Mathematics - 2012-09-02 (page 2 of 3)

7:00 AM

this is quite bizarre.

right.

and it's not like cos(1) could possibly have been negative, so it's not like I needed to include an absolute value for square rooting the square

I actually thought it might count an earlier problem I did wrong when I included the absolute value for that on my first attempt, but it counted everything right on my first try (as usual)

(I knew it technically >HAD< to have the absolute value, but I didn't know if the system would acknowledge that)

Fortuon Paendrag

My reason why the stingy professor should just hire a grader.

Gnintendo

(earlier problem I'm referring to, was actually more work than this problem: grab.by/fNLU )

Fortuon Paendrag

Or just do it himself.

Gnintendo

look, the online system is great when it works, but this is making me mad :|

Fortuon Paendrag

7:03 AM

But if $t>0$ what need for $||$?!

Gnintendo

eh, that's true

;)

didn't need it, but hey

I was wondering why they bothered to tack that on there, heehee

Fortuon Paendrag

:)

Also, why didnt you evaluate $\cos(0)$ and

$\sin(0)$

?

For your original question, I mean.

Gnintendo

I knew the system accepted it like that, so I left it so if I came back to do N and B I'd know what I had gotten for T

(easy to notice it was cos(t) and sin(t))

also, do you see where I got that sin(2) one

Fortuon Paendrag

meaning?

I do understand that you used $\sin(2t)=2\sin(t)\cos(t)$, if that's what you're saying.

Gnintendo

yeah

so, is there anything else I should do before I email my professor?

Fortuon Paendrag

7:09 AM

Your cause seems legit to me.

Gnintendo

"bitch, please, I got 100 on this assignment, the program is wrong" - your faithful student, Gnintendo"

send?

Fortuon Paendrag

Hahaha. Fire!

Gnintendo

I was about to email the professor, but I remembered people hang out in here

so I figured I'd have at least one "independent" review of my work before I pulled out the big guns

Fortuon Paendrag

ALways good.How did you hear about M.SE?

Gnintendo

oh, saw stack exchange stuff everywhere for a while

never actually used it, actually went to the site one time, was like "oh, this is cool"

saw there was a math one

was like "yay!"

about the only useful answer I've ever given, though: math.stackexchange.com/questions/145087/…

I spend most of my time tutoring people in my own classes though

Fortuon Paendrag

7:12 AM

You sound like you would fit right in here :)

Your story is similar to mine.

Gnintendo

I pride myself in giving concise and clear answers and explanations to people in my classes

Somebody told their friends I was a physics major as well and a group of 10 physics I students knocked on my dorm while I was answering an email about a Calculus III problem

Fortuon Paendrag

Uhh Probability. I stay away from distributions and the like.

I'm a Wannabe algebraist, thankyouverymuch.

Gnintendo

hehe

I had already taken AP Statistics in high school, and I used a slide rule in that class, so I had to come up with creative ways to find the area under the curve

Fortuon Paendrag

Ahahaha. That sounds awesome. Huge Ego boost to be sure?

Gnintendo

the method I described in that answer is actually what I used

although we didn't usually need to have that high of an accuracy, nor be that far out

so the math usually ended up being rather simple

well, I'm fine with the physics and math thing

but people figured out I wasn't taking any history or English classes because I got 5s on all the respective AP tests in high school, so now they're having me proof read their essays

and that sucks

Fortuon Paendrag

7:16 AM

Does your school not have "Division requirements"?

Gnintendo

It does, but I came in with 50 hours of AP credits

Fortuon Paendrag

Hohoho. Nice one. :)

Now you're just binging on Math and Physics?

Gnintendo

yeah...freshman? Junior by hours.

Fortuon Paendrag

I was too. I did the IB, you see.

Gnintendo

Well, this is first semester of 'freshman' year right now, so I have a couple of gen ed requirements left

second semester I'll be doing junior level+ math and physics exclusively

oh, and an "international dimension" credit

whatever the hell that is

Fortuon Paendrag

7:18 AM

Do you plan on going to grad school for math?

Are you an international student¿?

Gnintendo

quantum mechanics, ideally

and no, I'm from America

Fortuon Paendrag

A pity, that.

The first, I mean.

Gnintendo

:<

I really like math, though

Fortuon Paendrag

America is 2 continents, you know.

;)

Gnintendo

if I could I'd get a PhD in number theory and quantum mechanics

;)

(actually, I guess I can)

It's kind of a time thing.

Fortuon Paendrag

7:20 AM

"Simultaneously?" is the question.

Gnintendo

That would be interesting.

Fortuon Paendrag

It must be late for you, if you are in OK, no?

Gnintendo

yes, 2:22 AM

It's Saturday though

and there's no school on Monday (national holiday)

Fortuon Paendrag

Ah! That's nice.

Gnintendo

I was planning on staying up until I finished this homework

I've been on this problem on and off since about 1 AM, though

(to make sure I get a 'clean' start short-term memory wise)

Fortuon Paendrag

7:23 AM

Tough guy ;)

Gnintendo

I did the rest of the homework in about 30 minutes, you don't understand: I don't miss things

this was driving me INSANE

Fortuon Paendrag

I think I actually understand. I go insane when that happens too. :)

You might find this question interesting:math.stackexchange.com/questions/140384/…

I answered it wrong. Try your hand at it if you want torture.

Gnintendo

hm.

ogod

Fortuon Paendrag

I agree. the problem is simpler when the series is $\displaystyle \sum_{i=1}^\infty \frac{\epsilon_i}{10^i}$.

Gnintendo

but that's like a "duH"

Fortuon Paendrag

7:32 AM

Not quite that Duh though. There is a small subtlety in it.

Gnintendo

zooms

Fortuon Paendrag

Fine. It is duH. :P

Gnintendo

>.>

hmm

Fortuon Paendrag

How would you go about it?

Gnintendo

I need to word this email in mostly math

my Calculus III teacher is Japanese, he doesn't speak English very well

he's great at the math, just not talking

Fortuon Paendrag

7:34 AM

Ah. Unfortunately, he needs to talk math too no?

Gnintendo

right, we 'scare' numbers instead of square them, etc.

you get used to it

you just learn his pronunciation for various words and you're fine

Fortuon Paendrag

Ah, and it becomes endearing after a while. When I was in Budapest, all of my professors had odd accents

and pronounced SOMEthing odd.

Gnintendo

hehe

Fortuon Paendrag

@Gnintendo Anyway, I must call it a day. It was nice meeting you!

Goodluck with the rest of your course.

Gnintendo

thanks

I'm emailing the teacher now

Matt

8:16 AM

NARQ.

BenjaLim

8:28 AM

@FortuonPaendrag Hey

Gnintendo

hey BenjaLim

Matt

9:01 AM

Why on earth would anyone upvote this?

user34522

Sorry to barge in, but is anyone here interested in fielding a question on correlation?

@JayeshBadwaik, are you interested in statistics?

Jayesh Badwaik

@user34522 i don't have much background in it.

If the correlation question is a simple integral something, then may be I can attempt, else if it is something deep, Imight just waste your time.

user34522

0

Q: Product of standard deviations

If $u=cx+dy$ and $v=cx-dy$ and $R$ is the co-efficient of correlation between variables $x$ and $y$ and variables $u$ and $v$ have 0 correlation, then how can I prove that $$s_us_v=2cds_xs_y\sqrt{1-R^2}$$.I do not think I made any progress at all and I request a solution so that I can study it. ...

correlation

here it is

I am beginning to hate it.I had study a book in such a short time for my school. >.<

Automatically, my understanding is superficial.

Jayesh Badwaik

@user34522 you are in high school?

user34522

sadly, yes

Jayesh Badwaik

9:14 AM

btw, Robert Israel has tried answering your question. Do you follow his solution?

user34522

i am not sure.

@JayeshBadwaik,I have an exam tomorrow, :(

Jayesh Badwaik

@user34522 hmm. Do you understand the first paragraph of the solution given?

You can just ask him for more clarification and let him know in comments that you are a high school student.

He will edit the solution appropriately.

user34522

I think I understand it.

@JayeshBadwaik, I do not think I unerstand the motivation behind considering E(u^2).

Jayesh Badwaik

@user34522 are you familiar with this identity
$E((X-u)^{2}) = E(X^{2}) - u^{2}$

user34522

yes i am

!

@JayeshBadwaik, I am now absolutely frustrated.I am grappling with these problems since yesterday. :(

Jayesh Badwaik

9:32 AM

@user34522 hmm, hard luck. I don't think I can help you too much. I haven't done much random variables for a long time.

user34522

@robjohn, are you interested in statisitcs?

(let me try pinging people)

robjohn

@user34522 Probability

why do you ask?

user34522

I had a question on correlation.

0

Q: Product of standard deviations

If $u=cx+dy$ and $v=cx-dy$ and $R$ is the co-efficient of correlation between variables $x$ and $y$ and variables $u$ and $v$ have 0 correlation, then how can I prove that $$s_us_v=2cds_xs_y\sqrt{1-R^2}$$.I do not think I made any progress at all and I request a solution so that I can study it. ...

correlation

@robjohn, is that of any interest to you?

:)

robjohn

@user34522 Does Robert Israel's answer not suffice?

user34522

perhaps, my reading came in a short time and i am not familiar with this stuff.

So, it seems I cannot make much progress

Matt

10:35 AM

Call for votes.

Jayesh Badwaik

11:13 AM

Rudin is obscure! Not terse, obscure.

Jonas Teuwen

11:23 AM

Whatever. Did you ever try to complete it?

I read plenty of complaints about books, but not often questions about the content!

I would say: More reading, less complaining!

3

Matt

Turn back what?

Executioner needed.

Jayesh Badwaik

@JonasTeuwen Yes, I have almost completed it.

Last two chapters remain.

Just voicing my frustration on some particular result.

Jonas Teuwen

What result?

Jayesh Badwaik

11:43 AM

@JonasTeuwen I just read Riemann Rearrangement theorem from rudin and first thought it was a totally different thing than Apostol's one. Then I started reading in detail and finally worked out what he did, when he could have done it in a much more simpler way.

Jonas Teuwen

Perhaps there is a good reason to do that.

I mean often when you think: "this shit is stupid or wrong" often in the end it is you that is stupid or wrong.

Jayesh Badwaik

@JonasTeuwen Yeah, trying to rack my brain about what could be it though.

Comparing the differences in two proofs right now.

He basically does an extra step of constructing a new set of sequence, while apostol doesn't why I am trying to know right now.

@skullpatrol are you have some kind of image matching algorithm developer? :-)

skullpatrol

@JayeshBadwaik Maybe I am, maybe I'm not ;-)

hhh

Could someone help me to express planar wave?

I know how to express it in vector phone with the phase difference but struggling with the complex form, more http://en.wikipedia.org/wiki/Plane_wave:

$$U(\bar r, t) = A_0 e^{i \left( \bar k \cdot \bar r - wt + \phi \right)}$$

How can I specify the phase such as right-hand-circular-polarized in the Complex form?

P.s. Right-hand-circular-polarized means phase-difference $\phi=\pm \pi/2$ but only in $\sin$ -term or only in $\cos$ -term, not in both. If I use the complex form, I cannot see how I can express it with such as phase difference. Sho…

...apparently reading wrong material, should be reading wave-equation expressed in terms of differential equations. Not sure, investigating...

hhh

12:16 PM

Is this a planar wave?

$$\bar E=E \left( \hat i t + \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$$

I think it is: it moves in i-axis -direction and oscillates in j-k -plane

Jayesh Badwaik

It is not constant amplitude. Planar waves generally mean constant amplitude.

MaoYiyi

is there an easy and fast method for finding the coefficents of a factored polynomial?

Jayesh Badwaik

@hhh if you are dealing with transverse waves, then there is no $\hat{i}$ component (no component of $\bar{E}$ in the direction of propogation, though in practice the convention is towards $\hat{k}$.
${E}$ is one vector which will co-exist with a $\bar{H}$ vector and $\bar{S} = \bar{E} \times \bar{H}$ and the direction of propogation is the direction of $\bar{S}$.

So, you $\bar{E}$ will only be $E \left( \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$

Circular Polarized means the $\bar{H}$ is always perpendicular and equal in magnitude to $\bar{E}$

skullpatrol

@MaoYiyi Do you have an example?

Jayesh Badwaik

12:32 PM

The $\phi$ you have has more to do with the phase due to delay of propogation in both $\bar{E}$ and $\bar{H}$

MaoYiyi

@skullpatrol (x-7)^8 (x-5)^20, something like that.

Jayesh Badwaik

(According to the original equations that is)

@hhh original means these.

\begin{equation}
U(\bar r, t) = A_0 e^{i \left( \bar k \cdot \bar r - wt + \phi \right)}
\end{equation}

MaoYiyi

@skullpatrol I know I could do binomal expandsion but then I still need to multiply the terms.

is anyone here?

skullpatrol

Maybe try writing x-7 as x-5-2, then sub in a=x-5
(a-2)^8 a^20

Then expand and multiply.

@MaoYiyi Does that help?

MaoYiyi

12:48 PM

@skullpatrol yes, somewhat. just was hoping there was some nice formula for doing this for any given factored polynomial.

skullpatrol

Not that I know of.

MaoYiyi

@skullpatrol thanks.

do you think it would be a good idea if there were multiple answers to a question to randomly list them in order if they have the same upvotes?

skullpatrol

I would prefer to list them chronologically in that case.

MaoYiyi

1:07 PM

@skullpatrol why chronologically?

hhh

My book mentions that

1. if $\phi=\pm\pi/2$, then the polarisation is circular
2. if $\phi=0$, then the polarisation is linear

P.556-557, Understanding Physics.

@JayeshBadwaik So hence confused about this $\phi$ in the complex form. The $\phi$ is in both $\sin$ and $\cos$ -terms, not so in the non-complex -form.

Q here, physically.

skullpatrol

@MaoYiyi To me, it seems fairer than randomly.

Speed should count for something :)

MaoYiyi

1:26 PM

@skullpatrol yes, i see your point; but, sometimes it just which one gets posted first.

Jayesh Badwaik

@hhh the equation you have is about more complex waves than just normal plane waves

hhh

?
But they are both still about "planar waves"?

Jayesh Badwaik

is the book understanding physics by hulton et al?

@hhh he is probably talking about a different $\phi$ and the notation must have been confused.

hhh

@JayeshBadwaik By Michael Mansfiedld and Colm O'Sullivan.

Jayesh Badwaik

Is it possible for you to take a photo and upload it here, directly from the book?

hhh

1:30 PM

Wiley Praxis

skullpatrol

@MaoYiyi Yes, I agree and allowing for edits complicates matters.

MaoYiyi

@skullpatrol that is why I think they should be random because of reading fatigue. Who really scrolls all the way down.

hhh

@JayeshBadwaik There it mentions when the equations correspond to linear/circular -cases but I was asked to provide equation in "planar form" but not sure whether it needs to be expressed in terms of complex numbers...

Jayesh Badwaik

@hhh so the book has given the equation correctly that is
$\bar{E} = E \left( \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$

hhh

The book does not mention the general case with elliptic polarization.

Jayesh Badwaik

1:37 PM

Now you want to convert this equation to planar form right?

hhh

Yes.

skullpatrol

Generally, I believe answers should be put in an order determined by the preferences of the question asker and not by voters, since the question asker is the one who is trying to understand the answers, but that is just my humble opinion @MaoYiyi

Jayesh Badwaik

@hhh has your professor said something about planar form? Like what he wants from it?

I don't think that is a standard notation.

MaoYiyi

@hhh how did you post the picture?

@skullpatrol yes, that is what the accepted answer is for I thought.

hhh

Nothing, just requirement to have "planar" wave. I am not sure whethere this is the right form:

$$\bar{E} = E \left( \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$$

or the complex form, ideas?

Jayesh Badwaik

1:41 PM

No that is incorrect.

I am guessing that he simply means equation of a circle.

hhh

@MaoYiyi I used Android -phone through Wifi to upload the picture and then just copied it here.

skullpatrol

@MaoYiyi But after the accepted answer, the voters get to decide in what order the answers will be posted.

hhh

One of my friends suggested me to use Wave-equation with differential-equations.

...now more than confused what is looked for with this "planar form".

MaoYiyi

@skullpatrol didn't know that.

Jayesh Badwaik

@hhh simply ask your prof. I think there is not much to it.

MaoYiyi

1:44 PM

@hhh thanks, didn't know that was possible.

Jayesh Badwaik

He might have wanted to write polar.

and wrote planar instead

the polar form can be this
http://chat.stackexchange.com/transcript/message/6003965#6003965

hhh

@MaoYiyi Perhaps interesting to you: android.stackexchange.com/questions/28479/…

BenjaLim

@JayeshBadwaik Two group theory questions for me today :D

Jayesh Badwaik

@BenjaLim ?

BenjaLim

1:59 PM

@JayeshBadwaik I answered two today :D

Jayesh Badwaik

@BenjaLim Nice. :D

Mats Granvik

3:49 PM

Lets see if this latex works: $$7 \pi -\text{Log}\left[\frac{3}{2} e^{-3 \pi /2}+e^{5 \pi /2}+2 \pi \right]=14.13472554011971250976196...$$

Jeff

@Mats It displays correct for me

anon

up to those zeta zeroes again are we?

Mats Granvik

yes, I should stop

Peter Tamaroff

@anon Dawg.

@hhh Cooooooooooool!

@anon Anuun.

anon

what?

Peter Tamaroff

4:01 PM

@anon Could you explain to me what is the formal definition of "class" vs "set"? =)

Zhen Lin

@PeterTamaroff I'm sure we had a question about this in the last two weeks. I answered it.

anon

No, the formal distinction has something to do with predicates or model theory or blah that I don't know about. The informal distinction is that classes are bigger.

Peter Tamaroff

@ZhenLin Could you help?

Zhen Lin

See here.

Peter Tamaroff

@ZhenLin Great answer. Is your name Lin, Zhen, Zhen Lin, or non of the former?

Zhen Lin

4:07 PM

You can call me Zhen Lin.

Peter Tamaroff

@ZhenLin I guess I'll be able take the most of it after some more college studies.

Zhen Lin

shrug

It's not an important distinction if you're not concerned about formal mathematics.

Peter Tamaroff

@ZhenLin Maybe I am =)

Time will tell.

Zhen Lin

I have recently been wondering if I should be using Ackermann set theory... it seems more convenient than having just one kind of proper class, like in NBG or MK.

Peter Tamaroff

@ZhenLin I can't help you in the wondering... =P

anon

4:19 PM

Is there a name for the category of extensions of a given field K with morphisms those injective field homomorphisms that fix the base field?

I'm looking up some galois theory and it seems to work with those kind of diagrams a lot.

Zhen Lin

All field homomorphisms are injective. You can just call it the category of field extensions of $K$. Or you can write $K / \textbf{Fld}$ or something...

anon

Hmm, this text uses $\mathrm{Mono}_K(L,F)$ for monomorphisms $L\to F$ that fix a base field $K$ (obviously with $L,F/K$ extensions). I guess it's unnecessary to specify mono - it might as well just be $\hom_K$ for all field homomorphisms fixing $K$. I see that if a map between fields isn't injective then the kernel is nontrivial and $f(u)=0\implies f(1)=f(u^{-1}u)=0\ne1$, an impossibility.

Zhen Lin

Well, perhaps $\textrm{Hom}_K$ looks too much like $K$-linear maps between vector spaces...

anon

that's probably why, yeah

Kannappan Sampath

5:11 PM

Happy to note that we have John Senior.

@Jonas Yes, I have learnt this More Reading, less complaining art....

Kannappan Sampath

5:38 PM

Hmm, it's quiet in here. So, I'll be here later...

John Senior

Hi folks

Matt

5:56 PM

@JohnSenior Hello.

I just sent a first draft of my Bsc's thesis to my supervisor.

John Senior

seems very quiet in here recently

@Matt Excellent! - hope he likes it

robjohn

@JohnSenior too quiet

Matt

It's quite unfinished.

But yes, I also hope he likes it.

I like quiet.

The only thing that I don't like is that the teddy is absent.

John Senior

@Matt I am sure he will suggest things to add to it :)

robjohn

@JohnSenior Do we need to add a sound feed here? :-D

Matt

5:58 PM

: )

John Senior

@robjohn LOL

robjohn

It would be interesting to see if we could ever agree on any music to listen to.

Matt

How about Jack Johnson?

Or Bach?

Or Beatles!

John Senior

@robjohn I very much doubt it

robjohn

@JohnSenior I do, too.

John Senior

6:02 PM

I would probably turn off anything that isn't classical

Matt

@robjohn Did you mean the three of us or all chat room users?

robjohn

@Matt I was thinking of the chat room users

Matt

Ok, that makes it slightly more difficult.

robjohn

We three could settle on classical probably

Matt

Sure.

John Senior

6:03 PM

I used to hate very modern classical stuff, but Jonas has almost converted me to some of it at least

robjohn

I don't know where @anon's preferences in music lie.

Mine are fairly broad, but some of the more modern genres take some filtering and getting used to.

Matt

: )

John Senior

Anyone here know anything about class field theory?

robjohn

@JohnSenior Not I

John Senior

Me neither - yet - but I am trying to find out something about it, and struggling

Hi @KannappanSampath

robjohn

6:08 PM

@JohnSenior I should attempt a new topic sometime soon. I haven't really ventured out of bounds for a while.

@KannappanSampath: Howdy!

John Senior

@robjohn I think it is a good idea to venture a bit wider sometimes

Kannappan Sampath

Hi @JohnSenior and @robjohn

I came in here a few minutes ago, it was VERY quiet. :(

John Senior

@KannappanSampath It has got a bit less quiet recently :)

(probably due to me talking rubbish ...)

Kannappan Sampath

I made all my Group Theory answers CW some time ago... I am happy that I don't have to track some stupid downvotes.

@JohnSenior That's not true! =)

John Senior

I recently bought a book on class field theory - and one of the authors is called "Kato" ...

Kannappan Sampath

6:14 PM

Certainly not Mao Kato.

John Senior

@KannappanSampath I guess not :)

but "our" Kato has asked some questions quite similar to stuff in my book

Kannappan Sampath

Well, I hope it's taken the way it's intended; not serious.

John Senior

@KannappanSampath Of course :)

Kannappan Sampath

Well, polynomial rings are so awesome.

John Senior

Not sure I would call them awesome - maybe "interesting" or "useful"

Kannappan Sampath

6:27 PM

For one, what you can do with integers, you can do with polynomials. For another, you CAN prove FLT for any reasonable polynomial ring while for $\mathbb Z$, it took Wiles to do it. :)

John Senior

@KannappanSampath yes - that certainly makes them interesting

Steenrod

@JohnSenior, how are you doing?

:)

John Senior

@Steenrod Hi - not so bad, thanks - and you?

Steenrod

@JohnSenior,I just found out that undergraduate algebra is basically devoid of stuff mathematicians use .That means I won't learn what needs to be learnt any time soon. :(

John Senior

@Steenrod I don't believe that is true - I am sure mathematicians use linear algebra and groups rather a lot

(for example)

Steenrod

6:32 PM

Some books are using category theory.I came to know I would have to learn everything again in grad schoolBut I doubt if there are any tough, but self-contained detailed treatments of abstract algebra necessary for algebraic NT or algebraic geometry which are accessible to me.

John Senior

same with fields, although I am not sure how much field theory is done by undergrads these days - I was an undergrad a long time ago

Kannappan Sampath

@Steenrod Far from true, as John puts it. For one, what one learns as an undergraduate is a basic asset in the Mathematical Journey.

@Steenrod Well, perhaps, Ireland and Rosen is accessible while I myself have not worked through it to assert it with great amount of certainty.

@JohnSenior I'd be taught about fields through this and next semester.

John Senior

@KannappanSampath You are an undergrad already?

Steenrod

I mean accessing books like Neukirch(I saw some reviews stating it is the book) and Hartshorne.What are the pre-requisites for accessing them?

John Senior

@Steenrod which year of studies are you in?

Kannappan Sampath

6:36 PM

@JohnSenior Hmm, yes, I am an undergraduate. :(

John Senior

@KannappanSampath sorry - I was supposed to be asking @Steenrod :)

Steenrod

@JohnSenior, in high school.:D(That explains my over-enthusiasm)

John Senior

@Steenrod If you are in high school, I wouldn't be worrying about Neukirch and Hartshorne yet - but ought to be concentrating on covering a wide range of undergrad subjects first

Steenrod

I am quite weird.

Kannappan Sampath

@John should be able to assist you, @Steenrod with books accessible to you in number theory. From me, I suggest you'd first work through Dummit and Foote and Herstein, or perhaps Artin's Algebra before worrying about Category theoretic formulation.

John Senior

6:39 PM

@Steenrod most mathematicians are :)))

Steenrod

@JohnSenior, I just saw some amazon reviews on algebra chapter 0.

By Paulo Aluffi.Is it really self-contained as the title suggests?

John Senior

@Steenrod I don't know - I have never seen it, sorry

Steenrod

@JohnSenior, thanks. :)

Kannappan Sampath

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