I am back.

@DavidWheeler It is my intention to go to US for grad school.

Cool

Chris's Sis I hope will become a mathematician one day, but she still has not done her degree yet.

@ABeautifulMind my book is first. :-)))

@Chris'ssis Meeting me is second, lol.

@ABeautifulMind lol :-)))))

@ABeautifulMind I think despite the difficulties you're a great person.

@Chris'ssis I often wonder what I would be now if I did not have mental problems.

@ABeautifulMind one can never know such things.

@ABeautifulMind I agree that some diseases might prevent you from excelling in some areas, but at least one might try to use those resources that aren't affected by disease, for getting a better life.

@ABeautifulMind: I noticed you're considering grad school in the U.S. Are you not from the U.S., out of curiosity?

@Clarinetist I am not. I am from a tiny island in Asia.

Ah. Well, let me be quite honest with you - I'm a U.S. native: if I could've done it all over again, I would've done my undergrad in Europe or Canada.

or maybe try for that top-20 math school that I did get into. Ugh.

@Clarinetist OK. I might go to Canada instead.

-_-

I've been an "adult" for about a year now. Life is hard when you make some mistakes on the way.

I've learned. :/

@Clarinetist Mistakes can be corrected. Sometimes much harder to do, when you're older, but at least you have a clearer idea what you want.

Indeed... I should really seek a psychologist. I've been depressed for the past 2-3 months.

If I could change something I'd change that I start studying math earlier in life

@Clarinetist You're unhappy at work, right?

@Clarinetist I want to say one very important thing. Never let it get worse, or it might be very hard to get out later.

@ᴇʏᴇs As much as we'd like to, changing the past isn't going to happen. Focus on the future.

@DavidWheeler As much as we like to, that is very hard.

Indeed @David. I came into actuarial science education, left after 2 months, and am now in a traditional actuarial science job. I was doing fine for a while, but my supervisor left and now I'm left with this massive data cleanup job that involves a language written in the time of COBOL. I know this will be good work for the company, but I fear for my job prospects. I was misled to believe this would be a statistics job.

I've been here for a bit more than 6 months.

:20554213 Changing the future? Yes, it can be hard. Sometimes not making the effort can be just as bad, though.

@ABeautifulMind - Thanks, I will keep that in mind.

@Clarinetist At least you've learned something about how the industry "actually" works. It might not seem like it now, but that is valuable experience.

@DavidWheeler I think you tagged me by accident EDIT: Oh, you thought I was referring to the thing you were talking about. I was just popping in with a random math thing. (I deleted it when I realized you guys are in the middle of a serious conversation.)

I'm convinced that I don't have a future in actuarial science. The only reason why statisticians haven't taken over is because of the exams, which serve as nothing more than a barrier to entry.

@David - I hope that I can tell my future students about my experience, yes, but for now... I just need to focus on getting out.

@Clarinetist That may be true-but-a lot of businesses have proprietary custom-written software written in COBOL. Things like inventory management, or payroll. The need for people who understand these things isn't going to go away.

@columbus8myhw How are you

I moved 6 hours away from where I wanted to be to pursue that actuarial science education job, only to find that there was nothing different between my online work with them and that job besides that I was paid a bit less than what I could've made off-site, as I had done previously.

@David - It has been rather difficult to find jobs that find COBOL useful these days. In my job search ("statistics," "analyst," usually), I've only found one job that has found that useful, judging by the description. Right now I'm trying to find a job that uses SQL, SAS, R, Python - at least one of those.

@Clarinetist My point being-yes, it wasn't as "actuarial" as you hoped-but you've probably learned a LOT about how math and business intersect.

@DavidWheeler - It has been hard to see the bright side of this situation these days, but yeah, you're right.

A company I worked for for a decade had one guy (I think Jimmy was his name), who did nothing but maintain their out-of-date system software.

I think they paid him 75k a year, and he only worked part-time.

I gotta make sure I tag the right David lol.

@Clarinetist Lol

I gotta figure out how to bring some positive energy back.

If I weren't dealing with actuarial exams right now and trying to prepare myself for a data science job, I would be reading @TedShifrin's multivariable calc book a lot more.

@Clarinetist I think you'll find a good match, eventually. It might not be a "straight-line" path. Use the detours, to broaden your perspective.

Which, by the way, is an amazing read.

I want to buy it, but no monies.

It is easily the most readable multivariable calc book I've ever found.

If I get this job in ND, all that will change.

Oh, what job? :)

It's just a project manager job for a truss company.

Wow, sweet. :D

I know absolutely nothing about project management. Lol :P

I have to develop/oversee about 1.5 million in sales per year.

Whoa, that's neat

The pay's not astronomical, but it's an employee-owned company, so the stock options are sweet.

Hello @ᴇʏᴇs.

Hi @ABeautifulMind

I've been doing Integration since Wednesday, should I stop?

@Clarinetist One can parlay "abstract" knowledge into money, as long as one knows a specific industry well enough.

Tee dog said I should do more.

@Owatch You should stop when you know the answer before you write it down. If that's not happening, keep going :)

I said my fingers are sore and bleeding

He said he would beat me if I did not continue

I joke.

LOL I was gonna say!

I am not there yet, need more work.

Isn't there an entire forum dedicated to integration or something?...

Yeah, I didn't believe your fingers were bleeding. teadawg would beat you, however. I totally believe that.

Another thing on my reading list: Analysis I and II by Tao... :)

@Clarinetist There is a lot of stuff to read. I like the Samuel Johnson quote.

"A man should read just as his inclination leads him, for what he reads as a task will do him little good."

Haha, that's so true.

Which reminds me, I've had two jobs thus far which have hired me because I taught myself LaTeX.

Self-teaching is so much fun.

:)

I remember, when I was 12 or so, getting a hold of a CRC Mathematical Tables book. In it, I saw the entries: $d(u + v) = du + dv$ which I understood at once, and $d(uv) = udv + vdu$, which totally mystified me.

Lots of ping on the network, making me mad.

I HAD TO KNOW the WHY of that mystery....

My favourite song is now Bocelli's Because We Believe.

I think listening to it every day will help me get well.

@ABeautifulMind It's very pretty

@DavidWheeler You should listen to all the versions on youtube, amazing variations.

By various singers.

But it's not the Christian song.

Wow, I've heard the name but have never heard his music. What a talent.

Plus he sings some very difficult opera...

I should really get back to composing.

Some day.

@Clarinetist It's good to have things to look forward to.

I must go.

A bientot.

Adiós @Owatch

Au revoir

Back in my high school years, I taught myself how to write for orchestra. Dang, that was so much fun. :)

Have you ever given any thought to how systems analysis is like that?

@DavidWheeler Like orchestral writing?

Yep. See, this is how I see things-mathematicians study analogies. Linear maps, continuous functions, homomorphisms, these are just certain technical kinds of analogies. mathematicians have an entire tool-kit of analogies.

You know, that's an interesting thought.

I think my mind just naturally likes seeing others' final products and wanting to figure out all of the details so that I can create my own product, something that is truly mine.

Whether you see it or not, your skills in orchestrating translate to "orchestrating" in other arenas.

Moreover, these things are, well, "personal" to you. They have individual meaning in ideas you might not even be able to express verbally.

Keep that in mind as you wrestle with the corporate labyrinth.

Hmm.

Not everyone is capable of being creative AND analytic. It's rare, actually.

@Heinz Only if 1+2 = 2.

@Heinz and if THAT's true, then 1+1 = 1+ 2, leading ultimately to 0 = 1. A perfectly reasonable number-system, but rather dull, since everything is nothing.

Zero rings FTW

Exactly!

I think I have found the way to get well, but I need to believe in it.

Yo @ᴇʏᴇs still here?

@ABeautifulMind Yea

Nothing.

Hello @ᴇʏᴇs.

Hello @Committingtoachallenge.

Anyone home?

Hello @Abe

I am not at home no

I went out for a walk.

That's good, walks are nice

I was thinking how different my life would be if my father died when I was born.

I wish I could exercise. I will be able to tomorrow after I hand in this assignment that has taken up all of my time

@ABeautifulMind That's a depressing thought, but I can understand somewhat how you feel with that one.

@Committingtoachallenge Do you sometimes think like that too?

This world would be so much happier if there was no abuse.

@ABeautifulMind I thought depressing things like that in the past, but not so much now.

When I was depressed I had many disturbing thoughts.

I guess we have to accept that just like the world is full of good things, it is also full of bad things.

@ABeautifulMind The world is terrible and beautiful at the same time.

I feel very good now. I suddenly feel I can solve all problems, but I know this feeling may not last.

No, I am not taking heroin.

You don't strike me as a heroin kind of guy. Enjoy it while it lasts.

What if I really make it this time? I cannot imagine...

Then your life will be different, and hopefully better.

I have 1i,1ii,5 done so far, and I almost have 3,4 done, so only 2,6i,6ii,6ii to go really xD

I really suck at this, I have spent over 35 hours on the assignment I would say now

what assignment?

45.5 hours on the class since the 2nd, so I don't know how many on the assignment, but a hell of a lot

@DavidWheeler My abstract algebra II one that I have been learning heaps for

What structure are you studying?

I have 5 classes and the other 4 I have spent probably 30 hours on collectively since the 2nd, and just by itself I am on 45.5 hours for abstract

You should sleep more.

I am currently doing Matrices <----> Linear operators, how they are connected

He teaches them as two 'languages' that mean the same thing

@ABeautifulMind I sleep 8hrs a night right now, otherwise my brain doesn't function

"Sort of", they're only the same if you have a basis

I have all the statistics on how much time I have put into each class written down in a book, so I will put them on excel after I hand in tomorrow

@Committingtoachallenge Forget about the statistics.

You can have linear operators that operate on a space that has no known basis

@ABeautifulMind Why? My amount of time spent on each class has been a super good representation of my expected grade(as you would guess)

youtube.com/watch?v=d8Durwq5JxQ is good.

And "infinite matrices" don't always make sense

@DavidWheeler I haven't reached them yet I guess, I am on week 3 tomorrow

@Committingtoachallenge Wasting time.

@ABeautifulMind I just write down the time I start and the time I finish and calculate the number of minutes, so it only takes me less than a second

E.g I start at 12:32pm so I write 12:32, and then when I finish I write 1:12 and then I calculate number of minutes and then I put that on my computer

@DavidWheeler Yeah we aren't doing any functional analysis, but I am taking that as well

However, there is a linear isomorphism between $\text{Mat}_{m\times n}(F)$ and $\text{Hom}_F(F^n,F^m)$

@ABeautifulMind (oh and most importantly, I really enjoy keeping them for some reason, and have for 4 years)

A vector space is just a field acting on an abelian group.

I never think of it that way.

A vector space is just a space of vectors.

I think of it as a lattice with arrows

And by "action" I mean a ring-homomorphism $F \to \text{End}_{\Bbb Z}(A)$

I don't understand the above, but I am sure I will talk to you about it in the next few weeks when I am learning similar subjects @DavidW. I think I lack the prerequisite knowledge to appreciate it fully

Well, it's just a fancy way of combining all the 10 or so vector space axioms into one statement

Oh that is very powerful in that case

The first 4 or so axioms say: $(V,+)$ is an abelian group

For now I try to describe all $n\times n$ matrices satisfying $A^2=0$

I am here so far

Sometimes, I think: what if my problems lead me to greater joy than possible without them?

@ABeautifulMind In some sense that is guaranteed, but chemically it is supposedly impossible

@Committingtoachallenge Guaranteed?

@ABeautifulMind When you spend a long time in pain, you appreciate not being in pain more

The ring-homomorphism I described above, says that for every scalar $\alpha \in F$, we have a UNIQUE abelian group homomorphism $V \to V$.

This homomorphism is typically called $\alpha\cdot(-)$

@Committingtoachallenge I was thinking of other things. Like maybe because of my suffering, I would finally meet the girl of my dreams, lol.

@ABeautifulMind Oh, I thought 'greater joy than possible without them' meant that you would be happier than other people in the end because of it

@infinitesimal I am not going to talk in the Eng room anymore.

So, because it is an abelian group homomorphism, we have $\alpha\cdot(u+v) = \alpha\cdot u + \alpha\cdot v$

Since the mapping $\alpha \to \alpha\cdot (-)$ is a ring-homomorphism, we have: $(\alpha+\beta)\cdot(-) = \alpha\cdot(-)+\beta\cdot(-)$. In other words, for every $v \in V: (\alpha+\beta)\cdot v = \alpha\cdot v + \beta\cdot v$

And $(\alpha\beta)\cdot(-) = \alpha\cdot(-)\circ\beta\cdot(-)$, that is, for any $v \in V$, we have: $(\alpha\beta)\cdot v = \alpha\cdot(\beta\cdot v)$

Which also implies $1_F\cdot(-) = \text{id}_V$, that is $1\cdot v = v$.

And that's all the axioms covered, I believe.

I don't know ring homomorphisms yet sorry, I know the homomorphic property for general groups, but I don't know what $(-)$ means here

$(-)$ means "fill in the blank": like $x + (-)$ is the function that maps $y \to x+y$

Ahh alright, I thought that might be the case

@Committingtoachallenge I am also committing to a challenge. The challenge to solve my mental problems completely and enter grad school by 40.

So really it only simplifies in the sense that all of the properties are subproperties of that one statement

@ABeautifulMind Make a webpage for it ;)

Well ring homomorphisms are just like group homomorphisms, except you require both: $\phi(x+y) = \phi(x) + \phi(y)$ AND $\phi(xy) = \phi(x)\phi(y)$.

Ahhhh of course

Both binary operations need it

Fair enough

Do you mind telling me if I am going in the right direction here @DavidW meta.math.stackexchange.com/a/4726/142198

There's a very common ring homomorphism we learn as kids: $\Bbb Z[x] \to \Bbb Z$ where we sends $f(x) \to f(a)$, for some particular integer $a$.

If all sub-blocks are nilpotent with index $2$ then $A$ will be as well, but I am not sure how to do a similarity argument for finding all such $A$

@DavidWheeler Integer addition and multiplication

But we aren't invertible?

The "formal" name for that map is "evaluation at $a$"

Should it not classify as a ring without invertibility on $(\Bbb Z,\times)$

We have additive inverses...

Rings do not need to have multiplicative inverses, only fields.

Doesn't a group need inverse?

And a ring is two groups?

No, technically, a ring is: a group under addition, and a semigroup under multiplication, together with two compatibility conditions called distributive laws.

Ahhhh okay yes, an abelian group with another operation, I thought it was two abelian groups woops

@Committingtoachallenge Regarding your earlier question, yes, you need to look at the nilpotency index of Jordan blocks.

@Committingtoachallenge No, in fact, the multiplication need not be commutative-an example I'm sure you're aware of is the matrix ring $M_n(\Bbb R)$

Special attention in rings is given to invertible elements (these are called units)

Nilpotent elements are special examples of "zero divisors", in matrices, zero divisors are singular matrices.

Fair enough

@DavidWheeler Will all of my Jordan blocks be of size $2\times 2$ or $1\times 1$, I am pretty much sure this is the case

(with all eigenvalues $0$)

I think having a Jordan block of size $3\times 3$ will give me nilpotency of index $3$

I think so, too-can you prove it?

Hint: an n x n Jordan block with 0's on the main diagonal is called a "shift matrix"

all of these(Jordan blocks of size $k\times k$)

and my matrix of nilpotency $2$ just requires all the jordan blocks within to be of index 2 or less

Let $N = \begin{bmatrix}0&1&0&\dots&0\\0&0&1&\dots&0\\ \vdots&\vdots&\vdots&\ddots&\vdots\\0&0&0&\dots&1\\0&0&0&\dots&0\end{bmatrix}$ be a $n \times n$ matrix

Prove $N^n = 0$ and $N^{n-1} \neq 0$ (induction will work, if you think about "block matrices")

I have no idea how to write my final statement, which should basically say that all $n\times n$ matrices $A$, such that $A^2=0$ there is some Jordan form matrix $J$ such that $A$ is similar to $J$, where $J$ is a jordan matrix with jordan blocks equal to $1\times 1$ or $2\times 2$ with eigenvalues $0$

$\forall A,\exists J| A^2=0\implies A=P^{-1}J_lP$ for $$J=\b J_1&\dots\\0&J_2&\dots\\&\dots\\0&\dots&\dots&J_n\e=0$$

I don't know how to encompass the fact that it could be any permutation of the jordan blocks

Well, you could pick a "particular" Jordan form so that the 2 x 2 blocks came first.

All the 1 x 1 blocks correspond to the null space, and the 2x2 blocks correspond to a "generalized" eigenspace.

@Chris'ssis I'm back after a long time on M.S.E

@Chris'ssis do you have any new challenging integral which can be solved using just high school methods for me to try ?

Were you formerly known as "Prince?" :P

@infinitesimal me ? No this has been my name always

That was a joke :-)

Prince changed his name to "the artist"

:)

@infinitesimal where do u study at ? :)

@TheArtist Nowhere.

Can someone help me understand math.stackexchange.com/a/1189405/142198

Shall every jordan block have eigenvalue only $1$?

Wait no that would lead to having no nilpotency off of the diagonal

@Committingtoachallenge ahhh :D guess what...adelaide is awesome

@TheArtist That is good to hear

@TheArtist I am being destroyed right now in queensland

@Committingtoachallenge I have one question...I see that Australians are not very friendly with international students over here :/ is it the same over there?

I mean the first year students ^^^

Hi @DanielFischer

@TheArtist Oh really? I don't think that is the same at all here

@Committingtoachallenge since your an Australian too..did u find international students in your first year as a nuisance or something?

We are 50% international students

@Committingtoachallenge oh I see

@Committingtoachallenge here it's like 25%

Do Australians hate Asians? I heard so.

I have never found international students a nuisance, I am friends with many

Most of my good friends are Asian haha

@ABeautifulMind exactly what' I'm experiencing right now

I heard from many friends that Australians are particularly racist.

If you speak bad English, you often come off as rude and people will not like you

Uneducated australians are racist yes, especially towards muslims

What if their English is as good as mine?

@Committingtoachallenge bad English = rude ???

Oh I see

Bad english = rude yep

You don't follow polite mannerisms pretty much without good English unfortunately

You speak in a monotone disinterested voice and don't follow jokes well if you don't have good English

So people think of you as less human

Unfortunate thing I have witnessed a million times

@Committingtoachallenge I don't know...but it's the same for me, I won't call my English as bad. Less human?

More robotic*

Now I think many Americans have bad English, LOL.

I need to correct all their spellings in chat.

@Committingtoachallenge I thought it's because we are from another country, and maybe it seems like we are invading or something

More task oriented, less social

@TheArtist Not at uni, many uneducated people do feel that way though, but at uni most people are moral, atleast in queensland unis(which I have went to 3 and have friends in more than 10)

@Committingtoachallenge and like you all don't like us coming to Australia to stay..

Well I have to get back to my assignment now sorry haha, that's my quick 2cents

@Committingtoachallenge oh I see...

@Committingtoachallenge ok thanks ....

It's due tomorrow and I have spent over 35 hours on it haha

Seriously wow

Ok

Close to solving 2,3 and very close on 4

Then I have 6i,6ii,6iii that aren't close at all

@Committingtoachallenge good luck and cya

@ABeautifulMind It is spoken English that is all they care about, so I wouldn't know

@Committingtoachallenge I can put on a British or American accent. Australian accent is beyond me, LOL.

@ABeautifulMind We don't have an accent (jokes)

@Committingtoachallenge I find it very hard to understand some Australians.

Although it is no joke that I can't hear any accent on Australians, nor any of the americans I have heard

I will send you a voice recording later this week to see haha

I would rather you send me a pic.

Okay haha sure

After I hand in I will have free time

Don't worry, I am not gay, lol.

That wouldn't worry me haha, not homophobic at all

People never get me when I say this. I mean I am not hitting on you, LOL.

Still wouldn't worry me over the internet :P

A gay once approached me.

He did not say he was gay, but he stood beside me on the escalator, smiled and said hi.

That was when the escalator was very empty.

And he stood all the way until the end.

I felt awkward and began to suspect something.

Then I walked off in another direction.

That should let him know I am not gay, hehe.

Haha

@DavidW are you there for one quick question?

Someone said to me: "If the eigenvalue of one jordan block is equal to the eigenvalue of the one following, the blocks join" but I don't think that is true

Why not?

Because I have seen people do Jordan form with for example a 2x2 with two 1x1's

such as $\b0&1&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&0\e$

Which if what he is saying is true would make that not jordan form, for it would have to be

$$\b0&1&0&0\\0&0&1&0\\0&0&0&1\\0&0&0&0\e$$

The someone was another student, so I don't trust it really haha

What are the eigenvectors of the first matrix?

Oh sorry $0$ for both

All $0$'s

eigenVECTORS, not eigenvalues

I suppose there is one, and three in the other hmmmm

I am fairly sure eigenvectors are just the column vectors of the basis right?

Or have I failed a super trivial thing...

I'll be back in 1 hour, gotta go home from uni and then get back to this

Greetings

Seasons

@TheArtist Unfortunately no. I lost my creativity ... :-(

(poor me)

Does this mean the offer from Hallmark Cards is off the table?

:-)

@Chris'ssis really? :o

@TheArtist And particularly this morning since I have an ugly headache ...

@Chris'ssis oh I see

@Chris'ssis how much of ur book is complete so far?

@TheArtist more than 90% (I added it from what I planned). I'm almost done.

@Chris'ssis oh :) so we can expect to see the book soon :)

@TheArtist It doesn't depend on me only.

@Chris'ssis I mean the hard part is writing the book...that's almost done so yea

@TheArtist I only hope my book won't break many hearts.

@Chris'ssis why do you think it would disappoint other people?

@TheArtist I didn't mean this, but anyway, this is less important.

@Chris'ssis did you think about the book cover design ? :)

@TheArtist This is a hard part.

:-)

@Chris'ssis what colours are you planning on using ? :)

@TheArtist Dark colours, black, blue, purple.

@Chris'ssis ah I see :)

@Chris'ssis I love books with nice covers....it feels so nice when it's on my table or cupboard

@TheArtist Yeah, I know. Did you see Paul Nahin's book? Inside Interesting Integrals?

@Chris'ssis yes I've read it :) it's cover is very nice

@TheArtist It's the nicest one.

:) IMO Ive seen much nicer ones...but they are not books on mathematics

Sure, but I was referring to the ones involving math. ;)

;) okay

@Chris'ssis U have never told the story how you started getting into Integrals :)

@TheArtist I'm sure no one cares about that with some exceptions though (as I can see). ;)

The older I get, the more unsure I become as to what a number is.

It's more of a philosophical concern, I certainly know some "constructions" of the natural numbers.

Symbol or word indicating how many :P

The "standard view" is of little help to me, they are all based on set theory, and I have even MORE uncertainty as to what a set is.

@infinitesimal So "few" is therefore a number, yes? Which one?

Mind you, I have quite a GOOD idea of what a "finite set" is, but that certainly limits what numbers could be.

That is the "common usage."

:-)

Sure, but diecisiete is certainly a different word than seventeen.

Strangely the word "set" has the most definitions in the dictionary.

@Chris'ssis I care :) I'm interested..may I know?

@Chris'ssis Lol, you should open up more-just because people don't respond verbally, does not mean they aren't paying attention.

@DavidWheeler :-)))