sis

@JasperLoy A lot of time needed though ...

Jasper Loy

09:05

@Chris'ssis Hehe, maybe I won't write any at all. But it is my wish to write a whole series on all major branches of math.

Chris's sis

@JasperLoy Well, get a wife, have some chidlren, and then, if you don't manage to finish it, they might continue your work. It might be like a legacy in your family. ;)

Balarka Sen

Jasper Lang.

Disciple of Barney

When I write a math book all my "exercises" will be of the form "it is obvious ___" and "it is trivial to show ____", etc.

Jasper Loy

@Chris'ssis I won't be able to find a wife, unless it is someone like you, lol.

Balarka Sen

lol @DiscipleofBarney

iwriteonbananas

09:07

@JasperLoy russianbrides.com

Chris's sis

@JasperLoy lol, I don't see myself as a wife, but I prefer to be alone as long as I live.

Jasper Loy

@Chris'ssis OK, why is that so anyway?

iwriteonbananas

i like to consider myself a wife

eventhough im male and have never had a girlfriend

Jasper Loy

@Chris'ssis Sorry, maybe I should not ask you so many personal questions. I apologise.

Chris's sis

@JasperLoy No pb.

I'm preparing for some tutoring. BBL.

Jasper Loy

09:16

@BalarkaSen Maybe I will get you to add all the exercises, Balarka Lang.

iwriteonbananas

@BalarkaSen im not sure i understand what is written on page 109

if $\zeta$ is a cycle, all the (n-1) simplices of $K_{\zeta}$ come from canceling pairs, hence are faces of exactly two n-simplices of $K_{\zeta}$. Thus $K_{\zeta}$ is a manifold

why is it a manifold then?

Balarka Sen

09:45

@iwriteonbananas it's a manifold away from it's codimension 2 points, you're cutting out the whole statement

you have to prove it : this is precisely exercise 2.1.10 (a)

FreeMind

10:09

@BalarkaSen Long time no see :)

@BalarkaSen How you doing?

JC574

11:27

Think I've solved the problem I was stuck on in elliptic functions

Jasper Loy

@JC574 Hi.

JC574

hey Jasper!

I've solved the problem i was stuck on for aaages

i missed a simple solution

being stoopid

Jasper Loy

I have been stupid for 33 years. It's time to change.

@evinda Aha!

evinda

@JasperLoy Aha!

@JasperLoy Did you listen to the song?

Jasper Loy

@evinda No, sorry.

evinda

11:33

@JasperLoy Aha! :p

Jasper Loy

I am waiting for May to come. From 01 May to 31 May I will try to solve 99 per cent of all my life problems.

I have made some plans and I hope I succeed this time.

evinda

Why don't you begin this month? @JasperLoy

Jasper Loy

@evinda Because I am not quite mentally ready to do those difficult things.

evinda

@JasperLoy What is for example a plan that you have?

Jasper Loy

@evinda It's too complicated to describe here. I need to write an entire book to explain.

evinda

11:36

A nice idea to write a book @JasperLoy

Jasper Loy

@evinda I have been making these plans for the past few years, but never succeeded. So I hope I succeed next month.

evinda

Good luck

Jasper Loy

@evinda Aha!

Jasper Loy

11:54

Hello @did. Good to have you on MSE.

Transcript for

$Mathematics$ Mathematics